diff options
Diffstat (limited to 'src/share/algebra')
| -rw-r--r-- | src/share/algebra/browse.daase | 646 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1218 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1321 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8884 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 27188 |
5 files changed, 19629 insertions, 19628 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 4950f799..ad150493 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2283151 . 3449148017) +(2283240 . 3449227611) (-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 -3510) +(-32 R -3445) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p,{} n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p,{} x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL ((|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) @@ -88,11 +88,11 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -3510 UP UPUP -1983) +(-40 -3445 UP UPUP -1554) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4404 |has| (-407 |#2|) (-363)) (-4409 |has| (-407 |#2|) (-363)) (-4403 |has| (-407 |#2|) (-363)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-4030 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4030 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4030 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-4030 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) -(-41 R -3510) +((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-4007 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4007 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4007 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-4007 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) +(-41 R -3445) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,{}f,{}n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f,{} a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) @@ -111,7 +111,7 @@ NIL (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4411 . T) (-4412 . T)) -((-4030 (-12 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2423) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2423) (|devaluate| |#2|))))))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2423) (|devaluate| |#2|))))))) +((-4007 (-12 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1354) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1354) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|))))))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1354) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|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 @@ -125,7 +125,7 @@ NIL ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) ((|HasCategory| $ (QUOTE (-1046))) (|HasCategory| $ (LIST (QUOTE -1035) (QUOTE (-564))))) (-49) -((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) +((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) NIL NIL (-50 R |lVar|) @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -3510) +(-54 |Base| R -3445) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4412 . T) (-4411 . T)) -((-4030 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4030 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4007 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) -(-61 -4324) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +(-61 -4344) ((|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 -4324) +(-62 -4344) ((|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 -4324) +(-63 -4344) ((|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 -4324) +(-64 -4344) ((|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 -4324) +(-65 -4344) ((|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 -4324) +(-66 -4344) ((|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 -4324) +(-67 -4344) ((|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 -4324) +(-68 -4344) ((|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 -4324) +(-69 -4344) ((|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 -4324) +(-70 -4344) ((|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 -4324) +(-71 -4344) ((|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 -4324) +(-72 -4344) ((|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 -4324) +(-73 -4344) ((|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 -4324) +(-74 -4344) ((|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 -4324) +(-77 -4344) ((|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 -4324) +(-78 -4344) ((|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 -4324) +(-79 -4344) ((|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 -4324) +(-80 -4344) ((|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 -4324) +(-81 -4344) ((|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 -4324) +(-82 -4344) ((|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 -4324) +(-83 -4344) ((|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 -4324) +(-84 -4344) ((|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 -4324) +(-85 -4344) ((|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 -4324) +(-86 -4344) ((|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 -4324) +(-87 -4344) ((|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 -4324) +(-88 -4344) ((|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 -4324) +(-89 -4344) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -295,7 +295,7 @@ NIL (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -343,7 +343,7 @@ NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -363,7 +363,7 @@ NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4030 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4007 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -388,7 +388,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-115 -3510 UP) +(-115 -3445 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL @@ -399,7 +399,7 @@ NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-906))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1019))) (|HasCategory| (-116 |#1|) (QUOTE (-817))) (-4030 (|HasCategory| (-116 |#1|) (QUOTE (-817))) (|HasCategory| (-116 |#1|) (QUOTE (-847)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-906)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((|HasCategory| (-116 |#1|) (QUOTE (-906))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1019))) (|HasCategory| (-116 |#1|) (QUOTE (-817))) (-4007 (|HasCategory| (-116 |#1|) (QUOTE (-817))) (|HasCategory| (-116 |#1|) (QUOTE (-847)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-906)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) (-118 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -415,7 +415,7 @@ NIL (-121 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL @@ -435,15 +435,15 @@ NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-128) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,{}n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) ((-4412 . T) (-4411 . T)) -((-4030 (-12 (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-4030 (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-4030 (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-129) (QUOTE (-1094)))) (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) +((-4007 (-12 (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-4007 (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-4007 (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-129) (QUOTE (-1094)))) (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-129) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -468,11 +468,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4413 "*") . T)) NIL -(-135 |minix| -2781 S T$) +(-135 |minix| -2877 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -2781 R) +(-136 |minix| -2877 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -481,7 +481,7 @@ NIL NIL NIL (-138) -((|constructor| (NIL "This domain represents the unnamed category defined \\indented{2}{by a list of exported signatures}")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(c)} returns the list of exports in category syntax \\spad{`c'}.")) (|kind| (((|Symbol|) $) "\\spad{kind(c)} returns the kind of unnamed category,{} either 'domain' or 'package'."))) +((|constructor| (NIL "This domain represents the unnamed category defined \\indented{2}{by a list of exported signatures}")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(c)} returns the list of exports in category syntax \\spad{`c'}.")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(c)} returns the kind of unnamed category,{} either 'domain' or 'package'."))) NIL NIL (-139) @@ -495,7 +495,7 @@ NIL (-141) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4411 . T) (-4401 . T) (-4412 . T)) -((-4030 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-4007 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-142 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -520,7 +520,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4408 . T)) NIL -(-148 -3510 UP UPUP) +(-148 -3445 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 -3510) +(-158 R -3445) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n),{} n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n),{} n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n),{} n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n),{} n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f,{} x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n,{} r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n,{} r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -594,7 +594,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-999))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4407)) (|HasAttribute| |#2| (QUOTE -4410)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-847)))) (-166 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4404 -4030 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-906)))) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4407 |has| |#1| (-6 -4407)) (-4410 |has| |#1| (-6 -4410)) (-2315 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 -4007 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-906)))) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4407 |has| |#1| (-6 -4407)) (-4410 |has| |#1| (-6 -4410)) (-2472 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL (-167 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -606,8 +606,8 @@ NIL NIL (-169 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4404 -4030 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-906)))) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4407 |has| |#1| (-6 -4407)) (-4410 |has| |#1| (-6 -4410)) (-2315 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . 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T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-4007 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| 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(QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasAttribute| |#1| (QUOTE -4407)) (|HasAttribute| |#1| (QUOTE -4410)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170))))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-349))))) (-170 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -680,7 +680,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Symbol|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -3510) +(-188 R -3445) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,23 +788,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -3510 UP UPUP R) +(-215 -3445 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 -3510 FP) +(-216 -3445 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,{}k,{}v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,{}k,{}v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,{}k,{}v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,{}sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-217) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4030 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4007 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) (-218) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-219 R -3510) +(-219 R -3445) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -819,18 +819,18 @@ NIL (-222 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-223 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4408 . T)) NIL -(-224 R -3510) +(-224 R -3445) ((|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}."))) -((-2305 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-2460 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL (-226) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) @@ -839,7 +839,7 @@ NIL (-227 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,{}Y,{}Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4413 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4413 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-228 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL @@ -876,22 +876,22 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-237 S -2781 R) +(-237 S -2877 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL ((|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-790))) (|HasCategory| |#3| (QUOTE (-845))) (|HasAttribute| |#3| (QUOTE -4408)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-723))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (QUOTE (-1094)))) -(-238 -2781 R) +(-238 -2877 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) ((-4405 |has| |#2| (-1046)) (-4406 |has| |#2| (-1046)) (-4408 |has| |#2| (-6 -4408)) ((-4413 "*") |has| |#2| (-172)) (-4411 . T)) NIL -(-239 -2781 A B) +(-239 -2877 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 -2781 R) +(-240 -2877 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) ((-4405 |has| |#2| (-1046)) (-4406 |has| |#2| (-1046)) (-4408 |has| |#2| (-6 -4408)) ((-4413 "*") |has| |#2| (-172)) (-4411 . T)) -((-4030 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-723))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-790))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1046))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))))) (-4030 (-12 (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1046)))) (-12 (|HasCategory| |#2| (QUOTE (-1046))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1046))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564))))) 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -911,7 +911,7 @@ NIL (-245 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) ((-4412 . T) (-4411 . 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(|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -919,7 +919,7 @@ NIL (-247 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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(|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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(QUOTE -897) (QUOTE (-1170))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1046)))) (-4007 (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1046)))) (|HasCategory| |#3| (QUOTE (-723))) (-12 (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (LIST (QUOTE -897) (QUOTE (-1170)))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564))))) (-4007 (|HasCategory| |#3| (QUOTE (-1046))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1094)))) (-4007 (|HasAttribute| |#3| (QUOTE -4408)) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1046)))) (-12 (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (-252 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -987,7 +987,7 @@ NIL (-264 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4030 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-906))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) (-265 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1032,11 +1032,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-276 R -3510) +(-276 R -3445) ((|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 -3510) +(-277 R -3445) ((|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| -4172 -2164 |exactQuo|) +(-289 S R |Mod| -4008 -1642 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL @@ -1106,21 +1106,21 @@ NIL NIL (-294 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2423) (|devaluate| |#2|)))))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1354) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) (-296) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",{}\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-297 -3510 S) +(-297 -3445 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 -3510) +(-298 E -3445) ((|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 -3510) +(-310 -3445) ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,{}s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) NIL NIL @@ -1183,7 +1183,7 @@ NIL (-313 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-906))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1019))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-817))) (-4030 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-817))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-847)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-847))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-4030 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))))) +((|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-906))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1019))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-817))) (-4007 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-817))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-847)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-847))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-4007 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))))) (-314 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1194,9 +1194,9 @@ NIL NIL (-316 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4408 -4030 (-4267 (|has| |#1| (-1046)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-4030 (-4267 (|has| |#1| (-1046)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1046)) (|has| |#1| (-473)))) (|has| |#1| (-1046)) (|has| |#1| (-473))) (-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) ((-4413 "*") |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4409 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(QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1046)))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556)))) (-4030 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-4030 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-4030 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-4030 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-4030 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1046)))) (-4030 (-12 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| $ (QUOTE (-1046))) (|HasCategory| $ (LIST (QUOTE -1035) (QUOTE (-564))))) -(-317 R -3510) +((-4408 -4007 (-4260 (|has| |#1| (-1046)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-4007 (-4260 (|has| |#1| (-1046)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1046)) (|has| |#1| (-473)))) (|has| |#1| (-1046)) (|has| |#1| (-473))) (-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) ((-4413 "*") |has| |#1| (-556)) 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(LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1046)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1046)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1046)))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556)))) (-4007 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-4007 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-4007 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-4007 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-4007 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1046)))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| $ (QUOTE (-1046))) (|HasCategory| $ (LIST (QUOTE -1035) (QUOTE (-564))))) +(-317 R -3445) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1207,7 +1207,7 @@ NIL (-319 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4030 (|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 -3742) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4030 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3128) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4269) (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))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4007 (|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 -3713) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2397) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4275) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-320 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1239,12 +1239,12 @@ NIL (-327 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) ((-4412 . T) (-4411 . T)) -((-4030 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4030 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) -(-328 S -3510) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4007 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +(-328 S -3445) ((|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 -3510) +(-329 -3445) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL @@ -1264,15 +1264,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) NIL NIL -(-334 S -3510 UP UPUP R) +(-334 S -3445 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 -3510 UP UPUP R) +(-335 -3445 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 -3510 UP UPUP R) +(-336 -3445 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 -3510 UP UPUP) +(-341 S -3445 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 -3510 UP UPUP) +(-342 -3445 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4404 |has| (-407 |#2|) (-363)) (-4409 |has| (-407 |#2|) (-363)) (-4403 |has| (-407 |#2|) (-363)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL (-343 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4030 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#1|) (QUOTE (-145)))) +((-4007 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#1|) (QUOTE (-145)))) (-344 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4030 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4007 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-345 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4030 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4007 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-346 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1328,31 +1328,31 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL -(-350 R UP -3510) +(-350 R UP -3445) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-351 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4030 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#1|) (QUOTE (-145)))) +((-4007 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#1|) (QUOTE (-145)))) (-352 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4030 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4007 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-353 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4030 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4007 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-354 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4030 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#1|) (QUOTE (-145)))) +((-4007 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#1|) (QUOTE (-145)))) (-355 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4030 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) -(-356 -3510 GF) +((-4007 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +(-356 -3445 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 -3510 FP FPP) +(-358 -3445 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-359 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4030 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4007 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-360 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL @@ -1446,7 +1446,7 @@ NIL NIL (-379) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4394 . T) (-4402 . T) (-2305 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4394 . T) (-4402 . T) (-2460 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL (-380 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1496,7 +1496,7 @@ NIL ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-392 -3510 UP UPUP R) +(-392 -3445 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 -4324 |returnType| -2692 |symbols|) +(-398 -4344 |returnType| -2827 |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 -3510 UP) +(-399 -3445 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1546,7 +1546,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4394)) (|HasAttribute| |#1| (QUOTE -4402))) (-404) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-2305 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-2460 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL (-405 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) @@ -1559,7 +1559,7 @@ NIL (-407 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4398 -12 (|has| |#1| (-6 -4409)) (|has| |#1| (-452)) (|has| |#1| (-6 -4398))) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-817))) (-4030 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#1| (QUOTE (-847)))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (-4030 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825))))) (-4030 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4409)) (|HasAttribute| |#1| (QUOTE -4398)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-817))) (-4007 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#1| (QUOTE (-847)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825))))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4409)) (|HasAttribute| |#1| (QUOTE -4398)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) (-408 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1580,11 +1580,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-413 R -3510 UP A) +(-413 R -3445 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,{}...,{}fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} returns the vector \\spad{[f1,{}...,{}fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,{}...,{}fn])} returns the ideal \\spad{(f1,{}...,{}fn)}."))) ((-4408 . T)) NIL -(-414 R -3510 UP A |ibasis|) +(-414 R -3445 UP A |ibasis|) ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,{}...,{}fn])} = the module generated by \\spad{(f1,{}...,{}fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1035) (|devaluate| |#2|)))) @@ -1603,7 +1603,7 @@ NIL (-418 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) ((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1213))) (-4030 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1213)))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) +((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1213))) (-4007 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1213)))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) (-419 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}."))) NIL @@ -1632,7 +1632,7 @@ NIL ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4411 . T) (-4401 . T) (-4412 . T)) NIL -(-426 R -3510) +(-426 R -3445) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1640,7 +1640,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,{}r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,{}r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4398 -12 (|has| |#1| (-6 -4398)) (|has| |#2| (-6 -4398))) (-4405 . T) (-4406 . T) (-4408 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4398)) (|HasAttribute| |#2| (QUOTE -4398)))) -(-428 R -3510) +(-428 R -3445) ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL @@ -1650,17 +1650,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1046))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (-430 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4408 -4030 (|has| |#1| (-1046)) (|has| |#1| (-473))) (-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) ((-4413 "*") |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-556)) (-4403 |has| |#1| (-556))) +((-4408 -4007 (|has| |#1| (-1046)) (|has| |#1| (-473))) (-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) ((-4413 "*") |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-556)) (-4403 |has| |#1| (-556))) NIL -(-431 R -3510) +(-431 R -3445) ((|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 -3510) +(-432 R -3445) ((|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 -3510) +(-433 R -3445) ((|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 -3510 UP) +(-435 R -3445 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL ((|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-48))))) @@ -1700,7 +1700,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-443 R UP -3510) +(-443 R UP -3445) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,{}p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,{}n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1747,7 +1747,7 @@ NIL (-454 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4413 "*") |has| |#2| (-172)) (-4404 |has| |#2| (-556)) (-4409 |has| |#2| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#2| (QUOTE (-906))) (-4030 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4030 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4030 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4030 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4030 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-906))) (-4007 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4007 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4007 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4007 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4007 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) (-455 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1812,7 +1812,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-471 |lv| -3510 R) +(-471 |lv| -3445 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1827,11 +1827,11 @@ NIL (-474 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4030 (|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 -3742) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4030 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3128) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4269) (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))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4007 (|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 -3713) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2397) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4275) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-475 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2423) (|devaluate| |#2|)))))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-847))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094)))) +((-12 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1354) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-847))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094)))) (-476 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4412 . T) (-4411 . T)) @@ -1847,7 +1847,7 @@ NIL (-479 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2423) (|devaluate| |#2|)))))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1354) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) (-480) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1855,11 +1855,11 @@ NIL (-481 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4413 "*") |has| |#2| (-172)) (-4404 |has| |#2| (-556)) (-4409 |has| |#2| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . 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(QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-790))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1046))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-847))) (-12 (|HasCategory| |#2| (QUOTE (-1046))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1046)))) (-12 (|HasCategory| |#2| (QUOTE (-1046))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170))))) (-4007 (|HasCategory| |#2| (QUOTE (-1046))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) (-483) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL @@ -1867,8 +1867,8 @@ NIL (-484 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) -(-485 -3510 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +(-485 -3445 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1879,7 +1879,7 @@ NIL (-487) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4030 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4007 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) (-488 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1904,7 +1904,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-494 -3510 UP |AlExt| |AlPol|) +(-494 -3445 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL @@ -1915,16 +1915,16 @@ NIL (-496 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4412 . T) (-4411 . T)) -((-4030 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4030 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4007 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-497 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-498 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented"))) NIL NIL -(-499 R UP -3510) +(-499 R UP -3445) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1944,7 +1944,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-504 -3510 |Expon| |VarSet| |DPoly|) +(-504 -3445 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}"))) ((-4412 . T) (-4411 . T)) -((-4030 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4030 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4007 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-517) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL @@ -2003,15 +2003,15 @@ NIL (-518 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4030 (|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)))) +((-4007 (|HasCategory| (-581 |#1|) (QUOTE (-145))) (|HasCategory| (-581 |#1|) (QUOTE (-368)))) (|HasCategory| (-581 |#1|) (QUOTE (-147))) (|HasCategory| (-581 |#1|) (QUOTE (-368))) (|HasCategory| (-581 |#1|) (QUOTE (-145)))) (-519 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-520 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) ((-4412 . T) (-4411 . T)) -((-4030 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4030 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4007 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-521 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -2023,13 +2023,13 @@ NIL (-523 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4413 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4413 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-524) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL NIL (-525) -((|constructor| (NIL "This domain represents the `in' iterator syntax.")) (|sequence| (((|SpadAst|) $) "\\spad{sequence(i)} returns the sequence expression being iterated over by `i'.")) (|iterationVar| (((|Symbol|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the `in' iterator 'i'"))) +((|constructor| (NIL "This domain represents the `in' iterator syntax.")) (|sequence| (((|SpadAst|) $) "\\spad{sequence(i)} returns the sequence expression being iterated over by `i'.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the `in' iterator 'i'"))) NIL NIL (-526 S) @@ -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 -3510 |Par|) +(-532 K -3445 |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 -3510 |Par|) +(-538 K -3445 |Par|) ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,{}lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,{}lden,{}lvar,{}eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,{}eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,{}eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) NIL NIL @@ -2131,12 +2131,12 @@ NIL (-550 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2423) (|devaluate| |#2|)))))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) -(-551 R -3510) +((-12 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1354) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) +(-551 R -3445) ((|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 -3510 UP UPUP R) +(-552 R0 -3445 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."))) -((-2305 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-2460 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL (-555 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -2156,7 +2156,7 @@ NIL ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) ((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL -(-557 R -3510) +(-557 R -3445) ((|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 -3510 L) +(-560 R -3445 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 -3510 UP UPUP R) +(-562 -3445 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 -3510 UP) +(-563 -3445 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 -3510 L) +(-566 R -3445 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 -3510) +(-567 R -3445) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f,{} x)} returns \\spad{[c,{} g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-627))))) -(-568 -3510 UP) +(-568 -3445 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 -3510) +(-570 -3445) ((|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."))) -((-2305 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-2460 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL (-572) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-573 R -3510) +(-573 R -3445) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f,{} x,{} int,{} pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f,{} x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f,{} x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,{}...,{}fn],{}x)} returns the set-theoretic union of \\spad{(varselect(f1,{}x),{}...,{}varselect(fn,{}x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1,{} l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k,{} [k1,{}...,{}kn],{} x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,{}...,{}kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,{}...,{}kn],{} x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-627))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-284)))) (|HasCategory| |#1| (QUOTE (-556)))) -(-574 -3510 UP) +(-574 -3445 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 -3510) +(-575 R -3445) ((|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 -3510) +(-583 R -3445) ((|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 -3510) +(-584 E -3445) ((|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 -3510) +(-585 -3445) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,{}x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,{}D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,{}l,{}ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) ((-4406 . T) (-4405 . T)) ((|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-1170))))) @@ -2299,7 +2299,7 @@ NIL (-592 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4412 . T) (-4411 . T)) -((-4030 (-12 (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-4030 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-4030 (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094)))) (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-4007 (-12 (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-4007 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-4007 (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094)))) (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-593 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL @@ -2307,7 +2307,7 @@ NIL (-594 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,{}r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,{}r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,{}refer,{}var,{}cen,{}r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,{}g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,{}g,{}taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,{}f)} returns the series \\spad{sum(fn(n) * an * x^n,{}n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,{}n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,{}str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3742) (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))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3713) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564)))))) (-595 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) ((-4406 |has| |#1| (-556)) (-4405 |has| |#1| (-556)) ((-4413 "*") |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4408 . T)) @@ -2320,7 +2320,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented"))) NIL NIL -(-598 R -3510 FG) +(-598 R -3445 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2331,7 +2331,7 @@ NIL (-600 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4412 . T) (-4411 . T)) -((-4030 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4030 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4007 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-601 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2350,12 +2350,12 @@ NIL NIL (-605 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,{}b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4408 -4030 (-4267 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4406 . T) (-4405 . T)) -((-4030 (|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|)))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) +((-4408 -4007 (-4260 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4406 . T) (-4405 . T)) +((-4007 (|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|)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-606 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1327) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2423) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 |#1|)) (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1354) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 |#1|)) (LIST (QUOTE -611) (QUOTE (-859))))) (-607 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL @@ -2380,7 +2380,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-613 -3510 UP) +(-613 -3445 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2408,7 +2408,7 @@ NIL ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4405 . T) (-4406 . T) (-4408 . T)) ((|HasCategory| |#1| (QUOTE (-845)))) -(-620 R -3510) +(-620 R -3445) ((|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 -3510) +(-628 R -3445) ((|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| -3510) +(-629 |lv| -3445) ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL (-630) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1327) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2423) (QUOTE (-52))))))) (-4030 (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4030 (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-847))) (-4030 (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 (-52))) (QUOTE (-1094)))) +((-12 (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1354) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2577) (QUOTE (-52))))))) (-4007 (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4007 (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-847))) (-4007 (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 (-52))) (QUOTE (-1094)))) (-631 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2462,8 +2462,8 @@ NIL NIL (-633 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,{}b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-4408 -4030 (-4267 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4406 . T) (-4405 . T)) -((-4030 (|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|)))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) +((-4408 -4007 (-4260 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4406 . T) (-4405 . T)) +((-4007 (|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|)))) (-4007 (-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 -((-4255 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) +((-4248 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) (-637 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4408 . T)) @@ -2495,7 +2495,7 @@ NIL (-641 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) ((-4412 . T) (-4411 . T)) -((-4030 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4030 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4007 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-642 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2503,7 +2503,7 @@ NIL (-643 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-644 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2520,7 +2520,7 @@ NIL ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-648 R -3510 L) +(-648 R -3445 L) ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op,{} g,{} x,{} a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{op y = g,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op,{} g,{} x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) NIL NIL @@ -2540,11 +2540,11 @@ NIL ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) ((-4405 . T) (-4406 . T) (-4408 . T)) NIL -(-653 -3510 UP) +(-653 -3445 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 -2919) +(-654 A -2339) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) ((-4405 . T) (-4406 . T) (-4408 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) @@ -2580,11 +2580,11 @@ NIL ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) ((-4412 . T) (-4411 . T)) NIL -(-663 -3510) +(-663 -3445) ((|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 -3510 |Row| |Col| M) +(-664 -3445 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2595,7 +2595,7 @@ NIL (-666 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,{}R) b - b *\\$SQMATRIX(n,{}R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) ((-4408 . T) (-4411 . T) (-4405 . T) (-4406 . T)) -((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4030 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-4030 (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4007 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-4007 (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-667) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2615,7 +2615,7 @@ NIL (-671 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,{}x,{}y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,{}i,{}j,{}k,{}s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,{}i,{}j,{}k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,{}y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,{}j,{}k)} create a matrix with all zero terms"))) NIL -((-4030 (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-672) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2671,7 +2671,7 @@ NIL (-685 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) ((-4411 . T) (-4412 . T)) -((-4030 (-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))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4413 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4007 (-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))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4413 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-686 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2680,7 +2680,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-688 S -3510 FLAF FLAS) +(-688 S -3445 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,{}xlist,{}kl,{}ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,{}xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,{}xlist,{}k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,{}xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,{}xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,{}xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,{}xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2690,8 +2690,8 @@ NIL NIL (-690) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4404 . T) (-4409 |has| (-695) (-363)) (-4403 |has| (-695) (-363)) (-2315 . T) (-4410 |has| (-695) (-6 -4410)) (-4407 |has| (-695) (-6 -4407)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-695) (QUOTE (-147))) (|HasCategory| (-695) (QUOTE (-145))) (|HasCategory| (-695) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-368))) (|HasCategory| (-695) (QUOTE (-363))) (-4030 (|HasCategory| (-695) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-233))) (-4030 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (LIST (QUOTE -286) (QUOTE (-695)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -309) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-695) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (-4030 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-695) (QUOTE (-1019))) (|HasCategory| (-695) (QUOTE (-1194))) (-12 (|HasCategory| (-695) (QUOTE (-999))) (|HasCategory| (-695) (QUOTE (-1194)))) (-4030 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-363))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-906))))) (-4030 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (-12 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-906)))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-906))))) (|HasCategory| (-695) (QUOTE (-545))) (-12 (|HasCategory| (-695) (QUOTE (-1055))) (|HasCategory| (-695) (QUOTE (-1194)))) (|HasCategory| (-695) (QUOTE (-1055))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906))) (-4030 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-363)))) (-4030 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-556)))) (-12 (|HasCategory| (-695) (QUOTE (-233))) (|HasCategory| (-695) (QUOTE (-363)))) (-12 (|HasCategory| (-695) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-847))) (|HasCategory| (-695) (QUOTE (-556))) (|HasAttribute| (-695) (QUOTE -4410)) (|HasAttribute| (-695) (QUOTE -4407)) (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-145)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-349))))) +((-4404 . T) (-4409 |has| (-695) (-363)) (-4403 |has| (-695) (-363)) (-2472 . T) (-4410 |has| (-695) (-6 -4410)) (-4407 |has| (-695) (-6 -4407)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((|HasCategory| (-695) (QUOTE (-147))) (|HasCategory| (-695) (QUOTE (-145))) (|HasCategory| (-695) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-368))) (|HasCategory| (-695) (QUOTE (-363))) (-4007 (|HasCategory| (-695) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-233))) (-4007 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (LIST (QUOTE -286) (QUOTE (-695)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -309) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-695) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (-4007 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-695) (QUOTE (-1019))) (|HasCategory| (-695) (QUOTE (-1194))) (-12 (|HasCategory| (-695) (QUOTE (-999))) (|HasCategory| (-695) (QUOTE (-1194)))) (-4007 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-363))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-906))))) (-4007 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (-12 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-906)))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-906))))) (|HasCategory| (-695) (QUOTE (-545))) (-12 (|HasCategory| (-695) (QUOTE (-1055))) (|HasCategory| (-695) (QUOTE (-1194)))) (|HasCategory| (-695) (QUOTE (-1055))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906))) (-4007 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-363)))) (-4007 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-556)))) (-12 (|HasCategory| (-695) (QUOTE (-233))) (|HasCategory| (-695) (QUOTE (-363)))) (-12 (|HasCategory| (-695) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-847))) (|HasCategory| (-695) (QUOTE (-556))) (|HasAttribute| (-695) (QUOTE -4410)) (|HasAttribute| (-695) (QUOTE -4407)) (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-145)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-349))))) (-691 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,{}d,{}n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) ((-4412 . T)) @@ -2704,13 +2704,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) NIL NIL -(-694 OV E -3510 PG) +(-694 OV E -3445 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}"))) -((-2305 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-2460 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL (-696 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m,{} d,{} p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,{}p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m,{} d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2740,7 +2740,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-703 S -2124 I) +(-703 S -2264 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr,{} x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2760,14 +2760,14 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-708 R |Mod| -4172 -2164 |exactQuo|) +(-708 R |Mod| -4008 -1642 |exactQuo|) ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL (-709 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4407 |has| |#1| (-363)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4030 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) (-710 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2776,7 +2776,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) (-4408 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-712 R |Mod| -4172 -2164 |exactQuo|) +(-712 R |Mod| -4008 -1642 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4408 . T)) NIL @@ -2788,7 +2788,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4406 . T) (-4405 . T)) NIL -(-715 -3510) +(-715 -3445) ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,{}1],{}[1,{}0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,{}h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,{}0],{}[0,{}1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,{}h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,{}k],{}[0,{}1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,{}b,{}c,{}d)} returns \\spad{matrix [[a,{}b],{}[c,{}d]]}."))) ((-4408 . T)) NIL @@ -2824,7 +2824,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-724 -3510 UP) +(-724 -3445 UP) ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f,{} D)} returns \\spad{[p,{}n,{}s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f,{} D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p,{} D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m,{} s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p,{} D)} returns \\spad{[n,{}s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) NIL NIL @@ -2843,7 +2843,7 @@ NIL (-728 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) (((-4413 "*") |has| |#2| (-172)) (-4404 |has| |#2| (-556)) (-4409 |has| |#2| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#2| (QUOTE (-906))) (-4030 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4030 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4030 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4030 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4030 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-906))) (-4007 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4007 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4007 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4007 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4007 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) (-729 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,{}var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,{}var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,{}var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2976,11 +2976,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-762 -3510) +(-762 -3445) ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-763 P -3510) +(-763 P -3445) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL @@ -2988,7 +2988,7 @@ NIL NIL NIL NIL -(-765 UP -3510) +(-765 UP -3445) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3004,7 +3004,7 @@ NIL ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,{}b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) (((-4413 "*") . T)) NIL -(-769 R -3510) +(-769 R -3445) ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,{}y),{} N(x,{}y),{} y,{} x)} returns \\spad{F(x,{}y)} such that \\spad{F(x,{}y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,{}y) dx + N(x,{}y) dy = 0},{} or \"failed\" if no first-integral can be found."))) NIL NIL @@ -3024,7 +3024,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-774 -3510 |ExtF| |SUEx| |ExtP| |n|) +(-774 -3445 |ExtF| |SUEx| |ExtP| |n|) ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) NIL NIL @@ -3039,7 +3039,7 @@ NIL (-777 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) 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\\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3047,7 +3047,7 @@ NIL (-779 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4407 |has| |#1| (-363)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . 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(|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL @@ -3108,23 +3108,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4405 . T) (-4406 . T) (-4408 . T)) NIL -(-795 -4030 R OS S) +(-795 -4007 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-796 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-4030 (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4030 (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-4007 (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4007 (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (-797) ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-798 R -3510 L) +(-798 R -3445 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-799 R -3510) +(-799 R -3445) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m,{} x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m,{} v,{} x)} returns \\spad{[v_p,{} [v_1,{}...,{}v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3132,7 +3132,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-801 R -3510) +(-801 R -3445) ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f,{} x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f,{} x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) NIL NIL @@ -3140,11 +3140,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}epsabs,{}epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,{}R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-803 -3510 UP UPUP R) +(-803 -3445 UP UPUP R) ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) NIL NIL -(-804 -3510 UP L LQ) +(-804 -3445 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op,{} [g1,{}...,{}gm])} returns \\spad{op0,{} [h1,{}...,{}hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op,{} [g1,{}...,{}gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op,{} g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3152,38 +3152,38 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-806 -3510 UP L LQ) +(-806 -3445 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-807 -3510 UP) +(-807 -3445 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-808 -3510 L UP A LO) +(-808 -3445 L UP A LO) ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op,{} g)} returns \\spad{[m,{} v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,{}...,{}z_m) . (b_1,{}...,{}b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) NIL NIL -(-809 -3510 UP) +(-809 -3445 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-810 -3510 LO) +(-810 -3445 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,{}v)} returns \\spad{A,{}[[C_1,{}g_1,{}L_1,{}h_1],{}...,{}[C_k,{}g_k,{}L_k,{}h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-811 -3510 LODO) +(-811 -3445 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) 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|#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) (-813 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4030 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-906))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) (-814 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4413 "*") |has| |#2| (-363)) (-4404 |has| |#2| (-363)) (-4409 |has| |#2| (-363)) (-4403 |has| |#2| (-363)) (-4408 . T) (-4406 . T) (-4405 . T)) @@ -3251,7 +3251,7 @@ NIL (-830 R) ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) ((-4408 |has| |#1| (-845))) -((|HasCategory| |#1| (QUOTE (-845))) (-4030 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4030 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-845))) (-4007 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4007 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) (-831 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of `op'."))) NIL @@ -3291,12 +3291,12 @@ NIL (-840 R) ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4408 |has| |#1| (-845))) -((|HasCategory| |#1| (QUOTE (-845))) (-4030 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4030 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-845))) (-4007 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4007 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) (-841) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-842 -2781 S) +(-842 -2877 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3332,11 +3332,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) -(-851 R |sigma| -3178) +(-851 R |sigma| -2747) ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{} x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) ((-4405 . T) (-4406 . T) (-4408 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) -(-852 |x| R |sigma| -3178) +(-852 |x| R |sigma| -2747) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}."))) ((-4405 . T) (-4406 . T) (-4408 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-363)))) @@ -3403,15 +3403,15 @@ NIL (-868 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-867 |#1|) (QUOTE (-906))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-867 |#1|) (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-147))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-867 |#1|) (QUOTE (-1019))) (|HasCategory| (-867 |#1|) (QUOTE (-817))) (-4030 (|HasCategory| (-867 |#1|) (QUOTE (-817))) (|HasCategory| (-867 |#1|) (QUOTE (-847)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (QUOTE (-1145))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (QUOTE (-233))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -867) (|devaluate| |#1|)) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (QUOTE (-307))) (|HasCategory| (-867 |#1|) (QUOTE (-545))) (|HasCategory| (-867 |#1|) (QUOTE (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-906)))) (|HasCategory| (-867 |#1|) (QUOTE (-145))))) +((|HasCategory| (-867 |#1|) (QUOTE (-906))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-867 |#1|) (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-147))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-867 |#1|) (QUOTE (-1019))) (|HasCategory| (-867 |#1|) (QUOTE (-817))) (-4007 (|HasCategory| (-867 |#1|) (QUOTE (-817))) (|HasCategory| (-867 |#1|) (QUOTE (-847)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (QUOTE (-1145))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (QUOTE (-233))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -867) (|devaluate| |#1|)) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (QUOTE (-307))) (|HasCategory| (-867 |#1|) (QUOTE (-545))) (|HasCategory| (-867 |#1|) (QUOTE (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-906)))) (|HasCategory| (-867 |#1|) (QUOTE (-145))))) (-869 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-817))) (-4030 (|HasCategory| |#2| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-847)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-817))) (-4007 (|HasCategory| |#2| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-847)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) (-870 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,{}t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))))) (-871) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3467,7 +3467,7 @@ NIL (-884 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,{}...,{}en],{} pat)} matches the pattern pat on the list of expressions \\spad{[e1,{}...,{}en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,{}...,{}en],{} pat)} tests if the list of expressions \\spad{[e1,{}...,{}en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr,{} pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-4255 (|HasCategory| |#2| (QUOTE (-1046)))) (-4255 (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1046))) (-4255 (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170))))) +((-12 (-4248 (|HasCategory| |#2| (QUOTE (-1046)))) (-4248 (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1046))) (-4248 (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170))))) (-885 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3476,7 +3476,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-887 R -2124) +(-887 R -2264) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3500,7 +3500,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-893 UP -3510) +(-893 UP -3445) ((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,{}n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,{}q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,{}m,{}n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) NIL NIL @@ -3523,7 +3523,7 @@ NIL (-898 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-899 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL @@ -3539,7 +3539,7 @@ NIL (-902 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4408 . T)) -((-4030 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-847)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-847)))) +((-4007 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-847)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-847)))) (-903 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3560,7 +3560,7 @@ NIL ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) -(-908 R0 -3510 UP UPUP R) +(-908 R0 -3445 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) NIL NIL @@ -3588,7 +3588,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) NIL NIL -(-915 -3510) +(-915 -3445) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL @@ -3604,11 +3604,11 @@ NIL ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) (((-4413 "*") . T)) NIL -(-919 -3510 P) +(-919 -3445 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-920 |xx| -3510) +(-920 |xx| -3445) ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,{}lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,{}lf,{}lg)} \\undocumented"))) NIL NIL @@ -3632,7 +3632,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-926 R -3510) +(-926 R -3445) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3644,7 +3644,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-929 S R -3510) +(-929 S R -3445) ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL @@ -3664,11 +3664,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -883) (|devaluate| |#1|)))) -(-934 R -3510 -2124) +(-934 R -3445 -2264) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL -(-935 -2124) +(-935 -2264) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -3691,7 +3691,7 @@ NIL (-940 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4412 . T) (-4411 . T)) -((-4030 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4030 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4007 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-941 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL @@ -3716,7 +3716,7 @@ NIL ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) NIL -(-947 E V R P -3510) +(-947 E V R P -3445) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f,{} x,{} p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3727,8 +3727,8 @@ NIL (-949 R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,{}x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4030 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-950 E V R P -3510) +((|HasCategory| |#1| (QUOTE (-906))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-950 E V R P -3445) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-452)))) @@ -3751,12 +3751,12 @@ NIL (-955 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4412 . T) (-4411 . T)) -((-4030 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4030 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4007 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-956) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f,{} x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f,{} x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-957 -3510) +(-957 -3445) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3771,11 +3771,11 @@ NIL (-960 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4030 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4409))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4409))) (-961 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,{}b)} \\undocumented"))) ((-4408 -12 (|has| |#2| (-473)) (|has| |#1| (-473)))) -((-4030 (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790)))) (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-847))))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790)))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723)))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790))))) (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-847))))) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790)))) (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-847))))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723)))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790))))) (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-847))))) (-962) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3856,7 +3856,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,{}p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,{}v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,{}v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-982 K R UP -3510) +(-982 K R UP -3445) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -3915,11 +3915,11 @@ NIL (-996 R) ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) ((-4404 |has| |#1| (-290)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-4030 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (-4030 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-545)))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-4007 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-545)))) (-997 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,{}y,{}...,{}z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-998 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3928,14 +3928,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1000 -3510 UP UPUP |radicnd| |n|) +(-1000 -3445 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4404 |has| (-407 |#2|) (-363)) (-4409 |has| (-407 |#2|) (-363)) (-4403 |has| (-407 |#2|) (-363)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-4030 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4030 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4030 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-4030 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) +((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-4007 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4007 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4007 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-4007 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) (-1001 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4030 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4007 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) (-1002) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,{}b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL @@ -3968,19 +3968,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4404 . T) (-4409 . T) (-4403 . T) (-4406 . T) (-4405 . T) ((-4413 "*") . T) (-4408 . T)) NIL -(-1010 R -3510) +(-1010 R -3445) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n,{} f,{} g,{} x,{} lim,{} ext)} returns \\spad{[y,{} h,{} b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) NIL NIL -(-1011 R -3510) +(-1011 R -3445) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n,{} f,{} g_1,{} g_2,{} x,{}lim,{}ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,{}dy2/dx) + ((0,{} - n df/dx),{}(n df/dx,{}0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) NIL NIL -(-1012 -3510 UP) +(-1012 -3445 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a,{} B,{} C,{} n,{} D)} returns either: 1. \\spad{[Q,{} b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1,{} C1,{} m,{} \\alpha,{} \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f,{} g)} returns a \\spad{[y,{} b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,{}g,{}D)} returns \\spad{[A,{} B,{} C,{} T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-1013 -3510 UP) +(-1013 -3445 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f,{} g1,{} g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,{}g1,{}g2,{}D)} returns \\spad{[A,{} B,{} H,{} C1,{} C2,{} T]} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} has a solution if and only if \\spad{y1 = Q1 / T,{} y2 = Q2 / T},{} where \\spad{B,{}C1,{}C2,{}Q1,{}Q2} have no normal poles and satisfy A \\spad{(Q1',{} Q2') + ((H,{} -B),{} (B,{} H)) (Q1,{}Q2) = (C1,{}C2)} \\spad{D} is the derivation to use."))) NIL NIL @@ -4015,8 +4015,8 @@ NIL (-1021 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) ((-4404 . T) (-4409 . T) (-4403 . T) (-4406 . T) (-4405 . T) ((-4413 "*") . T) (-4408 . T)) -((-4030 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (QUOTE (-564))))) -(-1022 -3510 L) +((-4007 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (QUOTE (-564))))) +(-1022 -3445 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4052,14 +4052,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1031 -3510 |Expon| |VarSet| |FPol| |LFPol|) +(-1031 -3445 |Expon| |VarSet| |FPol| |LFPol|) ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) (((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL (-1032) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1327) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -2423) (QUOTE (-52))))))) (-4030 (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4030 (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-847))) (|HasCategory| (-52) (QUOTE (-1094))) (-4030 (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1354) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -2577) (QUOTE (-52))))))) (-4007 (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4007 (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-847))) (|HasCategory| (-52) (QUOTE (-1094))) (-4007 (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859))))) (-1033) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4116,7 +4116,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4408 . T)) NIL -(-1047 |xx| -3510) +(-1047 |xx| -3445) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4131,7 +4131,7 @@ NIL (-1050 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4411 . T) (-4406 . T) (-4405 . T)) -((-4030 (-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)))) (-4030 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4007 (-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)))) (-4007 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-859))))) (-1051 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL @@ -4163,7 +4163,7 @@ NIL (-1058) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,{}routineName,{}ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,{}s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,{}s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,{}s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,{}s,{}newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,{}s,{}newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,{}y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1327) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -2423) (QUOTE (-52))))))) (-4030 (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4030 (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-847))) (|HasCategory| (-52) (QUOTE (-1094))) (-4030 (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1354) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -2577) (QUOTE (-52))))))) (-4007 (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4007 (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-847))) (|HasCategory| (-52) (QUOTE (-1094))) (-4007 (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859))))) (-1059 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL @@ -4208,11 +4208,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1070 |Base| R -3510) +(-1070 |Base| R -3445) ((|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 -3510) +(-1071 |Base| R -3445) ((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,{}...,{}rn])} creates the rule set \\spad{{r1,{}...,{}rn}}."))) NIL NIL @@ -4227,7 +4227,7 @@ NIL (-1074 R UP M) ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) ((-4404 |has| |#1| (-363)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-4030 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-4030 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-4007 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) (-1075 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4255,7 +4255,7 @@ NIL (-1081 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4030 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-906))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1082 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4315,7 +4315,7 @@ NIL (-1096 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}"))) ((-4411 . T) (-4401 . T) (-4412 . T)) -((-4030 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1097 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL @@ -4359,7 +4359,7 @@ NIL (-1107 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 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(QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-790))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-845))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-847))) (-12 (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1046)))) (-12 (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (LIST (QUOTE -897) (QUOTE (-1170))))) (-4007 (|HasCategory| |#3| (QUOTE (-1046))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564)))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1094)))) (|HasAttribute| |#3| (QUOTE -4408)) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (-1108 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4368,7 +4368,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1110 R -3510) +(-1110 R -3445) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4407,16 +4407,16 @@ NIL (-1119 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4030 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4030 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-906))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1120 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-4030 (|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))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) (-1121 R E V P) ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) ((-4412 . T) (-4411 . T)) NIL -(-1122 UP -3510) +(-1122 UP -3445) ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,{}g,{}h,{}i,{}k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,{}g,{}h,{}j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,{}g,{}h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,{}g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,{}g,{}h,{}i,{}j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,{}g,{}h,{}i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,{}g,{}h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,{}g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,{}f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) NIL NIL @@ -4471,11 +4471,11 @@ NIL (-1135 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))) (-4030 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))))) (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))) (-4007 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))))) (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-859))))) (-1136 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) ((-4408 . T) (-4400 |has| |#2| (-6 (-4413 "*"))) (-4411 . T) (-4405 . T) (-4406 . T)) -((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4030 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (-4030 (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4007 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (-4007 (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-1137 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4495,7 +4495,7 @@ NIL (-1141 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,{}y,{}...,{}z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-1142 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL @@ -4507,7 +4507,7 @@ NIL (-1144 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2423) (|devaluate| |#2|)))))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-847))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094)))) +((-12 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1354) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-847))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094)))) (-1145) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4531,7 +4531,7 @@ NIL (-1150 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) ((-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-1151) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4412 . T) (-4411 . T)) @@ -4539,11 +4539,11 @@ NIL (-1152) NIL ((-4412 . T) (-4411 . T)) -((-4030 (-12 (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-4007 (-12 (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-1153 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1327) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2423) (|devaluate| |#1|)))))) (-4030 (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1094)))) (-4030 (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 |#1|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 |#1|)) (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 |#1|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1327 (-1152)) (|:| -2423 |#1|)) (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1354) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#1|)))))) (-4007 (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1094)))) (-4007 (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 |#1|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 |#1|)) (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 |#1|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1354 (-1152)) (|:| -2577 |#1|)) (LIST (QUOTE -611) (QUOTE (-859))))) (-1154 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL @@ -4574,9 +4574,9 @@ NIL NIL (-1161 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4413 "*") -4030 (-4267 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-817))) (|has| |#1| (-172)) (-4267 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-906)))) (-4404 -4030 (-4267 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-817))) (|has| |#1| (-556)) (-4267 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-906)))) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . 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the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4030 (|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 -3742) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4030 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3128) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4269) (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))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4007 (|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 -3713) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2397) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4275) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1168 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|)))) (|HasCategory| (-768) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasSignature| |#1| (LIST (QUOTE -3742) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasCategory| |#1| (QUOTE (-363))) (-4030 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3128) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4269) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|)))) (|HasCategory| (-768) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasSignature| |#1| (LIST (QUOTE -3713) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasCategory| |#1| (QUOTE (-363))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2397) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4275) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1169) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4030 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-968) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasAttribute| |#1| (QUOTE -4409))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-968) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasAttribute| |#1| (QUOTE -4409))) (-1173) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4629,7 +4629,7 @@ NIL NIL NIL (-1175) -((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{symbols,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: Integer,{} DoubleFloat,{} Symbol,{} String,{} SExpression. See Also: SExpression. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if \\spad{`x'} really is a String") (((|Boolean|) $ (|[\|\|]| (|Symbol|))) "\\spad{x case Symbol} is \\spad{true} if \\spad{`x'} really is a Symbol") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if \\spad{`x'} really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if \\spad{`x'} really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when \\spad{`x'} is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Symbol|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}. The value returned is itself a syntax if \\spad{`x'} really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when \\spad{`s'} is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Symbol|) (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.") (((|Symbol|) $) "\\spad{autoCoerce(s)} forcibly extracts a symbo from the Syntax domain \\spad{`s'}; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax \\spad{`s'}.") (((|Symbol|) $) "\\spad{coerce(s)} extracts a symbol from the syntax \\spad{`s'}.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when \\spad{`s'} is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) +((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{symbols,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: \\indented{2}{Integer,{} DoubleFloat,{} Identifier,{} String,{} SExpression.} See Also: SExpression,{} InputForm. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if \\spad{`x'} really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if \\spad{`x'} really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if \\spad{`x'} really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if \\spad{`x'} really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when \\spad{`x'} is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}. The value returned is itself a syntax if \\spad{`x'} really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when \\spad{`s'} is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} forcibly extracts an identifier from the Syntax domain \\spad{`s'}; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax \\spad{`s'}.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax \\spad{`s'}.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when \\spad{`s'} is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL (-1176 N) @@ -4659,7 +4659,7 @@ NIL (-1182 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2423) (|devaluate| |#2|)))))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4030 (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1354) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4007 (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) (-1183 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) NIL @@ -4711,7 +4711,7 @@ NIL (-1195 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1,{} t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4412 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-1196 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4720,7 +4720,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1198 R -3510) +(-1198 R -3445) ((|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 -3510) +(-1200 R -3445) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -883) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -883) (|devaluate| |#1|))))) @@ -4743,7 +4743,7 @@ NIL (-1203 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-4030 (|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))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) (-1204 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,{}ll,{}b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,{}b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4756,7 +4756,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) -(-1207 -3510) +(-1207 -3445) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,{}n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL @@ -4819,11 +4819,11 @@ NIL (-1222 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . 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the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4859,7 +4859,7 @@ NIL (-1232 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4413 "*") |has| |#2| (-172)) (-4404 |has| |#2| (-556)) (-4407 |has| |#2| (-363)) (-4409 |has| |#2| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . 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(|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4875,7 +4875,7 @@ NIL (-1236 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3742) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) +((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3713) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) (-1237 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) @@ -4903,15 +4903,15 @@ NIL (-1243 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4030 (|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 -3742) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4030 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3128) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4269) (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))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4007 (|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 -3713) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2397) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4275) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-1244 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4030 (|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 -3742) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4030 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3128) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4269) (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))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4007 (|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 -3713) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2397) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4275) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1245 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,{}f(var))}."))) (((-4413 "*") |has| (-1244 |#2| |#3| |#4|) (-172)) (-4404 |has| (-1244 |#2| |#3| |#4|) (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-172))) (-4030 (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-556)))) +((|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-172))) (-4007 (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-556)))) (-1246 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4927,7 +4927,7 @@ NIL (-1249 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-956))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -4269) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3128) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-956))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -4275) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2397) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) (-1250 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) @@ -4935,12 +4935,12 @@ NIL (-1251 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4030 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|)))) (|HasCategory| (-768) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasSignature| |#1| (LIST (QUOTE -3742) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasCategory| |#1| (QUOTE (-363))) (-4030 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3128) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4269) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4007 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|)))) (|HasCategory| (-768) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasSignature| |#1| (LIST (QUOTE -3713) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasCategory| |#1| (QUOTE (-363))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2397) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4275) (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 -3510 UP L UTS) +(-1253 -3445 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s,{} n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL ((|HasCategory| |#1| (QUOTE (-556)))) @@ -4967,7 +4967,7 @@ NIL (-1259 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4412 . T) (-4411 . T)) -((-4030 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4030 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4030 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4007 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4007 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1260) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -5000,7 +5000,7 @@ NIL ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,{}s,{}st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,{}ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,{}s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1268 K R UP -3510) +(-1268 K R UP -3445) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -5036,11 +5036,11 @@ NIL ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4404 |has| |#2| (-6 -4404)) (-4406 . T) (-4405 . T) (-4408 . T)) NIL -(-1277 S -3510) +(-1277 S -3445) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1278 -3510) +(-1278 -3445) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL @@ -5096,4 +5096,4 @@ NIL NIL NIL NIL -((-3 NIL 2283131 2283136 2283141 2283146) (-2 NIL 2283111 2283116 2283121 2283126) (-1 NIL 2283091 2283096 2283101 2283106) (0 NIL 2283071 2283076 2283081 2283086) (-1287 "ZMOD.spad" 2282880 2282893 2283009 2283066) (-1286 "ZLINDEP.spad" 2281924 2281935 2282870 2282875) (-1285 "ZDSOLVE.spad" 2271773 2271795 2281914 2281919) (-1284 "YSTREAM.spad" 2271266 2271277 2271763 2271768) (-1283 "XRPOLY.spad" 2270486 2270506 2271122 2271191) (-1282 "XPR.spad" 2268277 2268290 2270204 2270303) (-1281 "XPOLY.spad" 2267832 2267843 2268133 2268202) (-1280 "XPOLYC.spad" 2267149 2267165 2267758 2267827) (-1279 "XPBWPOLY.spad" 2265586 2265606 2266929 2266998) (-1278 "XF.spad" 2264047 2264062 2265488 2265581) (-1277 "XF.spad" 2262488 2262505 2263931 2263936) (-1276 "XFALG.spad" 2259512 2259528 2262414 2262483) (-1275 "XEXPPKG.spad" 2258763 2258789 2259502 2259507) (-1274 "XDPOLY.spad" 2258377 2258393 2258619 2258688) (-1273 "XALG.spad" 2258037 2258048 2258333 2258372) (-1272 "WUTSET.spad" 2253876 2253893 2257683 2257710) (-1271 "WP.spad" 2253075 2253119 2253734 2253801) (-1270 "WHILEAST.spad" 2252873 2252882 2253065 2253070) (-1269 "WHEREAST.spad" 2252544 2252553 2252863 2252868) (-1268 "WFFINTBS.spad" 2250107 2250129 2252534 2252539) (-1267 "WEIER.spad" 2248321 2248332 2250097 2250102) (-1266 "VSPACE.spad" 2247994 2248005 2248289 2248316) (-1265 "VSPACE.spad" 2247687 2247700 2247984 2247989) (-1264 "VOID.spad" 2247364 2247373 2247677 2247682) (-1263 "VIEW.spad" 2244986 2244995 2247354 2247359) (-1262 "VIEWDEF.spad" 2240183 2240192 2244976 2244981) (-1261 "VIEW3D.spad" 2224018 2224027 2240173 2240178) (-1260 "VIEW2D.spad" 2211755 2211764 2224008 2224013) (-1259 "VECTOR.spad" 2210430 2210441 2210681 2210708) (-1258 "VECTOR2.spad" 2209057 2209070 2210420 2210425) (-1257 "VECTCAT.spad" 2206957 2206968 2209025 2209052) (-1256 "VECTCAT.spad" 2204665 2204678 2206735 2206740) (-1255 "VARIABLE.spad" 2204445 2204460 2204655 2204660) (-1254 "UTYPE.spad" 2204089 2204098 2204435 2204440) (-1253 "UTSODETL.spad" 2203382 2203406 2204045 2204050) (-1252 "UTSODE.spad" 2201570 2201590 2203372 2203377) (-1251 "UTS.spad" 2196359 2196387 2200037 2200134) (-1250 "UTSCAT.spad" 2193810 2193826 2196257 2196354) (-1249 "UTSCAT.spad" 2190905 2190923 2193354 2193359) (-1248 "UTS2.spad" 2190498 2190533 2190895 2190900) (-1247 "URAGG.spad" 2185130 2185141 2190488 2190493) (-1246 "URAGG.spad" 2179726 2179739 2185086 2185091) (-1245 "UPXSSING.spad" 2177369 2177395 2178807 2178940) (-1244 "UPXS.spad" 2174517 2174545 2175501 2175650) (-1243 "UPXSCONS.spad" 2172274 2172294 2172649 2172798) (-1242 "UPXSCCA.spad" 2170839 2170859 2172120 2172269) (-1241 "UPXSCCA.spad" 2169546 2169568 2170829 2170834) (-1240 "UPXSCAT.spad" 2168127 2168143 2169392 2169541) (-1239 "UPXS2.spad" 2167668 2167721 2168117 2168122) (-1238 "UPSQFREE.spad" 2166080 2166094 2167658 2167663) (-1237 "UPSCAT.spad" 2163673 2163697 2165978 2166075) (-1236 "UPSCAT.spad" 2160972 2160998 2163279 2163284) (-1235 "UPOLYC.spad" 2155950 2155961 2160814 2160967) (-1234 "UPOLYC.spad" 2150820 2150833 2155686 2155691) (-1233 "UPOLYC2.spad" 2150289 2150308 2150810 2150815) (-1232 "UP.spad" 2147446 2147461 2147839 2147992) (-1231 "UPMP.spad" 2146336 2146349 2147436 2147441) (-1230 "UPDIVP.spad" 2145899 2145913 2146326 2146331) (-1229 "UPDECOMP.spad" 2144136 2144150 2145889 2145894) (-1228 "UPCDEN.spad" 2143343 2143359 2144126 2144131) (-1227 "UP2.spad" 2142705 2142726 2143333 2143338) (-1226 "UNISEG.spad" 2142058 2142069 2142624 2142629) (-1225 "UNISEG2.spad" 2141551 2141564 2142014 2142019) (-1224 "UNIFACT.spad" 2140652 2140664 2141541 2141546) (-1223 "ULS.spad" 2131204 2131232 2132297 2132726) (-1222 "ULSCONS.spad" 2123598 2123618 2123970 2124119) (-1221 "ULSCCAT.spad" 2121327 2121347 2123444 2123593) (-1220 "ULSCCAT.spad" 2119164 2119186 2121283 2121288) (-1219 "ULSCAT.spad" 2117380 2117396 2119010 2119159) (-1218 "ULS2.spad" 2116892 2116945 2117370 2117375) (-1217 "UINT8.spad" 2116769 2116778 2116882 2116887) (-1216 "UINT64.spad" 2116645 2116654 2116759 2116764) (-1215 "UINT32.spad" 2116521 2116530 2116635 2116640) (-1214 "UINT16.spad" 2116397 2116406 2116511 2116516) (-1213 "UFD.spad" 2115462 2115471 2116323 2116392) (-1212 "UFD.spad" 2114589 2114600 2115452 2115457) (-1211 "UDVO.spad" 2113436 2113445 2114579 2114584) (-1210 "UDPO.spad" 2110863 2110874 2113392 2113397) (-1209 "TYPE.spad" 2110795 2110804 2110853 2110858) (-1208 "TYPEAST.spad" 2110714 2110723 2110785 2110790) (-1207 "TWOFACT.spad" 2109364 2109379 2110704 2110709) (-1206 "TUPLE.spad" 2108848 2108859 2109263 2109268) (-1205 "TUBETOOL.spad" 2105685 2105694 2108838 2108843) (-1204 "TUBE.spad" 2104326 2104343 2105675 2105680) (-1203 "TS.spad" 2102915 2102931 2103891 2103988) (-1202 "TSETCAT.spad" 2090042 2090059 2102883 2102910) (-1201 "TSETCAT.spad" 2077155 2077174 2089998 2090003) (-1200 "TRMANIP.spad" 2071521 2071538 2076861 2076866) (-1199 "TRIMAT.spad" 2070480 2070505 2071511 2071516) (-1198 "TRIGMNIP.spad" 2068997 2069014 2070470 2070475) (-1197 "TRIGCAT.spad" 2068509 2068518 2068987 2068992) (-1196 "TRIGCAT.spad" 2068019 2068030 2068499 2068504) (-1195 "TREE.spad" 2066590 2066601 2067626 2067653) (-1194 "TRANFUN.spad" 2066421 2066430 2066580 2066585) (-1193 "TRANFUN.spad" 2066250 2066261 2066411 2066416) (-1192 "TOPSP.spad" 2065924 2065933 2066240 2066245) (-1191 "TOOLSIGN.spad" 2065587 2065598 2065914 2065919) (-1190 "TEXTFILE.spad" 2064144 2064153 2065577 2065582) (-1189 "TEX.spad" 2061276 2061285 2064134 2064139) (-1188 "TEX1.spad" 2060832 2060843 2061266 2061271) (-1187 "TEMUTL.spad" 2060387 2060396 2060822 2060827) (-1186 "TBCMPPK.spad" 2058480 2058503 2060377 2060382) (-1185 "TBAGG.spad" 2057516 2057539 2058460 2058475) (-1184 "TBAGG.spad" 2056560 2056585 2057506 2057511) (-1183 "TANEXP.spad" 2055936 2055947 2056550 2056555) (-1182 "TABLE.spad" 2054347 2054370 2054617 2054644) (-1181 "TABLEAU.spad" 2053828 2053839 2054337 2054342) (-1180 "TABLBUMP.spad" 2050611 2050622 2053818 2053823) (-1179 "SYSTEM.spad" 2049839 2049848 2050601 2050606) (-1178 "SYSSOLP.spad" 2047312 2047323 2049829 2049834) (-1177 "SYSNNI.spad" 2046492 2046503 2047302 2047307) (-1176 "SYSINT.spad" 2045896 2045907 2046482 2046487) (-1175 "SYNTAX.spad" 2042166 2042175 2045886 2045891) (-1174 "SYMTAB.spad" 2040222 2040231 2042156 2042161) (-1173 "SYMS.spad" 2036207 2036216 2040212 2040217) (-1172 "SYMPOLY.spad" 2035214 2035225 2035296 2035423) (-1171 "SYMFUNC.spad" 2034689 2034700 2035204 2035209) (-1170 "SYMBOL.spad" 2032116 2032125 2034679 2034684) (-1169 "SWITCH.spad" 2028873 2028882 2032106 2032111) (-1168 "SUTS.spad" 2025772 2025800 2027340 2027437) (-1167 "SUPXS.spad" 2022907 2022935 2023904 2024053) (-1166 "SUP.spad" 2019676 2019687 2020457 2020610) (-1165 "SUPFRACF.spad" 2018781 2018799 2019666 2019671) (-1164 "SUP2.spad" 2018171 2018184 2018771 2018776) (-1163 "SUMRF.spad" 2017137 2017148 2018161 2018166) (-1162 "SUMFS.spad" 2016770 2016787 2017127 2017132) (-1161 "SULS.spad" 2007309 2007337 2008415 2008844) (-1160 "SUCHTAST.spad" 2007078 2007087 2007299 2007304) (-1159 "SUCH.spad" 2006758 2006773 2007068 2007073) (-1158 "SUBSPACE.spad" 1998765 1998780 2006748 2006753) (-1157 "SUBRESP.spad" 1997925 1997939 1998721 1998726) (-1156 "STTF.spad" 1994024 1994040 1997915 1997920) (-1155 "STTFNC.spad" 1990492 1990508 1994014 1994019) (-1154 "STTAYLOR.spad" 1982890 1982901 1990373 1990378) (-1153 "STRTBL.spad" 1981395 1981412 1981544 1981571) (-1152 "STRING.spad" 1980804 1980813 1980818 1980845) (-1151 "STRICAT.spad" 1980592 1980601 1980772 1980799) (-1150 "STREAM.spad" 1977450 1977461 1980117 1980132) (-1149 "STREAM3.spad" 1976995 1977010 1977440 1977445) (-1148 "STREAM2.spad" 1976063 1976076 1976985 1976990) (-1147 "STREAM1.spad" 1975767 1975778 1976053 1976058) (-1146 "STINPROD.spad" 1974673 1974689 1975757 1975762) (-1145 "STEP.spad" 1973874 1973883 1974663 1974668) (-1144 "STBL.spad" 1972400 1972428 1972567 1972582) (-1143 "STAGG.spad" 1971475 1971486 1972390 1972395) (-1142 "STAGG.spad" 1970548 1970561 1971465 1971470) (-1141 "STACK.spad" 1969899 1969910 1970155 1970182) (-1140 "SREGSET.spad" 1967603 1967620 1969545 1969572) (-1139 "SRDCMPK.spad" 1966148 1966168 1967593 1967598) (-1138 "SRAGG.spad" 1961245 1961254 1966116 1966143) (-1137 "SRAGG.spad" 1956362 1956373 1961235 1961240) (-1136 "SQMATRIX.spad" 1953978 1953996 1954894 1954981) (-1135 "SPLTREE.spad" 1948530 1948543 1953414 1953441) (-1134 "SPLNODE.spad" 1945118 1945131 1948520 1948525) (-1133 "SPFCAT.spad" 1943895 1943904 1945108 1945113) (-1132 "SPECOUT.spad" 1942445 1942454 1943885 1943890) (-1131 "SPADXPT.spad" 1934584 1934593 1942435 1942440) (-1130 "spad-parser.spad" 1934049 1934058 1934574 1934579) (-1129 "SPADAST.spad" 1933750 1933759 1934039 1934044) (-1128 "SPACEC.spad" 1917763 1917774 1933740 1933745) (-1127 "SPACE3.spad" 1917539 1917550 1917753 1917758) (-1126 "SORTPAK.spad" 1917084 1917097 1917495 1917500) (-1125 "SOLVETRA.spad" 1914841 1914852 1917074 1917079) (-1124 "SOLVESER.spad" 1913361 1913372 1914831 1914836) (-1123 "SOLVERAD.spad" 1909371 1909382 1913351 1913356) (-1122 "SOLVEFOR.spad" 1907791 1907809 1909361 1909366) (-1121 "SNTSCAT.spad" 1907391 1907408 1907759 1907786) (-1120 "SMTS.spad" 1905651 1905677 1906956 1907053) (-1119 "SMP.spad" 1903090 1903110 1903480 1903607) (-1118 "SMITH.spad" 1901933 1901958 1903080 1903085) (-1117 "SMATCAT.spad" 1900043 1900073 1901877 1901928) (-1116 "SMATCAT.spad" 1898085 1898117 1899921 1899926) (-1115 "SKAGG.spad" 1897046 1897057 1898053 1898080) (-1114 "SINT.spad" 1895872 1895881 1896912 1897041) (-1113 "SIMPAN.spad" 1895600 1895609 1895862 1895867) (-1112 "SIG.spad" 1894928 1894937 1895590 1895595) (-1111 "SIGNRF.spad" 1894036 1894047 1894918 1894923) (-1110 "SIGNEF.spad" 1893305 1893322 1894026 1894031) (-1109 "SIGAST.spad" 1892686 1892695 1893295 1893300) (-1108 "SHP.spad" 1890604 1890619 1892642 1892647) (-1107 "SHDP.spad" 1880315 1880342 1880824 1880955) (-1106 "SGROUP.spad" 1879923 1879932 1880305 1880310) (-1105 "SGROUP.spad" 1879529 1879540 1879913 1879918) (-1104 "SGCF.spad" 1872410 1872419 1879519 1879524) (-1103 "SFRTCAT.spad" 1871338 1871355 1872378 1872405) (-1102 "SFRGCD.spad" 1870401 1870421 1871328 1871333) (-1101 "SFQCMPK.spad" 1865038 1865058 1870391 1870396) (-1100 "SFORT.spad" 1864473 1864487 1865028 1865033) (-1099 "SEXOF.spad" 1864316 1864356 1864463 1864468) (-1098 "SEX.spad" 1864208 1864217 1864306 1864311) (-1097 "SEXCAT.spad" 1861759 1861799 1864198 1864203) (-1096 "SET.spad" 1860059 1860070 1861180 1861219) (-1095 "SETMN.spad" 1858493 1858510 1860049 1860054) (-1094 "SETCAT.spad" 1857978 1857987 1858483 1858488) (-1093 "SETCAT.spad" 1857461 1857472 1857968 1857973) (-1092 "SETAGG.spad" 1853982 1853993 1857441 1857456) (-1091 "SETAGG.spad" 1850511 1850524 1853972 1853977) (-1090 "SEQAST.spad" 1850214 1850223 1850501 1850506) (-1089 "SEGXCAT.spad" 1849336 1849349 1850204 1850209) (-1088 "SEG.spad" 1849149 1849160 1849255 1849260) (-1087 "SEGCAT.spad" 1848056 1848067 1849139 1849144) (-1086 "SEGBIND.spad" 1847128 1847139 1848011 1848016) (-1085 "SEGBIND2.spad" 1846824 1846837 1847118 1847123) (-1084 "SEGAST.spad" 1846538 1846547 1846814 1846819) (-1083 "SEG2.spad" 1845963 1845976 1846494 1846499) (-1082 "SDVAR.spad" 1845239 1845250 1845953 1845958) (-1081 "SDPOL.spad" 1842629 1842640 1842920 1843047) (-1080 "SCPKG.spad" 1840708 1840719 1842619 1842624) (-1079 "SCOPE.spad" 1839861 1839870 1840698 1840703) (-1078 "SCACHE.spad" 1838543 1838554 1839851 1839856) (-1077 "SASTCAT.spad" 1838452 1838461 1838533 1838538) (-1076 "SAOS.spad" 1838324 1838333 1838442 1838447) (-1075 "SAERFFC.spad" 1838037 1838057 1838314 1838319) (-1074 "SAE.spad" 1836212 1836228 1836823 1836958) (-1073 "SAEFACT.spad" 1835913 1835933 1836202 1836207) (-1072 "RURPK.spad" 1833554 1833570 1835903 1835908) (-1071 "RULESET.spad" 1832995 1833019 1833544 1833549) (-1070 "RULE.spad" 1831199 1831223 1832985 1832990) (-1069 "RULECOLD.spad" 1831051 1831064 1831189 1831194) (-1068 "RSTRCAST.spad" 1830768 1830777 1831041 1831046) (-1067 "RSETGCD.spad" 1827146 1827166 1830758 1830763) (-1066 "RSETCAT.spad" 1816930 1816947 1827114 1827141) (-1065 "RSETCAT.spad" 1806734 1806753 1816920 1816925) (-1064 "RSDCMPK.spad" 1805186 1805206 1806724 1806729) (-1063 "RRCC.spad" 1803570 1803600 1805176 1805181) (-1062 "RRCC.spad" 1801952 1801984 1803560 1803565) (-1061 "RPTAST.spad" 1801654 1801663 1801942 1801947) (-1060 "RPOLCAT.spad" 1781014 1781029 1801522 1801649) (-1059 "RPOLCAT.spad" 1760088 1760105 1780598 1780603) (-1058 "ROUTINE.spad" 1755951 1755960 1758735 1758762) (-1057 "ROMAN.spad" 1755279 1755288 1755817 1755946) (-1056 "ROIRC.spad" 1754359 1754391 1755269 1755274) (-1055 "RNS.spad" 1753262 1753271 1754261 1754354) (-1054 "RNS.spad" 1752251 1752262 1753252 1753257) (-1053 "RNG.spad" 1751986 1751995 1752241 1752246) (-1052 "RMODULE.spad" 1751624 1751635 1751976 1751981) (-1051 "RMCAT2.spad" 1751032 1751089 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(-476 "GTSET.spad" 800872 800888 801579 801606) (-475 "GSTBL.spad" 799391 799426 799565 799580) (-474 "GSERIES.spad" 796558 796585 797523 797672) (-473 "GROUP.spad" 795827 795835 796538 796553) (-472 "GROUP.spad" 795104 795114 795817 795822) (-471 "GROEBSOL.spad" 793592 793613 795094 795099) (-470 "GRMOD.spad" 792163 792175 793582 793587) (-469 "GRMOD.spad" 790732 790746 792153 792158) (-468 "GRIMAGE.spad" 783337 783345 790722 790727) (-467 "GRDEF.spad" 781716 781724 783327 783332) (-466 "GRAY.spad" 780175 780183 781706 781711) (-465 "GRALG.spad" 779222 779234 780165 780170) (-464 "GRALG.spad" 778267 778281 779212 779217) (-463 "GPOLSET.spad" 777721 777744 777949 777976) (-462 "GOSPER.spad" 776986 777004 777711 777716) (-461 "GMODPOL.spad" 776124 776151 776954 776981) (-460 "GHENSEL.spad" 775193 775207 776114 776119) (-459 "GENUPS.spad" 771294 771307 775183 775188) (-458 "GENUFACT.spad" 770871 770881 771284 771289) (-457 "GENPGCD.spad" 770455 770472 770861 770866) (-456 "GENMFACT.spad" 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722587) (-435 "FSUPFACT.spad" 720655 720674 721691 721696) (-434 "FST.spad" 718741 718749 720645 720650) (-433 "FSRED.spad" 718219 718235 718731 718736) (-432 "FSPRMELT.spad" 717043 717059 718176 718181) (-431 "FSPECF.spad" 715120 715136 717033 717038) (-430 "FS.spad" 709182 709192 714895 715115) (-429 "FS.spad" 703022 703034 708737 708742) (-428 "FSINT.spad" 702680 702696 703012 703017) (-427 "FSERIES.spad" 701867 701879 702500 702599) (-426 "FSCINT.spad" 701180 701196 701857 701862) (-425 "FSAGG.spad" 700297 700307 701136 701175) (-424 "FSAGG.spad" 699376 699388 700217 700222) (-423 "FSAGG2.spad" 698075 698091 699366 699371) (-422 "FS2UPS.spad" 692558 692592 698065 698070) (-421 "FS2.spad" 692203 692219 692548 692553) (-420 "FS2EXPXP.spad" 691326 691349 692193 692198) (-419 "FRUTIL.spad" 690268 690278 691316 691321) (-418 "FR.spad" 683962 683972 689292 689361) (-417 "FRNAALG.spad" 679049 679059 683904 683957) (-416 "FRNAALG.spad" 674148 674160 679005 679010) (-415 "FRNAAF2.spad" 673602 673620 674138 674143) (-414 "FRMOD.spad" 672996 673026 673533 673538) (-413 "FRIDEAL.spad" 672191 672212 672976 672991) (-412 "FRIDEAL2.spad" 671793 671825 672181 672186) (-411 "FRETRCT.spad" 671304 671314 671783 671788) (-410 "FRETRCT.spad" 670681 670693 671162 671167) (-409 "FRAMALG.spad" 669009 669022 670637 670676) (-408 "FRAMALG.spad" 667369 667384 668999 669004) (-407 "FRAC.spad" 664468 664478 664871 665044) (-406 "FRAC2.spad" 664071 664083 664458 664463) (-405 "FR2.spad" 663405 663417 664061 664066) (-404 "FPS.spad" 660214 660222 663295 663400) (-403 "FPS.spad" 657051 657061 660134 660139) (-402 "FPC.spad" 656093 656101 656953 657046) (-401 "FPC.spad" 655221 655231 656083 656088) (-400 "FPATMAB.spad" 654983 654993 655211 655216) (-399 "FPARFRAC.spad" 653456 653473 654973 654978) (-398 "FORTRAN.spad" 651962 652005 653446 653451) (-397 "FORT.spad" 650891 650899 651952 651957) (-396 "FORTFN.spad" 648061 648069 650881 650886) (-395 "FORTCAT.spad" 647745 647753 648051 648056) (-394 "FORMULA.spad" 645209 645217 647735 647740) (-393 "FORMULA1.spad" 644688 644698 645199 645204) (-392 "FORDER.spad" 644379 644403 644678 644683) (-391 "FOP.spad" 643580 643588 644369 644374) (-390 "FNLA.spad" 643004 643026 643548 643575) (-389 "FNCAT.spad" 641591 641599 642994 642999) (-388 "FNAME.spad" 641483 641491 641581 641586) (-387 "FMTC.spad" 641281 641289 641409 641478) (-386 "FMONOID.spad" 638336 638346 641237 641242) (-385 "FM.spad" 638031 638043 638270 638297) (-384 "FMFUN.spad" 635061 635069 638021 638026) (-383 "FMC.spad" 634113 634121 635051 635056) (-382 "FMCAT.spad" 631767 631785 634081 634108) (-381 "FM1.spad" 631124 631136 631701 631728) (-380 "FLOATRP.spad" 628845 628859 631114 631119) (-379 "FLOAT.spad" 622133 622141 628711 628840) (-378 "FLOATCP.spad" 619550 619564 622123 622128) (-377 "FLINEXP.spad" 619262 619272 619530 619545) (-376 "FLINEXP.spad" 618928 618940 619198 619203) (-375 "FLASORT.spad" 618248 618260 618918 618923) (-374 "FLALG.spad" 615894 615913 618174 618243) (-373 "FLAGG.spad" 612912 612922 615874 615889) (-372 "FLAGG.spad" 609831 609843 612795 612800) (-371 "FLAGG2.spad" 608512 608528 609821 609826) (-370 "FINRALG.spad" 606541 606554 608468 608507) (-369 "FINRALG.spad" 604496 604511 606425 606430) (-368 "FINITE.spad" 603648 603656 604486 604491) (-367 "FINAALG.spad" 592629 592639 603590 603643) (-366 "FINAALG.spad" 581622 581634 592585 592590) (-365 "FILE.spad" 581205 581215 581612 581617) (-364 "FILECAT.spad" 579723 579740 581195 581200) (-363 "FIELD.spad" 579129 579137 579625 579718) (-362 "FIELD.spad" 578621 578631 579119 579124) (-361 "FGROUP.spad" 577230 577240 578601 578616) (-360 "FGLMICPK.spad" 576017 576032 577220 577225) (-359 "FFX.spad" 575392 575407 575733 575826) (-358 "FFSLPE.spad" 574881 574902 575382 575387) (-357 "FFPOLY.spad" 566133 566144 574871 574876) (-356 "FFPOLY2.spad" 565193 565210 566123 566128) (-355 "FFP.spad" 564590 564610 564909 565002) (-354 "FF.spad" 564038 564054 564271 564364) (-353 "FFNBX.spad" 562550 562570 563754 563847) (-352 "FFNBP.spad" 561063 561080 562266 562359) (-351 "FFNB.spad" 559528 559549 560744 560837) (-350 "FFINTBAS.spad" 556942 556961 559518 559523) (-349 "FFIELDC.spad" 554517 554525 556844 556937) (-348 "FFIELDC.spad" 552178 552188 554507 554512) (-347 "FFHOM.spad" 550926 550943 552168 552173) (-346 "FFF.spad" 548361 548372 550916 550921) (-345 "FFCGX.spad" 547208 547228 548077 548170) (-344 "FFCGP.spad" 546097 546117 546924 547017) (-343 "FFCG.spad" 544889 544910 545778 545871) (-342 "FFCAT.spad" 537916 537938 544728 544884) (-341 "FFCAT.spad" 531022 531046 537836 537841) (-340 "FFCAT2.spad" 530767 530807 531012 531017) (-339 "FEXPR.spad" 522476 522522 530523 530562) (-338 "FEVALAB.spad" 522182 522192 522466 522471) (-337 "FEVALAB.spad" 521673 521685 521959 521964) (-336 "FDIV.spad" 521115 521139 521663 521668) (-335 "FDIVCAT.spad" 519157 519181 521105 521110) (-334 "FDIVCAT.spad" 517197 517223 519147 519152) (-333 "FDIV2.spad" 516851 516891 517187 517192) (-332 "FCPAK1.spad" 515404 515412 516841 516846) (-331 "FCOMP.spad" 514783 514793 515394 515399) (-330 "FC.spad" 504698 504706 514773 514778) (-329 "FAXF.spad" 497633 497647 504600 504693) (-328 "FAXF.spad" 490620 490636 497589 497594) (-327 "FARRAY.spad" 488766 488776 489803 489830) (-326 "FAMR.spad" 486886 486898 488664 488761) (-325 "FAMR.spad" 484990 485004 486770 486775) (-324 "FAMONOID.spad" 484640 484650 484944 484949) (-323 "FAMONC.spad" 482862 482874 484630 484635) (-322 "FAGROUP.spad" 482468 482478 482758 482785) (-321 "FACUTIL.spad" 480664 480681 482458 482463) (-320 "FACTFUNC.spad" 479840 479850 480654 480659) (-319 "EXPUPXS.spad" 476673 476696 477972 478121) (-318 "EXPRTUBE.spad" 473901 473909 476663 476668) (-317 "EXPRODE.spad" 470773 470789 473891 473896) (-316 "EXPR.spad" 466048 466058 466762 467169) (-315 "EXPR2UPS.spad" 462140 462153 466038 466043) (-314 "EXPR2.spad" 461843 461855 462130 462135) (-313 "EXPEXPAN.spad" 458781 458806 459415 459508) (-312 "EXIT.spad" 458452 458460 458771 458776) (-311 "EXITAST.spad" 458188 458196 458442 458447) (-310 "EVALCYC.spad" 457646 457660 458178 458183) (-309 "EVALAB.spad" 457210 457220 457636 457641) (-308 "EVALAB.spad" 456772 456784 457200 457205) (-307 "EUCDOM.spad" 454314 454322 456698 456767) (-306 "EUCDOM.spad" 451918 451928 454304 454309) (-305 "ESTOOLS.spad" 443758 443766 451908 451913) (-304 "ESTOOLS2.spad" 443359 443373 443748 443753) (-303 "ESTOOLS1.spad" 443044 443055 443349 443354) (-302 "ES.spad" 435591 435599 443034 443039) (-301 "ES.spad" 428044 428054 435489 435494) (-300 "ESCONT.spad" 424817 424825 428034 428039) (-299 "ESCONT1.spad" 424566 424578 424807 424812) (-298 "ES2.spad" 424061 424077 424556 424561) (-297 "ES1.spad" 423627 423643 424051 424056) (-296 "ERROR.spad" 420948 420956 423617 423622) (-295 "EQTBL.spad" 419420 419442 419629 419656) (-294 "EQ.spad" 414294 414304 417093 417205) (-293 "EQ2.spad" 414010 414022 414284 414289) (-292 "EP.spad" 410324 410334 414000 414005) (-291 "ENV.spad" 409000 409008 410314 410319) (-290 "ENTIRER.spad" 408668 408676 408944 408995) (-289 "EMR.spad" 407869 407910 408594 408663) (-288 "ELTAGG.spad" 406109 406128 407859 407864) (-287 "ELTAGG.spad" 404313 404334 406065 406070) (-286 "ELTAB.spad" 403760 403778 404303 404308) (-285 "ELFUTS.spad" 403139 403158 403750 403755) (-284 "ELEMFUN.spad" 402828 402836 403129 403134) (-283 "ELEMFUN.spad" 402515 402525 402818 402823) (-282 "ELAGG.spad" 400458 400468 402495 402510) (-281 "ELAGG.spad" 398338 398350 400377 400382) (-280 "ELABEXPR.spad" 397269 397277 398328 398333) (-279 "EFUPXS.spad" 394045 394075 397225 397230) (-278 "EFULS.spad" 390881 390904 394001 394006) (-277 "EFSTRUC.spad" 388836 388852 390871 390876) (-276 "EF.spad" 383602 383618 388826 388831) (-275 "EAB.spad" 381878 381886 383592 383597) (-274 "E04UCFA.spad" 381414 381422 381868 381873) (-273 "E04NAFA.spad" 380991 380999 381404 381409) (-272 "E04MBFA.spad" 380571 380579 380981 380986) (-271 "E04JAFA.spad" 380107 380115 380561 380566) (-270 "E04GCFA.spad" 379643 379651 380097 380102) (-269 "E04FDFA.spad" 379179 379187 379633 379638) (-268 "E04DGFA.spad" 378715 378723 379169 379174) (-267 "E04AGNT.spad" 374557 374565 378705 378710) (-266 "DVARCAT.spad" 371242 371252 374547 374552) (-265 "DVARCAT.spad" 367925 367937 371232 371237) (-264 "DSMP.spad" 365356 365370 365661 365788) (-263 "DROPT.spad" 359301 359309 365346 365351) (-262 "DROPT1.spad" 358964 358974 359291 359296) (-261 "DROPT0.spad" 353791 353799 358954 358959) (-260 "DRAWPT.spad" 351946 351954 353781 353786) (-259 "DRAW.spad" 344546 344559 351936 351941) (-258 "DRAWHACK.spad" 343854 343864 344536 344541) (-257 "DRAWCX.spad" 341296 341304 343844 343849) (-256 "DRAWCURV.spad" 340833 340848 341286 341291) (-255 "DRAWCFUN.spad" 330005 330013 340823 340828) (-254 "DQAGG.spad" 328173 328183 329973 330000) (-253 "DPOLCAT.spad" 323514 323530 328041 328168) (-252 "DPOLCAT.spad" 318941 318959 323470 323475) (-251 "DPMO.spad" 311167 311183 311305 311606) (-250 "DPMM.spad" 303406 303424 303531 303832) (-249 "DOMCTOR.spad" 303298 303306 303396 303401) (-248 "DOMAIN.spad" 302429 302437 303288 303293) (-247 "DMP.spad" 299651 299666 300223 300350) (-246 "DLP.spad" 298999 299009 299641 299646) (-245 "DLIST.spad" 297578 297588 298182 298209) (-244 "DLAGG.spad" 295989 295999 297568 297573) (-243 "DIVRING.spad" 295531 295539 295933 295984) (-242 "DIVRING.spad" 295117 295127 295521 295526) (-241 "DISPLAY.spad" 293297 293305 295107 295112) (-240 "DIRPROD.spad" 282877 282893 283517 283648) (-239 "DIRPROD2.spad" 281685 281703 282867 282872) (-238 "DIRPCAT.spad" 280627 280643 281549 281680) (-237 "DIRPCAT.spad" 279298 279316 280222 280227) (-236 "DIOSP.spad" 278123 278131 279288 279293) (-235 "DIOPS.spad" 277107 277117 278103 278118) (-234 "DIOPS.spad" 276065 276077 277063 277068) (-233 "DIFRING.spad" 275357 275365 276045 276060) (-232 "DIFRING.spad" 274657 274667 275347 275352) (-231 "DIFEXT.spad" 273816 273826 274637 274652) (-230 "DIFEXT.spad" 272892 272904 273715 273720) (-229 "DIAGG.spad" 272522 272532 272872 272887) (-228 "DIAGG.spad" 272160 272172 272512 272517) (-227 "DHMATRIX.spad" 270464 270474 271617 271644) (-226 "DFSFUN.spad" 263872 263880 270454 270459) (-225 "DFLOAT.spad" 260593 260601 263762 263867) (-224 "DFINTTLS.spad" 258802 258818 260583 260588) (-223 "DERHAM.spad" 256712 256744 258782 258797) (-222 "DEQUEUE.spad" 256030 256040 256319 256346) (-221 "DEGRED.spad" 255645 255659 256020 256025) (-220 "DEFINTRF.spad" 253170 253180 255635 255640) (-219 "DEFINTEF.spad" 251666 251682 253160 253165) (-218 "DEFAST.spad" 251034 251042 251656 251661) (-217 "DECIMAL.spad" 249140 249148 249501 249594) (-216 "DDFACT.spad" 246939 246956 249130 249135) (-215 "DBLRESP.spad" 246537 246561 246929 246934) (-214 "DBASE.spad" 245191 245201 246527 246532) (-213 "DATAARY.spad" 244653 244666 245181 245186) (-212 "D03FAFA.spad" 244481 244489 244643 244648) (-211 "D03EEFA.spad" 244301 244309 244471 244476) (-210 "D03AGNT.spad" 243381 243389 244291 244296) (-209 "D02EJFA.spad" 242843 242851 243371 243376) (-208 "D02CJFA.spad" 242321 242329 242833 242838) (-207 "D02BHFA.spad" 241811 241819 242311 242316) (-206 "D02BBFA.spad" 241301 241309 241801 241806) (-205 "D02AGNT.spad" 236105 236113 241291 241296) (-204 "D01WGTS.spad" 234424 234432 236095 236100) (-203 "D01TRNS.spad" 234401 234409 234414 234419) (-202 "D01GBFA.spad" 233923 233931 234391 234396) (-201 "D01FCFA.spad" 233445 233453 233913 233918) (-200 "D01ASFA.spad" 232913 232921 233435 233440) (-199 "D01AQFA.spad" 232359 232367 232903 232908) (-198 "D01APFA.spad" 231783 231791 232349 232354) (-197 "D01ANFA.spad" 231277 231285 231773 231778) (-196 "D01AMFA.spad" 230787 230795 231267 231272) (-195 "D01ALFA.spad" 230327 230335 230777 230782) (-194 "D01AKFA.spad" 229853 229861 230317 230322) (-193 "D01AJFA.spad" 229376 229384 229843 229848) (-192 "D01AGNT.spad" 225435 225443 229366 229371) (-191 "CYCLOTOM.spad" 224941 224949 225425 225430) (-190 "CYCLES.spad" 221773 221781 224931 224936) (-189 "CVMP.spad" 221190 221200 221763 221768) (-188 "CTRIGMNP.spad" 219680 219696 221180 221185) (-187 "CTOR.spad" 219375 219383 219670 219675) (-186 "CTORKIND.spad" 218978 218986 219365 219370) (-185 "CTORCAT.spad" 218227 218235 218968 218973) (-184 "CTORCAT.spad" 217474 217484 218217 218222) (-183 "CTORCALL.spad" 217054 217062 217464 217469) (-182 "CSTTOOLS.spad" 216297 216310 217044 217049) (-181 "CRFP.spad" 210001 210014 216287 216292) (-180 "CRCEAST.spad" 209721 209729 209991 209996) (-179 "CRAPACK.spad" 208764 208774 209711 209716) (-178 "CPMATCH.spad" 208264 208279 208689 208694) (-177 "CPIMA.spad" 207969 207988 208254 208259) (-176 "COORDSYS.spad" 202862 202872 207959 207964) (-175 "CONTOUR.spad" 202273 202281 202852 202857) (-174 "CONTFRAC.spad" 197885 197895 202175 202268) (-173 "CONDUIT.spad" 197643 197651 197875 197880) (-172 "COMRING.spad" 197317 197325 197581 197638) (-171 "COMPPROP.spad" 196831 196839 197307 197312) (-170 "COMPLPAT.spad" 196598 196613 196821 196826) (-169 "COMPLEX.spad" 190622 190632 190866 191127) (-168 "COMPLEX2.spad" 190335 190347 190612 190617) (-167 "COMPFACT.spad" 189937 189951 190325 190330) (-166 "COMPCAT.spad" 188005 188015 189671 189932) (-165 "COMPCAT.spad" 185766 185778 187434 187439) (-164 "COMMUPC.spad" 185512 185530 185756 185761) (-163 "COMMONOP.spad" 185045 185053 185502 185507) (-162 "COMM.spad" 184854 184862 185035 185040) (-161 "COMMAAST.spad" 184617 184625 184844 184849) (-160 "COMBOPC.spad" 183522 183530 184607 184612) (-159 "COMBINAT.spad" 182267 182277 183512 183517) (-158 "COMBF.spad" 179635 179651 182257 182262) (-157 "COLOR.spad" 178472 178480 179625 179630) (-156 "COLONAST.spad" 178138 178146 178462 178467) (-155 "CMPLXRT.spad" 177847 177864 178128 178133) (-154 "CLLCTAST.spad" 177509 177517 177837 177842) (-153 "CLIP.spad" 173601 173609 177499 177504) (-152 "CLIF.spad" 172240 172256 173557 173596) (-151 "CLAGG.spad" 168725 168735 172230 172235) (-150 "CLAGG.spad" 165081 165093 168588 168593) (-149 "CINTSLPE.spad" 164406 164419 165071 165076) (-148 "CHVAR.spad" 162484 162506 164396 164401) (-147 "CHARZ.spad" 162399 162407 162464 162479) (-146 "CHARPOL.spad" 161907 161917 162389 162394) (-145 "CHARNZ.spad" 161660 161668 161887 161902) (-144 "CHAR.spad" 159528 159536 161650 161655) (-143 "CFCAT.spad" 158844 158852 159518 159523) (-142 "CDEN.spad" 158002 158016 158834 158839) (-141 "CCLASS.spad" 156151 156159 157413 157452) (-140 "CATEGORY.spad" 155241 155249 156141 156146) (-139 "CATCTOR.spad" 155132 155140 155231 155236) (-138 "CATAST.spad" 154759 154767 155122 155127) (-137 "CASEAST.spad" 154473 154481 154749 154754) (-136 "CARTEN.spad" 149576 149600 154463 154468) (-135 "CARTEN2.spad" 148962 148989 149566 149571) (-134 "CARD.spad" 146251 146259 148936 148957) (-133 "CAPSLAST.spad" 146025 146033 146241 146246) (-132 "CACHSET.spad" 145647 145655 146015 146020) (-131 "CABMON.spad" 145200 145208 145637 145642) (-130 "BYTEORD.spad" 144875 144883 145190 145195) (-129 "BYTE.spad" 144300 144308 144865 144870) (-128 "BYTEBUF.spad" 142157 142165 143469 143496) (-127 "BTREE.spad" 141226 141236 141764 141791) (-126 "BTOURN.spad" 140229 140239 140833 140860) (-125 "BTCAT.spad" 139617 139627 140197 140224) (-124 "BTCAT.spad" 139025 139037 139607 139612) (-123 "BTAGG.spad" 138147 138155 138993 139020) (-122 "BTAGG.spad" 137289 137299 138137 138142) (-121 "BSTREE.spad" 136024 136034 136896 136923) (-120 "BRILL.spad" 134219 134230 136014 136019) (-119 "BRAGG.spad" 133143 133153 134209 134214) (-118 "BRAGG.spad" 132031 132043 133099 133104) (-117 "BPADICRT.spad" 130012 130024 130267 130360) (-116 "BPADIC.spad" 129676 129688 129938 130007) (-115 "BOUNDZRO.spad" 129332 129349 129666 129671) (-114 "BOP.spad" 124796 124804 129322 129327) (-113 "BOP1.spad" 122182 122192 124752 124757) (-112 "BOOLEAN.spad" 121506 121514 122172 122177) (-111 "BMODULE.spad" 121218 121230 121474 121501) (-110 "BITS.spad" 120637 120645 120854 120881) (-109 "BINDING.spad" 120056 120064 120627 120632) (-108 "BINARY.spad" 118167 118175 118523 118616) (-107 "BGAGG.spad" 117364 117374 118147 118162) (-106 "BGAGG.spad" 116569 116581 117354 117359) (-105 "BFUNCT.spad" 116133 116141 116549 116564) (-104 "BEZOUT.spad" 115267 115294 116083 116088) (-103 "BBTREE.spad" 112086 112096 114874 114901) (-102 "BASTYPE.spad" 111758 111766 112076 112081) (-101 "BASTYPE.spad" 111428 111438 111748 111753) (-100 "BALFACT.spad" 110867 110880 111418 111423) (-99 "AUTOMOR.spad" 110314 110323 110847 110862) (-98 "ATTREG.spad" 107033 107040 110066 110309) (-97 "ATTRBUT.spad" 103056 103063 107013 107028) (-96 "ATTRAST.spad" 102773 102780 103046 103051) (-95 "ATRIG.spad" 102243 102250 102763 102768) (-94 "ATRIG.spad" 101711 101720 102233 102238) (-93 "ASTCAT.spad" 101615 101622 101701 101706) (-92 "ASTCAT.spad" 101517 101526 101605 101610) (-91 "ASTACK.spad" 100850 100859 101124 101151) (-90 "ASSOCEQ.spad" 99650 99661 100806 100811) (-89 "ASP9.spad" 98731 98744 99640 99645) (-88 "ASP8.spad" 97774 97787 98721 98726) (-87 "ASP80.spad" 97096 97109 97764 97769) (-86 "ASP7.spad" 96256 96269 97086 97091) (-85 "ASP78.spad" 95707 95720 96246 96251) (-84 "ASP77.spad" 95076 95089 95697 95702) (-83 "ASP74.spad" 94168 94181 95066 95071) (-82 "ASP73.spad" 93439 93452 94158 94163) (-81 "ASP6.spad" 92306 92319 93429 93434) (-80 "ASP55.spad" 90815 90828 92296 92301) (-79 "ASP50.spad" 88632 88645 90805 90810) (-78 "ASP4.spad" 87927 87940 88622 88627) (-77 "ASP49.spad" 86926 86939 87917 87922) (-76 "ASP42.spad" 85333 85372 86916 86921) (-75 "ASP41.spad" 83912 83951 85323 85328) (-74 "ASP35.spad" 82900 82913 83902 83907) (-73 "ASP34.spad" 82201 82214 82890 82895) (-72 "ASP33.spad" 81761 81774 82191 82196) (-71 "ASP31.spad" 80901 80914 81751 81756) (-70 "ASP30.spad" 79793 79806 80891 80896) (-69 "ASP29.spad" 79259 79272 79783 79788) (-68 "ASP28.spad" 70532 70545 79249 79254) (-67 "ASP27.spad" 69429 69442 70522 70527) (-66 "ASP24.spad" 68516 68529 69419 69424) (-65 "ASP20.spad" 67980 67993 68506 68511) (-64 "ASP1.spad" 67361 67374 67970 67975) (-63 "ASP19.spad" 62047 62060 67351 67356) (-62 "ASP12.spad" 61461 61474 62037 62042) (-61 "ASP10.spad" 60732 60745 61451 61456) (-60 "ARRAY2.spad" 60092 60101 60339 60366) (-59 "ARRAY1.spad" 58927 58936 59275 59302) (-58 "ARRAY12.spad" 57596 57607 58917 58922) (-57 "ARR2CAT.spad" 53258 53279 57564 57591) (-56 "ARR2CAT.spad" 48940 48963 53248 53253) (-55 "ARITY.spad" 48508 48515 48930 48935) (-54 "APPRULE.spad" 47752 47774 48498 48503) (-53 "APPLYORE.spad" 47367 47380 47742 47747) (-52 "ANY.spad" 45709 45716 47357 47362) (-51 "ANY1.spad" 44780 44789 45699 45704) (-50 "ANTISYM.spad" 43219 43235 44760 44775) (-49 "ANON.spad" 42916 42923 43209 43214) (-48 "AN.spad" 41217 41224 42732 42825) (-47 "AMR.spad" 39396 39407 41115 41212) (-46 "AMR.spad" 37412 37425 39133 39138) (-45 "ALIST.spad" 34824 34845 35174 35201) (-44 "ALGSC.spad" 33947 33973 34696 34749) (-43 "ALGPKG.spad" 29656 29667 33903 33908) (-42 "ALGMFACT.spad" 28845 28859 29646 29651) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 "ALGFACT.spad" 23701 23711 24570 24575) (-38 "ALGEBRA.spad" 23534 23543 23657 23696) (-37 "ALGEBRA.spad" 23399 23410 23524 23529) (-36 "ALAGG.spad" 22909 22930 23367 23394) (-35 "AHYP.spad" 22290 22297 22899 22904) (-34 "AGG.spad" 20599 20606 22280 22285) (-33 "AGG.spad" 18872 18881 20555 20560) (-32 "AF.spad" 17297 17312 18807 18812) (-31 "ADDAST.spad" 16975 16982 17287 17292) (-30 "ACPLOT.spad" 15546 15553 16965 16970) (-29 "ACFS.spad" 13297 13306 15448 15541) (-28 "ACFS.spad" 11134 11145 13287 13292) (-27 "ACF.spad" 7736 7743 11036 11129) (-26 "ACF.spad" 4424 4433 7726 7731) (-25 "ABELSG.spad" 3965 3972 4414 4419) (-24 "ABELSG.spad" 3504 3513 3955 3960) (-23 "ABELMON.spad" 3047 3054 3494 3499) (-22 "ABELMON.spad" 2588 2597 3037 3042) (-21 "ABELGRP.spad" 2160 2167 2578 2583) (-20 "ABELGRP.spad" 1730 1739 2150 2155) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2283220 2283225 2283230 2283235) (-2 NIL 2283200 2283205 2283210 2283215) (-1 NIL 2283180 2283185 2283190 2283195) (0 NIL 2283160 2283165 2283170 2283175) (-1287 "ZMOD.spad" 2282969 2282982 2283098 2283155) (-1286 "ZLINDEP.spad" 2282013 2282024 2282959 2282964) (-1285 "ZDSOLVE.spad" 2271862 2271884 2282003 2282008) (-1284 "YSTREAM.spad" 2271355 2271366 2271852 2271857) (-1283 "XRPOLY.spad" 2270575 2270595 2271211 2271280) (-1282 "XPR.spad" 2268366 2268379 2270293 2270392) (-1281 "XPOLY.spad" 2267921 2267932 2268222 2268291) (-1280 "XPOLYC.spad" 2267238 2267254 2267847 2267916) (-1279 "XPBWPOLY.spad" 2265675 2265695 2267018 2267087) (-1278 "XF.spad" 2264136 2264151 2265577 2265670) (-1277 "XF.spad" 2262577 2262594 2264020 2264025) (-1276 "XFALG.spad" 2259601 2259617 2262503 2262572) (-1275 "XEXPPKG.spad" 2258852 2258878 2259591 2259596) (-1274 "XDPOLY.spad" 2258466 2258482 2258708 2258777) (-1273 "XALG.spad" 2258126 2258137 2258422 2258461) (-1272 "WUTSET.spad" 2253965 2253982 2257772 2257799) (-1271 "WP.spad" 2253164 2253208 2253823 2253890) (-1270 "WHILEAST.spad" 2252962 2252971 2253154 2253159) (-1269 "WHEREAST.spad" 2252633 2252642 2252952 2252957) (-1268 "WFFINTBS.spad" 2250196 2250218 2252623 2252628) (-1267 "WEIER.spad" 2248410 2248421 2250186 2250191) (-1266 "VSPACE.spad" 2248083 2248094 2248378 2248405) (-1265 "VSPACE.spad" 2247776 2247789 2248073 2248078) (-1264 "VOID.spad" 2247453 2247462 2247766 2247771) (-1263 "VIEW.spad" 2245075 2245084 2247443 2247448) (-1262 "VIEWDEF.spad" 2240272 2240281 2245065 2245070) (-1261 "VIEW3D.spad" 2224107 2224116 2240262 2240267) (-1260 "VIEW2D.spad" 2211844 2211853 2224097 2224102) (-1259 "VECTOR.spad" 2210519 2210530 2210770 2210797) (-1258 "VECTOR2.spad" 2209146 2209159 2210509 2210514) (-1257 "VECTCAT.spad" 2207046 2207057 2209114 2209141) (-1256 "VECTCAT.spad" 2204754 2204767 2206824 2206829) (-1255 "VARIABLE.spad" 2204534 2204549 2204744 2204749) (-1254 "UTYPE.spad" 2204178 2204187 2204524 2204529) (-1253 "UTSODETL.spad" 2203471 2203495 2204134 2204139) (-1252 "UTSODE.spad" 2201659 2201679 2203461 2203466) (-1251 "UTS.spad" 2196448 2196476 2200126 2200223) (-1250 "UTSCAT.spad" 2193899 2193915 2196346 2196443) (-1249 "UTSCAT.spad" 2190994 2191012 2193443 2193448) (-1248 "UTS2.spad" 2190587 2190622 2190984 2190989) (-1247 "URAGG.spad" 2185219 2185230 2190577 2190582) (-1246 "URAGG.spad" 2179815 2179828 2185175 2185180) (-1245 "UPXSSING.spad" 2177458 2177484 2178896 2179029) (-1244 "UPXS.spad" 2174606 2174634 2175590 2175739) (-1243 "UPXSCONS.spad" 2172363 2172383 2172738 2172887) (-1242 "UPXSCCA.spad" 2170928 2170948 2172209 2172358) (-1241 "UPXSCCA.spad" 2169635 2169657 2170918 2170923) (-1240 "UPXSCAT.spad" 2168216 2168232 2169481 2169630) (-1239 "UPXS2.spad" 2167757 2167810 2168206 2168211) (-1238 "UPSQFREE.spad" 2166169 2166183 2167747 2167752) (-1237 "UPSCAT.spad" 2163762 2163786 2166067 2166164) (-1236 "UPSCAT.spad" 2161061 2161087 2163368 2163373) (-1235 "UPOLYC.spad" 2156039 2156050 2160903 2161056) (-1234 "UPOLYC.spad" 2150909 2150922 2155775 2155780) (-1233 "UPOLYC2.spad" 2150378 2150397 2150899 2150904) (-1232 "UP.spad" 2147535 2147550 2147928 2148081) (-1231 "UPMP.spad" 2146425 2146438 2147525 2147530) (-1230 "UPDIVP.spad" 2145988 2146002 2146415 2146420) (-1229 "UPDECOMP.spad" 2144225 2144239 2145978 2145983) (-1228 "UPCDEN.spad" 2143432 2143448 2144215 2144220) (-1227 "UP2.spad" 2142794 2142815 2143422 2143427) (-1226 "UNISEG.spad" 2142147 2142158 2142713 2142718) (-1225 "UNISEG2.spad" 2141640 2141653 2142103 2142108) (-1224 "UNIFACT.spad" 2140741 2140753 2141630 2141635) (-1223 "ULS.spad" 2131293 2131321 2132386 2132815) (-1222 "ULSCONS.spad" 2123687 2123707 2124059 2124208) (-1221 "ULSCCAT.spad" 2121416 2121436 2123533 2123682) (-1220 "ULSCCAT.spad" 2119253 2119275 2121372 2121377) (-1219 "ULSCAT.spad" 2117469 2117485 2119099 2119248) (-1218 "ULS2.spad" 2116981 2117034 2117459 2117464) (-1217 "UINT8.spad" 2116858 2116867 2116971 2116976) (-1216 "UINT64.spad" 2116734 2116743 2116848 2116853) (-1215 "UINT32.spad" 2116610 2116619 2116724 2116729) (-1214 "UINT16.spad" 2116486 2116495 2116600 2116605) (-1213 "UFD.spad" 2115551 2115560 2116412 2116481) (-1212 "UFD.spad" 2114678 2114689 2115541 2115546) (-1211 "UDVO.spad" 2113525 2113534 2114668 2114673) (-1210 "UDPO.spad" 2110952 2110963 2113481 2113486) (-1209 "TYPE.spad" 2110884 2110893 2110942 2110947) (-1208 "TYPEAST.spad" 2110803 2110812 2110874 2110879) (-1207 "TWOFACT.spad" 2109453 2109468 2110793 2110798) (-1206 "TUPLE.spad" 2108937 2108948 2109352 2109357) (-1205 "TUBETOOL.spad" 2105774 2105783 2108927 2108932) (-1204 "TUBE.spad" 2104415 2104432 2105764 2105769) (-1203 "TS.spad" 2103004 2103020 2103980 2104077) (-1202 "TSETCAT.spad" 2090131 2090148 2102972 2102999) (-1201 "TSETCAT.spad" 2077244 2077263 2090087 2090092) (-1200 "TRMANIP.spad" 2071610 2071627 2076950 2076955) (-1199 "TRIMAT.spad" 2070569 2070594 2071600 2071605) (-1198 "TRIGMNIP.spad" 2069086 2069103 2070559 2070564) (-1197 "TRIGCAT.spad" 2068598 2068607 2069076 2069081) (-1196 "TRIGCAT.spad" 2068108 2068119 2068588 2068593) (-1195 "TREE.spad" 2066679 2066690 2067715 2067742) (-1194 "TRANFUN.spad" 2066510 2066519 2066669 2066674) (-1193 "TRANFUN.spad" 2066339 2066350 2066500 2066505) (-1192 "TOPSP.spad" 2066013 2066022 2066329 2066334) (-1191 "TOOLSIGN.spad" 2065676 2065687 2066003 2066008) (-1190 "TEXTFILE.spad" 2064233 2064242 2065666 2065671) (-1189 "TEX.spad" 2061365 2061374 2064223 2064228) (-1188 "TEX1.spad" 2060921 2060932 2061355 2061360) (-1187 "TEMUTL.spad" 2060476 2060485 2060911 2060916) (-1186 "TBCMPPK.spad" 2058569 2058592 2060466 2060471) (-1185 "TBAGG.spad" 2057605 2057628 2058549 2058564) (-1184 "TBAGG.spad" 2056649 2056674 2057595 2057600) (-1183 "TANEXP.spad" 2056025 2056036 2056639 2056644) (-1182 "TABLE.spad" 2054436 2054459 2054706 2054733) (-1181 "TABLEAU.spad" 2053917 2053928 2054426 2054431) (-1180 "TABLBUMP.spad" 2050700 2050711 2053907 2053912) (-1179 "SYSTEM.spad" 2049928 2049937 2050690 2050695) (-1178 "SYSSOLP.spad" 2047401 2047412 2049918 2049923) (-1177 "SYSNNI.spad" 2046581 2046592 2047391 2047396) (-1176 "SYSINT.spad" 2045985 2045996 2046571 2046576) (-1175 "SYNTAX.spad" 2042183 2042192 2045975 2045980) (-1174 "SYMTAB.spad" 2040239 2040248 2042173 2042178) (-1173 "SYMS.spad" 2036224 2036233 2040229 2040234) (-1172 "SYMPOLY.spad" 2035231 2035242 2035313 2035440) (-1171 "SYMFUNC.spad" 2034706 2034717 2035221 2035226) (-1170 "SYMBOL.spad" 2032133 2032142 2034696 2034701) (-1169 "SWITCH.spad" 2028890 2028899 2032123 2032128) (-1168 "SUTS.spad" 2025789 2025817 2027357 2027454) (-1167 "SUPXS.spad" 2022924 2022952 2023921 2024070) (-1166 "SUP.spad" 2019693 2019704 2020474 2020627) (-1165 "SUPFRACF.spad" 2018798 2018816 2019683 2019688) (-1164 "SUP2.spad" 2018188 2018201 2018788 2018793) (-1163 "SUMRF.spad" 2017154 2017165 2018178 2018183) (-1162 "SUMFS.spad" 2016787 2016804 2017144 2017149) (-1161 "SULS.spad" 2007326 2007354 2008432 2008861) (-1160 "SUCHTAST.spad" 2007095 2007104 2007316 2007321) (-1159 "SUCH.spad" 2006775 2006790 2007085 2007090) (-1158 "SUBSPACE.spad" 1998782 1998797 2006765 2006770) (-1157 "SUBRESP.spad" 1997942 1997956 1998738 1998743) (-1156 "STTF.spad" 1994041 1994057 1997932 1997937) (-1155 "STTFNC.spad" 1990509 1990525 1994031 1994036) (-1154 "STTAYLOR.spad" 1982907 1982918 1990390 1990395) (-1153 "STRTBL.spad" 1981412 1981429 1981561 1981588) (-1152 "STRING.spad" 1980821 1980830 1980835 1980862) (-1151 "STRICAT.spad" 1980609 1980618 1980789 1980816) (-1150 "STREAM.spad" 1977467 1977478 1980134 1980149) (-1149 "STREAM3.spad" 1977012 1977027 1977457 1977462) (-1148 "STREAM2.spad" 1976080 1976093 1977002 1977007) (-1147 "STREAM1.spad" 1975784 1975795 1976070 1976075) (-1146 "STINPROD.spad" 1974690 1974706 1975774 1975779) (-1145 "STEP.spad" 1973891 1973900 1974680 1974685) (-1144 "STBL.spad" 1972417 1972445 1972584 1972599) (-1143 "STAGG.spad" 1971492 1971503 1972407 1972412) (-1142 "STAGG.spad" 1970565 1970578 1971482 1971487) (-1141 "STACK.spad" 1969916 1969927 1970172 1970199) (-1140 "SREGSET.spad" 1967620 1967637 1969562 1969589) (-1139 "SRDCMPK.spad" 1966165 1966185 1967610 1967615) (-1138 "SRAGG.spad" 1961262 1961271 1966133 1966160) (-1137 "SRAGG.spad" 1956379 1956390 1961252 1961257) (-1136 "SQMATRIX.spad" 1953995 1954013 1954911 1954998) (-1135 "SPLTREE.spad" 1948547 1948560 1953431 1953458) (-1134 "SPLNODE.spad" 1945135 1945148 1948537 1948542) (-1133 "SPFCAT.spad" 1943912 1943921 1945125 1945130) (-1132 "SPECOUT.spad" 1942462 1942471 1943902 1943907) (-1131 "SPADXPT.spad" 1934601 1934610 1942452 1942457) (-1130 "spad-parser.spad" 1934066 1934075 1934591 1934596) (-1129 "SPADAST.spad" 1933767 1933776 1934056 1934061) (-1128 "SPACEC.spad" 1917780 1917791 1933757 1933762) (-1127 "SPACE3.spad" 1917556 1917567 1917770 1917775) (-1126 "SORTPAK.spad" 1917101 1917114 1917512 1917517) (-1125 "SOLVETRA.spad" 1914858 1914869 1917091 1917096) (-1124 "SOLVESER.spad" 1913378 1913389 1914848 1914853) (-1123 "SOLVERAD.spad" 1909388 1909399 1913368 1913373) (-1122 "SOLVEFOR.spad" 1907808 1907826 1909378 1909383) (-1121 "SNTSCAT.spad" 1907408 1907425 1907776 1907803) (-1120 "SMTS.spad" 1905668 1905694 1906973 1907070) (-1119 "SMP.spad" 1903107 1903127 1903497 1903624) (-1118 "SMITH.spad" 1901950 1901975 1903097 1903102) (-1117 "SMATCAT.spad" 1900060 1900090 1901894 1901945) (-1116 "SMATCAT.spad" 1898102 1898134 1899938 1899943) (-1115 "SKAGG.spad" 1897063 1897074 1898070 1898097) (-1114 "SINT.spad" 1895889 1895898 1896929 1897058) (-1113 "SIMPAN.spad" 1895617 1895626 1895879 1895884) (-1112 "SIG.spad" 1894945 1894954 1895607 1895612) (-1111 "SIGNRF.spad" 1894053 1894064 1894935 1894940) (-1110 "SIGNEF.spad" 1893322 1893339 1894043 1894048) (-1109 "SIGAST.spad" 1892703 1892712 1893312 1893317) (-1108 "SHP.spad" 1890621 1890636 1892659 1892664) (-1107 "SHDP.spad" 1880332 1880359 1880841 1880972) (-1106 "SGROUP.spad" 1879940 1879949 1880322 1880327) (-1105 "SGROUP.spad" 1879546 1879557 1879930 1879935) (-1104 "SGCF.spad" 1872427 1872436 1879536 1879541) (-1103 "SFRTCAT.spad" 1871355 1871372 1872395 1872422) (-1102 "SFRGCD.spad" 1870418 1870438 1871345 1871350) (-1101 "SFQCMPK.spad" 1865055 1865075 1870408 1870413) (-1100 "SFORT.spad" 1864490 1864504 1865045 1865050) (-1099 "SEXOF.spad" 1864333 1864373 1864480 1864485) (-1098 "SEX.spad" 1864225 1864234 1864323 1864328) (-1097 "SEXCAT.spad" 1861776 1861816 1864215 1864220) (-1096 "SET.spad" 1860076 1860087 1861197 1861236) (-1095 "SETMN.spad" 1858510 1858527 1860066 1860071) (-1094 "SETCAT.spad" 1857995 1858004 1858500 1858505) (-1093 "SETCAT.spad" 1857478 1857489 1857985 1857990) (-1092 "SETAGG.spad" 1853999 1854010 1857458 1857473) (-1091 "SETAGG.spad" 1850528 1850541 1853989 1853994) (-1090 "SEQAST.spad" 1850231 1850240 1850518 1850523) (-1089 "SEGXCAT.spad" 1849353 1849366 1850221 1850226) (-1088 "SEG.spad" 1849166 1849177 1849272 1849277) (-1087 "SEGCAT.spad" 1848073 1848084 1849156 1849161) (-1086 "SEGBIND.spad" 1847145 1847156 1848028 1848033) (-1085 "SEGBIND2.spad" 1846841 1846854 1847135 1847140) (-1084 "SEGAST.spad" 1846555 1846564 1846831 1846836) (-1083 "SEG2.spad" 1845980 1845993 1846511 1846516) (-1082 "SDVAR.spad" 1845256 1845267 1845970 1845975) (-1081 "SDPOL.spad" 1842646 1842657 1842937 1843064) (-1080 "SCPKG.spad" 1840725 1840736 1842636 1842641) (-1079 "SCOPE.spad" 1839878 1839887 1840715 1840720) (-1078 "SCACHE.spad" 1838560 1838571 1839868 1839873) (-1077 "SASTCAT.spad" 1838469 1838478 1838550 1838555) (-1076 "SAOS.spad" 1838341 1838350 1838459 1838464) (-1075 "SAERFFC.spad" 1838054 1838074 1838331 1838336) (-1074 "SAE.spad" 1836229 1836245 1836840 1836975) (-1073 "SAEFACT.spad" 1835930 1835950 1836219 1836224) (-1072 "RURPK.spad" 1833571 1833587 1835920 1835925) (-1071 "RULESET.spad" 1833012 1833036 1833561 1833566) (-1070 "RULE.spad" 1831216 1831240 1833002 1833007) (-1069 "RULECOLD.spad" 1831068 1831081 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T)) (((|#1| (-968)) . T)) (((#0=(-867 |#1|) $) |has| #0# (-286 #0# #0#))) @@ -313,7 +313,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1145)) -((((-2 (|:| -1327 (-1152)) (|:| -2423 |#1|))) . T)) +((((-2 (|:| -1354 (-1152)) (|:| -2577 |#1|))) . T)) (|has| (-1245 |#1| |#2| |#3| |#4|) (-145)) (|has| (-1245 |#1| |#2| |#3| |#4|) (-147)) (|has| |#1| (-145)) @@ -325,27 +325,27 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) -((((-1119 |#1| (-1170))) . T) (((-564)) . T) (((-815 (-1170))) . T) (($) -4030 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) . T) (((-407 (-564))) -4030 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1035 (-407 (-564))))) (((-1170)) . T)) +((((-1119 |#1| (-1170))) . T) (((-564)) . T) (((-815 (-1170))) . T) (($) -4007 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) . T) (((-407 (-564))) -4007 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1035 (-407 (-564))))) (((-1170)) . 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T)) (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) @@ -474,10 +474,10 @@ ((((-564) |#4|) . T)) ((((-564) |#3|) . T)) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) -(-4030 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4007 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) ((((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-407 (-564))) . T) (((-564)) . T)) -((((-859)) -4030 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4007 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -488,7 +488,7 @@ ((((-564)) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T)) (((|#1| |#1|) . T) (($ $) . T) ((#0=(-407 (-564)) #0#) . 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T)) @@ -802,7 +802,7 @@ ((((-641 |#1|)) . T)) ((((-859)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -(-4030 (|has| |#1| (-847)) (|has| |#1| (-1094))) +(-4007 (|has| |#1| (-847)) (|has| |#1| (-1094))) (((|#2|) |has| |#2| (-309 |#2|))) (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -812,7 +812,7 @@ (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T)) (|has| |#2| (-368)) -(-4030 (|has| |#1| (-847)) (|has| |#1| (-1094))) +(-4007 (|has| |#1| (-847)) (|has| |#1| (-1094))) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) @@ -826,8 +826,8 @@ ((((-859)) . T)) ((((-859)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-859)) -4030 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) -((($) . T) (((-407 (-564))) -4030 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . 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T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-112)) . T)) @@ -851,26 +851,26 @@ ((((-859)) . T)) ((((-1175)) . T)) (|has| |#1| (-817)) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4007 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (|has| |#1| (-847)) -(-4030 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-4007 (|has| |#1| (-172)) (|has| |#1| (-556))) (|has| |#1| (-556)) ((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) ((|#1|) . T) (((-564)) . T)) (|has| |#1| (-906)) (((|#1|) . T)) (|has| |#1| (-1094)) ((((-859)) . 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T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#) ((|#2|) . T) (((-564)) . T)) (((|#1| |#2| |#3|) . T)) -(-4030 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) +(-4007 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) (|has| $ (-147)) (|has| $ (-147)) ((((-1175)) . T)) @@ -944,14 +944,14 @@ ((((-859)) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-4030 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1046)) (|has| |#1| (-1106))) +(-4007 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1046)) (|has| |#1| (-1106))) ((($ $) |has| |#1| (-286 $ $)) ((|#1| $) |has| |#1| (-286 |#1| |#1|))) (((|#1| (-407 (-564))) . T)) (((|#1|) . T)) ((((-1170)) . T)) (|has| |#1| (-556)) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4007 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4007 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) @@ -962,7 +962,7 @@ (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#4| (-845)) -(((|#2| (-240 (-2641 |#1|) (-768)) (-861 |#1|)) . T)) +(((|#2| (-240 (-2780 |#1|) (-768)) (-861 |#1|)) . T)) (|has| |#3| (-845)) (((|#1| (-531 |#3|) |#3|) . T)) (|has| |#1| (-147)) @@ -977,20 +977,20 @@ (|has| |#1| (-145)) ((((-407 (-564))) |has| |#2| (-363)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-4030 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) -(-4030 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-4007 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4007 (|has| |#1| (-349)) (|has| |#1| (-368))) ((((-1136 |#2| |#1|)) . T) ((|#1|) . 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T)) (((|#1|) |has| |#1| (-309 |#1|))) @@ -1129,11 +1129,11 @@ (|has| |#1| (-368)) ((((-1170) $) |has| |#1| (-514 (-1170) $)) (($ $) |has| |#1| (-309 $)) ((|#1| |#1|) |has| |#1| (-309 |#1|)) (((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|))) ((((-1170)) |has| |#1| (-897 (-1170)))) -(-4030 (-12 (|has| |#1| (-233)) (|has| |#1| (-363))) (|has| |#1| (-349))) +(-4007 (-12 (|has| |#1| (-233)) (|has| |#1| (-363))) (|has| |#1| (-349))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-388) |#1|) . T)) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4007 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-1094)) (((|#2|) . T) (((-859)) . T)) ((((-859)) . T)) @@ -1141,8 +1141,8 @@ ((((-907 |#1|)) . T)) ((((-859)) . T) (((-1175)) . T)) ((((-1175)) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -4030 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -4030 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -4007 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) +((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -4007 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1151,16 +1151,16 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) (((|#1| |#1|) . T)) (((#0=(-867 |#1|)) |has| #0# (-309 #0#))) -((((-564)) . 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T)) (|has| |#1| (-1194)) (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((((-407 (-564))) . T) (($) . T)) @@ -1171,8 +1171,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-407 (-564)) #0#) . T)) (|has| |#1| (-363)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) -((($ $) . T) ((#0=(-407 (-564)) #0#) -4030 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) -((((-859)) -4030 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((($ $) . T) ((#0=(-407 (-564)) #0#) -4007 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) +((((-859)) -4007 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) ((((-859)) . T)) ((((-859)) . T)) @@ -1187,14 +1187,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-845)) (|has| |#1| (-845)) -((($) . T) (((-407 (-564))) -4030 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) -(-4030 (|has| |#1| (-172)) (|has| |#1| (-556))) +((($) . 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T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-859)) -4030 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) -(((|#2|) -4030 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1046))) (($) |has| |#2| (-172))) +((((-859)) -4007 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +(((|#2|) -4007 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1046))) (($) |has| |#2| (-172))) (|has| $ (-147)) ((((-407 |#2|)) . T)) ((((-890 |#1|)) . T) ((|#2|) . T) (((-564)) . T) (((-816 |#1|)) . T)) @@ -1335,11 +1335,11 @@ (((|#3|) |has| |#3| (-172))) (|has| |#1| (-147)) (|has| |#1| (-145)) -(-4030 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4007 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-4030 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4007 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-4030 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4007 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) (((|#1|) . T)) (|has| |#2| (-233)) @@ -1376,7 +1376,7 @@ ((((-996 |#1|)) . T) ((|#1|) . T)) ((((-859)) . T)) ((((-859)) . T)) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) ((((-407 (-564))) . T) (((-407 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1166 |#1|)) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1384,9 +1384,9 @@ (|has| |#1| (-847)) (((|#2|) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) -((((-2 (|:| -1327 (-1152)) (|:| -2423 |#1|))) . T)) +((((-2 (|:| -1354 (-1152)) (|:| -2577 |#1|))) . T)) ((((-564) |#2|) . T)) -((((-859)) -4030 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4007 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (((|#2|) . T)) ((((-564) |#3|) . T)) (((|#2|) . T)) @@ -1399,7 +1399,7 @@ (|has| |#1| (-1094)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) #0#) |has| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (-309 (-2 (|:| -1327 |#1|) (|:| -2423 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) #0#) |has| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (-309 (-2 (|:| -1354 |#1|) (|:| -2577 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-38 (-407 (-564)))) (((|#2|) . T)) @@ -1434,19 +1434,19 @@ (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1| |#2|) . T)) ((((-564) (-144)) . T)) -(((#0=(-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) #0#) |has| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (-309 (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) -((($) -4030 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +(((#0=(-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) #0#) |has| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (-309 (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) +((($) -4007 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (|has| |#1| (-847)) (((|#2| (-768) (-1076)) . T)) (((|#1| |#2|) . T)) -(-4030 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-4007 (|has| |#1| (-172)) (|has| |#1| (-556))) (|has| |#1| (-788)) (((|#1|) |has| |#1| (-172))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-4030 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) -(-4030 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) +(-4007 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) +(-4007 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) (((|#4|) . T)) (|has| |#1| (-145)) ((((-1152) |#1|) . T)) @@ -1460,10 +1460,10 @@ (((|#3|) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-859)) . T)) -(-4030 (|has| |#1| (-847)) (|has| |#1| (-1094))) +(-4007 (|has| |#1| (-847)) (|has| |#1| (-1094))) (((|#1|) . T)) -((((-859)) -4030 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) -((((-859)) -4030 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094))) (((-955 |#1|)) . T)) +((((-859)) -4007 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4007 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094))) (((-955 |#1|)) . T)) (|has| |#1| (-845)) (|has| |#1| (-845)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -1477,8 +1477,8 @@ ((($) . T)) ((((-388) (-1152)) . T)) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-859)) -4030 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-859))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -1327 (-1152)) (|:| -2423 #0#))) . T)) +((((-859)) -4007 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-859))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -1354 (-1152)) (|:| -2577 #0#))) . T)) (((|#1|) . T)) ((((-859)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) @@ -1486,7 +1486,7 @@ (|has| |#2| (-145)) (|has| |#2| (-147)) (|has| |#1| (-473)) -(-4030 (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) +(-4007 (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) (|has| |#1| (-363)) ((((-859)) . T)) (|has| |#1| (-38 (-407 (-564)))) @@ -1497,8 +1497,8 @@ (|has| |#1| (-845)) ((((-859)) . T)) (((|#2|) . T)) -((((-407 (-564))) -4030 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4030 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) -(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -4030 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4030 (|has| |#1| (-363)) (|has| |#1| (-556)))) +((((-407 (-564))) -4007 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4007 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) +(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -4007 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4007 (|has| |#1| (-363)) (|has| |#1| (-556)))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#2|) . T) (((-564)) . T) (((-816 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1507,7 +1507,7 @@ ((((-859)) . T)) ((((-859)) . T)) (|has| |#1| (-1094)) -(((|#2| (-482 (-2641 |#1|) (-768)) (-861 |#1|)) . T)) +(((|#2| (-482 (-2780 |#1|) (-768)) (-861 |#1|)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1| (-531 (-1170)) (-1170)) . T)) (((|#1|) . T)) @@ -1527,16 +1527,16 @@ (|has| |#1| (-147)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -1327 (-1152)) (|:| -2423 |#1|))) . T)) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) -((((-2 (|:| -1327 (-1170)) (|:| -2423 (-52)))) . T)) +(((|#1|) . T) (((-2 (|:| -1354 (-1152)) (|:| -2577 |#1|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -1354 (-1170)) (|:| -2577 (-52)))) . T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) ((((-1170) (-52)) . T)) ((($ $) . T)) (((|#1| (-564)) . T)) ((((-907 |#1|)) . T)) -(((|#1|) -4030 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1046))) (($) -4030 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)))) +(((|#1|) -4007 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1046))) (($) -4007 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)))) (((|#1|) . T) (((-564)) |has| |#1| (-1035 (-564))) (((-407 (-564))) |has| |#1| (-1035 (-407 (-564))))) (|has| |#1| (-847)) (|has| |#1| (-847)) @@ -1555,11 +1555,11 @@ (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) (|has| |#2| (-847)) (|has| |#1| (-847)) -(((|#3|) -4030 (|has| |#3| (-172)) (|has| |#3| (-363)))) -(-4030 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-906))) +(((|#3|) -4007 (|has| |#3| (-172)) (|has| |#3| (-363)))) +(-4007 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-906))) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) ((((-564) |#2|) . T)) -(((|#2|) -4030 (|has| |#2| (-172)) (|has| |#2| (-363)))) +(((|#2|) -4007 (|has| |#2| (-172)) (|has| |#2| (-363)))) (|has| |#1| (-349)) (((|#3| |#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1094)))) (((|#2|) . T) (((-564)) . T)) @@ -1568,7 +1568,7 @@ (|has| |#1| (-817)) (|has| |#1| (-817)) (((|#1|) . T)) -(-4030 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4007 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-845)) (|has| |#1| (-845)) (|has| |#1| (-845)) @@ -1577,13 +1577,13 @@ ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4007 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) ((((-1170)) |has| |#1| (-897 (-1170))) (((-1076)) . T)) (((|#1|) . T)) (|has| |#1| (-845)) -(((#0=(-2 (|:| -1327 (-1152)) (|:| -2423 (-52))) #0#) |has| (-2 (|:| -1327 (-1152)) (|:| -2423 (-52))) (-309 (-2 (|:| -1327 (-1152)) (|:| -2423 (-52)))))) +(((#0=(-2 (|:| -1354 (-1152)) (|:| -2577 (-52))) #0#) |has| (-2 (|:| -1354 (-1152)) (|:| -2577 (-52))) (-309 (-2 (|:| -1354 (-1152)) (|:| -2577 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#1| (-1094)) ((((-859)) . T) (((-1175)) . T)) @@ -1602,11 +1602,11 @@ (((|#1| (-768) (-1076)) . T)) (((|#3|) . T)) ((((-144)) . T)) -((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) -4030 (|has| |#1| (-845)) (|has| |#1| (-1035 (-564)))) ((|#1|) . T)) +((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) -4007 (|has| |#1| (-845)) (|has| |#1| (-1035 (-564)))) ((|#1|) . T)) (((|#1|) . T)) ((((-144)) . T)) (((|#2|) |has| |#2| (-172))) -(-4030 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) +(-4007 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (((|#1|) . T)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -1629,32 +1629,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1|) . T)) (((|#1| |#2|) . 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T)) ((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) |has| |#1| (-556))) -((((-407 (-564))) -4030 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4030 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1168 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) -(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -4030 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4030 (|has| |#1| (-363)) (|has| |#1| (-556)))) +((((-407 (-564))) -4007 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4007 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1168 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) +(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -4007 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4007 (|has| |#1| (-363)) (|has| |#1| (-556)))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-2 (|:| -1327 (-1170)) (|:| -2423 (-52)))) . T)) +((((-2 (|:| -1354 (-1170)) (|:| -2577 (-52)))) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) ((((-668 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1663,7 +1663,7 @@ ((((-859)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-859)) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -4030 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -4007 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) ((((-1175)) . T)) ((((-407 (-564))) . T) (($) . T) (((-407 |#1|)) . T) ((|#1|) . T) (((-564)) . T)) (((|#3|) . T) (((-564)) . T) (((-610 $)) . T)) @@ -1671,12 +1671,12 @@ ((((-859)) . T)) ((((-859)) . T)) (((|#2|) . T)) -(-4030 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-723)) (|has| |#3| (-790)) (|has| |#3| (-845)) (|has| |#3| (-1046)) (|has| |#3| (-1094))) -(-4030 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4007 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-723)) (|has| |#3| (-790)) (|has| |#3| (-845)) (|has| |#3| (-1046)) (|has| |#3| (-1094))) +(-4007 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) ((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) |has| |#1| (-1035 (-564))) ((|#1|) . T)) (|has| |#1| (-1194)) (|has| |#1| (-1194)) -(-4030 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) +(-4007 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (|has| |#1| (-1194)) (|has| |#1| (-1194)) (((|#3| |#3|) . T)) @@ -1689,16 +1689,16 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((((-1152) (-52)) . T)) (|has| |#1| (-1094)) -(-4030 (|has| |#2| (-817)) (|has| |#2| (-847))) +(-4007 (|has| |#2| (-817)) (|has| |#2| (-847))) (((|#1|) . T)) (((|#1|) |has| |#1| (-172)) (($) . T)) -((($) -4030 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -4030 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) -4007 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -4007 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((($) . T)) ((((-1168 |#1| |#2| |#3|)) -12 (|has| (-1168 |#1| |#2| |#3|) (-309 (-1168 |#1| |#2| |#3|))) (|has| |#1| (-363)))) ((((-859)) . T)) ((((-564)) . T) (($) . T)) ((((-768)) . T)) -(-4030 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4007 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-859)) . T)) ((($) . T) (((-564)) . T)) @@ -1706,30 +1706,30 @@ (|has| |#2| (-906)) (|has| |#1| (-363)) (((|#2|) |has| |#2| (-1094))) -(-4030 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) -(-4030 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4007 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4007 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4007 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((((-536)) . T) (((-407 (-1166 (-564)))) . T) (((-225)) . T) (((-379)) . T)) ((((-379)) . T) (((-225)) . T) (((-859)) . T)) (|has| |#1| (-906)) (|has| |#1| (-906)) (|has| |#1| (-906)) -(-4030 (|has| |#1| (-452)) (|has| |#1| (-906))) +(-4007 (|has| |#1| (-452)) (|has| |#1| (-906))) ((($) . T) ((|#2|) . T)) -(-4030 (|has| |#1| (-847)) (|has| |#1| (-1094))) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-906))) +(-4007 (|has| |#1| (-847)) (|has| |#1| (-1094))) +(-4007 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-906))) ((((-859)) . T)) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((($ $) . T)) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) ((($ $) . T)) ((((-564) (-112)) . T)) ((($) . T)) (((|#1|) . T)) ((((-564)) . T)) ((((-112)) . T)) -(-4030 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4007 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-38 (-407 (-564)))) (((|#1| (-564)) . T)) ((($) . T)) @@ -1751,7 +1751,7 @@ (((|#1| (-1223 |#1| |#2| |#3|)) . T)) (((|#1| (-768)) . T)) (((|#1|) . T)) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) ((((-859)) . T)) (|has| |#1| (-1094)) ((((-1152) |#1|) . T)) @@ -1771,18 +1771,18 @@ (((|#1|) . T)) ((((-564)) . T)) ((((-859)) . T)) -(-4030 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-4007 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-859)) . T)) (((|#3|) . T)) -(-4030 (|has| |#3| (-172)) (|has| |#3| (-845)) (|has| |#3| (-1046))) +(-4007 (|has| |#3| (-172)) (|has| |#3| (-845)) (|has| |#3| (-1046))) ((((-859)) . T)) ((((-1244 |#2| |#3| |#4|)) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-859)) . T)) -((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (((-610 $)) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1035 (-564))) (((-407 (-564))) -4030 (-12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (|has| |#1| (-1035 (-407 (-564))))) (((-407 (-949 |#1|))) |has| |#1| (-556)) (((-949 |#1|)) |has| |#1| (-1046)) (((-1170)) . T)) +((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (((-610 $)) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1035 (-564))) (((-407 (-564))) -4007 (-12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (|has| |#1| (-1035 (-407 (-564))))) (((-407 (-949 |#1|))) |has| |#1| (-556)) (((-949 |#1|)) |has| |#1| (-1046)) (((-1170)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-768)) . T)) -((($) -4030 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -4030 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -4007 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -4007 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (((|#1|) |has| |#1| (-309 |#1|))) ((((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-564)) |has| |#1| (-883 (-564))) (((-379)) |has| |#1| (-883 (-379)))) @@ -1790,7 +1790,7 @@ (|has| |#1| (-556)) (((|#1|) . T)) ((((-859)) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) |has| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (-309 (-2 (|:| -1327 |#1|) (|:| -2423 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) |has| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (-309 (-2 (|:| -1354 |#1|) (|:| -2577 |#2|))))) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -1798,7 +1798,7 @@ (((|#1|) . T)) (((|#3|) |has| |#3| (-1094))) ((((-907 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) -(((|#2|) -4030 (|has| |#2| (-172)) (|has| |#2| (-363)))) +(((|#2|) -4007 (|has| |#2| (-172)) (|has| |#2| (-363)))) ((((-1244 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-817)) @@ -1808,8 +1808,8 @@ (|has| |#1| (-845)) (|has| |#1| (-845)) (((|#1| (-564) (-1076)) . T)) -(-4030 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +(-4007 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) (((|#1| (-407 (-564)) (-1076)) . T)) (((|#1| (-768) (-1076)) . T)) (|has| |#1| (-847)) @@ -1822,33 +1822,33 @@ (|has| |#1| (-1094)) ((((-907 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-1094)) -((((-564)) -4030 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)))) +((((-564)) -4007 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)))) (((|#1|) . T)) (|has| |#1| (-1094)) ((((-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-637 (-564)))) ((|#2|) |has| |#1| (-363))) -(-4030 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) -((((-685 (-339 (-3753) (-3753 (QUOTE X) (QUOTE HESS)) (-695)))) . T)) +(-4007 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) +((((-685 (-339 (-3725) (-3725 (QUOTE X) (QUOTE HESS)) (-695)))) . T)) (((|#2|) |has| |#2| (-172))) (((|#1|) |has| |#1| (-172))) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) -((((-2 (|:| -1327 (-1152)) (|:| -2423 |#1|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -1354 (-1152)) (|:| -2577 |#1|))) . T)) ((((-859)) . T)) (|has| |#3| (-845)) ((((-859)) . T)) ((((-1244 |#2| |#3| |#4|) (-319 |#2| |#3| |#4|)) . T)) ((((-859)) . T)) -(((|#1| |#1|) -4030 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1046)))) +(((|#1| |#1|) -4007 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1046)))) (((|#1|) . T)) ((((-564)) . T)) ((((-564)) . T)) -(((|#1|) -4030 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1046)))) +(((|#1|) -4007 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1046)))) (((|#2|) |has| |#2| (-363))) ((($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-363))) (|has| |#1| (-847)) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -1327 (-1170)) (|:| -2423 (-52)))) |has| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (-309 (-2 (|:| -1327 (-1170)) (|:| -2423 (-52)))))) -(-4030 (|has| |#1| (-452)) (|has| |#1| (-906))) +((((-2 (|:| -1354 (-1170)) (|:| -2577 (-52)))) |has| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (-309 (-2 (|:| -1354 (-1170)) (|:| -2577 (-52)))))) +(-4007 (|has| |#1| (-452)) (|has| |#1| (-906))) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) ((((-859)) . T)) ((((-859)) . T)) @@ -1879,25 +1879,25 @@ (|has| |#1| (-145)) ((((-564)) . T) ((|#1|) . T) (($) . T) (((-407 (-564))) . T) (((-1170)) |has| |#1| (-1035 (-1170)))) (((|#1| |#2|) . T)) -((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) -4030 (|has| |#1| (-845)) (|has| |#1| (-1035 (-564)))) ((|#1|) . T)) +((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) -4007 (|has| |#1| (-845)) (|has| |#1| (-1035 (-564)))) ((|#1|) . T)) ((((-144)) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (((|#1|) . T)) -(-4030 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4007 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) (((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) . T) (($ $) . T)) (((|#2|) . T) ((|#1|) . T) (((-564)) . T)) ((((-859)) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-859)) -4030 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4007 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| (-407 |#2|) (-233)) ((((-641 |#1|)) . T)) (|has| |#1| (-906)) (((|#2|) |has| |#2| (-1046))) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) |has| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (-309 (-2 (|:| -1327 |#1|) (|:| -2423 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) |has| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (-309 (-2 (|:| -1354 |#1|) (|:| -2577 |#2|))))) (|has| |#1| (-363)) (((|#1|) |has| |#1| (-172))) (((|#1| |#1|) . T)) @@ -1924,7 +1924,7 @@ (((|#1| (-407 (-564)) (-1076)) . T)) (((|#1| (-768) (-1076)) . T)) (((#0=(-407 |#2|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-564)) -4030 (|has| (-407 (-564)) (-1035 (-564))) (|has| |#1| (-1035 (-564)))) (((-407 (-564))) . T)) +(((|#1|) . T) (((-564)) -4007 (|has| (-407 (-564)) (-1035 (-564))) (|has| |#1| (-1035 (-564)))) (((-407 (-564))) . T)) (((|#1| (-600 |#1| |#3|) (-600 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -1945,25 +1945,25 @@ (((|#2|) |has| |#2| (-172))) (|has| |#2| (-845)) ((((-564)) . T) ((|#2|) . T) (((-407 (-564))) |has| |#2| (-1035 (-407 (-564))))) -((((-112)) |has| |#1| (-1094)) (((-859)) -4030 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)) (|has| |#1| (-1106)) (|has| |#1| (-1094)))) +((((-112)) |has| |#1| (-1094)) (((-859)) -4007 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)) (|has| |#1| (-1106)) (|has| |#1| (-1094)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -1327 (-1152)) (|:| -2423 (-52)))) . T)) +((((-2 (|:| -1354 (-1152)) (|:| -2577 (-52)))) . T)) ((((-859)) . T)) ((((-564) |#1|) . T)) ((((-859)) . T)) ((((-695)) . T) (((-407 (-564))) . T) (((-564)) . T)) (((|#1| |#1|) |has| |#1| (-172))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) |has| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (-309 (-2 (|:| -1327 |#1|) (|:| -2423 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) |has| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (-309 (-2 (|:| -1354 |#1|) (|:| -2577 |#2|))))) ((((-379)) . T)) ((((-695)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1|) |has| |#1| (-172))) ((((-407 (-949 |#1|))) . T)) (((|#2| |#2|) . T)) -(-4030 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) -(-4030 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4007 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4007 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-847)) @@ -1974,14 +1974,14 @@ (((|#3|) |has| |#3| (-1046))) ((((-1170)) |has| |#2| (-897 (-1170)))) ((((-859)) . T)) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) ((((-407 (-564))) . T) (($) . T)) (|has| |#1| (-473)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-363)) -(-4030 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1046)) (|has| |#1| (-1106))) +(-4007 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1046)) (|has| |#1| (-1106))) (|has| |#1| (-38 (-407 (-564)))) ((((-116 |#1|)) . T)) ((((-116 |#1|)) . T)) @@ -2002,11 +2002,11 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-847)) -((((-2 (|:| -1327 (-1152)) (|:| -2423 |#1|))) . T)) +((((-2 (|:| -1354 (-1152)) (|:| -2577 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) |has| (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)) (-309 (-2 (|:| -1327 |#1|) (|:| -2423 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) |has| (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)) (-309 (-2 (|:| -1354 |#1|) (|:| -2577 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2024,11 +2024,11 @@ ((((-536)) |has| |#1| (-612 (-536))) (((-889 (-564))) |has| |#1| (-612 (-889 (-564)))) (((-889 (-379))) |has| |#1| (-612 (-889 (-379)))) (((-379)) . #0=(|has| |#1| (-1019))) (((-225)) . #0#)) (((|#1|) |has| |#1| (-363))) ((((-859)) . T)) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) ((($ $) . T) (((-610 $) $) . T)) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4007 (|has| |#1| (-363)) (|has| |#1| (-556))) ((($) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T) (((-407 (-564))) . T)) -((($) -4030 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-556))) +((($) -4007 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| |#1| (-363)) @@ -2039,11 +2039,11 @@ ((((-379)) . T)) (((|#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1094)))) ((((-859)) . T)) -(-4030 (|has| |#2| (-452)) (|has| |#2| (-906))) +(-4007 (|has| |#2| (-452)) (|has| |#2| (-906))) (((|#1|) . T)) (|has| |#1| (-847)) (|has| |#1| (-847)) -((((-859)) -4030 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4007 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) ((((-536)) |has| |#1| (-612 (-536)))) (((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((((-768)) . T)) @@ -2054,13 +2054,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((((-564)) . T)) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4007 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4007 (|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)) -(-4030 (-12 (|has| (-1251 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) -(-4030 (-12 (|has| (-1251 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) +(-4007 (-12 (|has| (-1251 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) +(-4007 (-12 (|has| (-1251 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) (|has| |#1| (-363)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -2075,23 +2075,23 @@ (((|#2|) . T)) (|has| |#1| (-1094)) (((|#1| |#2|) . T)) -((((-564)) . T) ((|#1|) . T) (((-407 (-564))) -4030 (|has| |#1| (-363)) (|has| |#1| (-1035 (-407 (-564)))))) +((((-564)) . T) ((|#1|) . T) (((-407 (-564))) -4007 (|has| |#1| (-363)) (|has| |#1| (-1035 (-407 (-564)))))) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) (((|#3|) |has| |#3| (-172))) -(-4030 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) +(-4007 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) ((((-859)) . T)) ((((-564)) . T)) (((|#1| $) |has| |#1| (-286 |#1| |#1|))) ((((-407 (-564))) . T) (($) . T) (((-407 |#1|)) . T) ((|#1|) . T)) ((((-949 |#1|)) . T) (((-859)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -4030 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-564)) #0#) |has| |#1| (-363))) -((((-2 (|:| -1327 (-1170)) (|:| -2423 (-52)))) . T)) +(((|#1| |#1|) . T) (($ $) -4007 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-564)) #0#) |has| |#1| (-363))) +((((-2 (|:| -1354 (-1170)) (|:| -2577 (-52)))) . T)) ((((-949 |#1|)) . T)) ((($) . T)) ((((-564) |#1|) . T)) ((((-1170)) |has| (-407 |#2|) (-897 (-1170)))) -(((|#1|) . T) (($) -4030 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-564))) |has| |#1| (-363))) +(((|#1|) . T) (($) -4007 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-564))) |has| |#1| (-363))) ((((-536)) |has| |#2| (-612 (-536)))) ((((-685 |#2|)) . T) (((-859)) . T)) (((|#1|) . T)) @@ -2099,8 +2099,8 @@ (((|#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) ((((-867 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-4030 (|has| |#4| (-790)) (|has| |#4| (-845))) -(-4030 (|has| |#3| (-790)) (|has| |#3| (-845))) +(-4007 (|has| |#4| (-790)) (|has| |#4| (-845))) +(-4007 (|has| |#3| (-790)) (|has| |#3| (-845))) ((((-859)) . T)) ((((-859)) . T)) (((|#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) @@ -2116,17 +2116,17 @@ ((((-407 (-564))) . T) (($) . T)) ((((-407 (-564))) . T) (($) . T)) ((((-407 (-564))) . T) (($) . T)) -(-4030 (|has| |#1| (-452)) (|has| |#1| (-1213))) +(-4007 (|has| |#1| (-452)) (|has| |#1| (-1213))) ((($) . T)) ((((-407 (-564))) |has| #0=(-407 |#2|) (-1035 (-407 (-564)))) (((-564)) |has| #0# (-1035 (-564))) ((#0#) . T)) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) (((|#1| (-768)) . T)) (|has| |#1| (-847)) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) -((($) -4030 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -4030 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) -4007 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -4007 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((((-564)) . T)) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -1327 (-1152)) (|:| -2423 (-52)))) |has| (-2 (|:| -1327 (-1152)) (|:| -2423 (-52))) (-309 (-2 (|:| -1327 (-1152)) (|:| -2423 (-52)))))) +((((-2 (|:| -1354 (-1152)) (|:| -2577 (-52)))) |has| (-2 (|:| -1354 (-1152)) (|:| -2577 (-52))) (-309 (-2 (|:| -1354 (-1152)) (|:| -2577 (-52)))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#1| (-845)) (|has| |#1| (-38 (-407 (-564)))) @@ -2148,31 +2148,31 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -((((-1152)) . T) (((-1170)) . T) (((-225)) . T) (((-564)) . T)) +((((-1152)) . T) (((-506)) . T) (((-225)) . T) (((-564)) . T)) ((((-859)) . T)) -(((|#2|) . T) (((-564)) . 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T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -((($) -4030 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -4007 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-536)) |has| |#4| (-612 (-536)))) ((((-859)) . T) (((-641 |#4|)) . T)) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-845)) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -1327 (-1152)) (|:| -2423 |#1|))) |has| (-2 (|:| -1327 (-1152)) (|:| -2423 |#1|)) (-309 (-2 (|:| -1327 (-1152)) (|:| -2423 |#1|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -1354 (-1152)) (|:| -2577 |#1|))) |has| (-2 (|:| -1354 (-1152)) (|:| -2577 |#1|)) (-309 (-2 (|:| -1354 (-1152)) (|:| -2577 |#1|))))) (|has| |#1| (-1094)) (|has| |#1| (-363)) (|has| |#1| (-847)) @@ -2181,16 +2181,16 @@ (((|#1|) . T)) ((((-668 |#1|)) . T)) ((($) . T) (((-407 (-564))) . T)) -((($) -4030 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -4030 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -4007 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -4007 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (|has| |#1| (-145)) (|has| |#1| (-147)) -(-4030 (-12 (|has| (-1168 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) -(-4030 (-12 (|has| (-1168 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) +(-4007 (-12 (|has| (-1168 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) +(-4007 (-12 (|has| (-1168 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-859)) -4030 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4007 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) (|has| |#1| (-845)) (((|#1| |#2|) . T)) @@ -2214,9 +2214,9 @@ ((((-859)) . T)) ((((-859)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -(((|#1|) -4030 (|has| |#1| (-172)) (|has| |#1| (-363)))) +(((|#1|) -4007 (|has| |#1| (-172)) (|has| |#1| (-363)))) ((((-316 |#1|)) . T)) (((|#2|) |has| |#2| (-363))) (((|#2|) . T)) @@ -2238,13 +2238,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((($ $) . T)) -(-4030 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)) (|has| |#1| (-1106)) (|has| |#1| (-1094))) +(-4007 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)) (|has| |#1| (-1106)) (|has| |#1| (-1094))) (|has| |#1| (-556)) (((|#2|) . T)) ((((-564)) . T)) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) (((|#1|) . T)) -(-4030 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) +(-4007 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) (((|#1| (-59 |#1|) (-59 |#1|)) . T)) ((((-581 |#1|)) . T)) ((($) . T)) @@ -2260,7 +2260,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-1244 |#2| |#3| |#4|)) . T) (((-564)) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-407 (-564))) . T)) -((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (((-564)) -4030 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1035 (-564))) (|has| |#1| (-1046))) ((|#1|) . T) (((-610 $)) . T) (($) |has| |#1| (-556)) (((-407 (-564))) -4030 (|has| |#1| (-556)) (|has| |#1| (-1035 (-407 (-564))))) (((-407 (-949 |#1|))) |has| |#1| (-556)) (((-949 |#1|)) |has| |#1| (-1046)) (((-1170)) . T)) +((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (((-564)) -4007 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1035 (-564))) (|has| |#1| (-1046))) ((|#1|) . T) (((-610 $)) . T) (($) |has| |#1| (-556)) (((-407 (-564))) -4007 (|has| |#1| (-556)) (|has| |#1| (-1035 (-407 (-564))))) (((-407 (-949 |#1|))) |has| |#1| (-556)) (((-949 |#1|)) |has| |#1| (-1046)) (((-1170)) . T)) ((((-407 (-564))) |has| |#2| (-1035 (-407 (-564)))) (((-564)) |has| |#2| (-1035 (-564))) ((|#2|) . T) (((-861 |#1|)) . T)) ((($) . T) (((-116 |#1|)) . T) (((-407 (-564))) . T)) ((((-1119 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1035 (-564))) (((-407 (-564))) |has| |#1| (-1035 (-407 (-564))))) @@ -2273,12 +2273,12 @@ (((|#1| |#2|) . T)) ((((-1170) |#1|) . T)) (((|#4|) . T)) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4007 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1170) (-52)) . T)) ((((-1244 |#2| |#3| |#4|) (-319 |#2| |#3| |#4|)) . T)) ((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) |has| |#1| (-1035 (-564))) ((|#1|) . T)) ((((-859)) . T)) -(-4030 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) +(-4007 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (((#0=(-1245 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-172)) ((#0=(-407 (-564)) #0#) |has| |#1| (-556)) (($ $) |has| |#1| (-556))) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) @@ -2298,14 +2298,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((|#2| |#3|) . T)) -(-4030 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4007 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) (((|#1| (-531 |#2|)) . T)) (((|#1| (-768)) . T)) (((|#1| (-531 (-1082 (-1170)))) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (|has| |#2| (-906)) -(-4030 (|has| |#2| (-790)) (|has| |#2| (-845))) +(-4007 (|has| |#2| (-790)) (|has| |#2| (-845))) ((((-859)) . T)) ((($ $) . T) ((#0=(-1244 |#2| |#3| |#4|) #0#) . T) ((#1=(-407 (-564)) #1#) |has| #0# (-38 (-407 (-564))))) ((((-907 |#1|)) . T)) @@ -2314,14 +2314,14 @@ ((((-859)) . T)) ((($) . T)) ((($) . T)) -(-4030 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) +(-4007 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-363)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1244 |#2| |#3| |#4|)) . T) (((-407 (-564))) |has| #0# (-38 (-407 (-564))))) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -(-4030 (-12 (|has| |#1| (-307)) (|has| |#1| (-906))) (|has| |#1| (-363)) (|has| |#1| (-349))) -(-4030 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) +(-4007 (-12 (|has| |#1| (-307)) (|has| |#1| (-906))) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4007 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) ((((-564)) |has| |#1| (-637 (-564))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-859)) . T)) @@ -2354,27 +2354,27 @@ (((|#1|) |has| |#1| (-172))) ((((-859)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) -(((|#2|) -4030 (|has| |#2| (-6 (-4413 "*"))) (|has| |#2| (-172)))) -(-4030 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) -(-4030 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(((|#2|) -4007 (|has| |#2| (-6 (-4413 "*"))) (|has| |#2| (-172)))) +(-4007 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4007 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (|has| |#2| (-847)) (|has| |#2| (-906)) (|has| |#1| (-906)) (((|#2|) |has| |#2| (-172))) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-859)) . T)) ((((-859)) . T)) ((((-536)) . T) (((-564)) . T) (((-889 (-564))) . T) (((-379)) . T) (((-225)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) -((((-2 (|:| -1327 (-1152)) (|:| -2423 (-52)))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -1354 (-1152)) (|:| -2577 (-52)))) . T)) (((|#1|) . T)) ((((-859)) . T)) (((|#1| |#2|) . T)) (((|#1| (-407 (-564))) . T)) (((|#1|) . T)) -(-4030 (|has| |#1| (-290)) (|has| |#1| (-363))) +(-4007 (|has| |#1| (-290)) (|has| |#1| (-363))) ((((-144)) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) (|has| |#1| (-845)) @@ -2390,7 +2390,7 @@ ((((-859)) . T)) ((((-859)) . T)) ((((-187)) . T) (((-859)) . T)) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-859)) . T)) ((((-859)) . T)) @@ -2403,7 +2403,7 @@ ((((-859)) . T)) ((((-1152)) . T)) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -((((-2 (|:| -1327 (-1152)) (|:| -2423 |#1|))) . T)) +((((-2 (|:| -1354 (-1152)) (|:| -2577 |#1|))) . T)) (|has| |#1| (-847)) ((((-859)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) @@ -2415,16 +2415,16 @@ (((|#2|) . T)) ((((-907 |#1|)) . T) (((-407 (-564))) . T) (($) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T) (((-610 $)) . T)) -(-4030 (|has| |#4| (-172)) (|has| |#4| (-723)) (|has| |#4| (-845)) (|has| |#4| (-1046))) -(-4030 (|has| |#3| (-172)) (|has| |#3| (-723)) (|has| |#3| (-845)) (|has| |#3| (-1046))) +(-4007 (|has| |#4| (-172)) (|has| |#4| (-723)) (|has| |#4| (-845)) (|has| |#4| (-1046))) +(-4007 (|has| |#3| (-172)) (|has| |#3| (-723)) (|has| |#3| (-845)) (|has| |#3| (-1046))) ((((-1170) (-52)) . T)) -(-4030 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4007 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4007 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-4030 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) -(-4030 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4007 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4007 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-845)) (|has| |#2| (-1046))) (|has| |#1| (-906)) ((((-907 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) (|has| |#1| (-906)) @@ -2441,12 +2441,12 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4007 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (|has| |#1| (-817)) (((#0=(-907 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-564)) #1#) . T)) ((((-407 |#2|)) . T)) (|has| |#1| (-845)) -((((-1195 |#1|)) . T) (((-859)) -4030 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-1195 |#1|)) . T) (((-859)) -4007 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) . T) ((#1=(-564) #1#) . T) (($ $) . T)) ((((-907 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) (((|#2|) |has| |#2| (-1046)) (((-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1046)))) @@ -2457,11 +2457,11 @@ (((|#2|) . T)) ((((-859)) . T)) ((((-407 (-564))) . T) (((-695)) . T) (($) . T) (((-564)) . T)) -(-4030 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-4030 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-4030 (|has| |#1| (-145)) (|has| |#1| (-368))) -((((-2 (|:| -1327 (-1170)) (|:| -2423 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -1327 (-1170)) (|:| -2423 #0#))) . T)) +(-4007 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4007 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4007 (|has| |#1| (-145)) (|has| |#1| (-368))) +((((-2 (|:| -1354 (-1170)) (|:| -2577 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -1354 (-1170)) (|:| -2577 #0#))) . T)) (|has| |#1| (-349)) ((((-564)) . T)) ((((-859)) . T)) @@ -2469,15 +2469,15 @@ (((#0=(-1245 |#1| |#2| |#3| |#4|) $) |has| #0# (-286 #0# #0#))) (|has| |#1| (-363)) (((#0=(-1076) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4007 (|has| |#1| (-363)) (|has| |#1| (-349))) (((#0=(-407 (-564)) #0#) . T) ((#1=(-695) #1#) . T) (($ $) . T)) ((((-316 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) |has| |#1| (-363))) ((((-859)) . T)) (|has| |#1| (-1094)) (((|#1|) . T)) -(((|#1|) -4030 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) -(((|#1|) -4030 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -4007 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -4007 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) (((|#2|) . T)) ((((-407 (-564))) . T) (((-695)) . T) (($) . T)) ((((-579)) . T)) @@ -2500,7 +2500,7 @@ (((|#1|) . T)) ((((-564)) . T)) (((|#2|) . T) (((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) ((|#1|) . T) (($) . T) (((-564)) . T)) -(-4030 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4007 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2538,7 +2538,7 @@ (|has| |#2| (-1019)) ((($) . T)) (|has| |#1| (-906)) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2546,9 +2546,9 @@ ((($) . T)) (|has| |#1| (-363)) ((((-907 |#1|)) . T)) -((($) -4030 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -4007 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) -(-4030 (|has| |#1| (-368)) (|has| |#1| (-847))) +(-4007 (|has| |#1| (-368)) (|has| |#1| (-847))) (((|#1|) . T)) ((((-768)) . T)) ((((-859)) . T)) @@ -2559,16 +2559,16 @@ ((((-564)) . T) (($) . T)) ((((-564)) . T) (($) . T)) ((((-768) |#1|) . T)) -(((|#2| (-240 (-2641 |#1|) (-768))) . T)) +(((|#2| (-240 (-2780 |#1|) (-768))) . T)) (((|#1| (-531 |#3|)) . T)) ((((-407 (-564))) . T)) -(-4030 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4007 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((((-1152)) . T) (((-859)) . T)) -(((#0=(-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) #0#) |has| (-2 (|:| -1327 (-1170)) (|:| -2423 (-52))) (-309 (-2 (|:| -1327 (-1170)) (|:| -2423 (-52)))))) +(((#0=(-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) #0#) |has| (-2 (|:| -1354 (-1170)) (|:| -2577 (-52))) (-309 (-2 (|:| -1354 (-1170)) (|:| -2577 (-52)))))) ((((-1152)) . T)) (|has| |#1| (-906)) (|has| |#2| (-363)) -(-4030 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4007 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-859)) . T)) (((|#1|) . T)) @@ -2585,11 +2585,11 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-4030 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4007 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) (-12 (|has| |#1| (-545)) (|has| |#1| (-825))) ((((-859)) . T)) -((((-1170)) -4030 (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-897 (-1170)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-897 (-1170)))))) +((((-1170)) -4007 (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-897 (-1170)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-897 (-1170)))))) (|has| |#1| (-363)) ((((-1170)) -12 (|has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) (|has| |#1| (-897 (-1170))))) (|has| |#1| (-363)) @@ -2600,7 +2600,7 @@ (((|#2|) |has| |#1| (-363))) (((|#2|) |has| |#1| (-363))) ((((-564)) . T) (($) . T)) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . 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T)) (|has| |#1| (-38 (-407 (-564)))) -(-4030 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4007 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) ((((-1152) |#1|) . T)) -(-4030 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4007 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-4030 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4007 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) ((((-581 |#1|)) . T)) ((($) . T)) @@ -2659,7 +2659,7 @@ (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-4030 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-4007 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-859)) . T)) ((($) . T)) @@ -2686,7 +2686,7 @@ ((((-859)) . T)) ((((-907 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-859)) -4030 (|has| |#1| (-611 (-859))) (|has| |#1| (-847)) (|has| |#1| (-1094)))) +((((-859)) -4007 (|has| |#1| (-611 (-859))) (|has| |#1| (-847)) (|has| |#1| (-1094)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2708,7 +2708,7 @@ ((((-564)) . T)) ((((-859)) . T)) ((((-564)) . T)) -(-4030 (|has| |#2| (-790)) (|has| |#2| (-845))) +(-4007 (|has| |#2| (-790)) (|has| |#2| (-845))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-859)) . T)) ((((-859)) . T)) @@ -2720,9 +2720,9 @@ (((|#1|) . T) (($) . T) (((-407 (-564))) . 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T)) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4007 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4007 (|has| |#1| (-363)) (|has| |#1| (-556))) ((((-379)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2752,7 +2752,7 @@ (|has| |#1| (-556)) (|has| |#1| (-1094)) ((((-777 |#1| (-861 |#2|))) |has| (-777 |#1| (-861 |#2|)) (-309 (-777 |#1| (-861 |#2|))))) -(-4030 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4007 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -2764,13 +2764,13 @@ (|has| |#2| (-363)) ((((-581 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) -((((-2 (|:| -1327 (-1152)) (|:| -2423 (-52)))) . T)) +((((-2 (|:| -1354 (-1152)) (|:| -2577 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-564)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-859)) . T)) ((((-859)) . 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T) (($ $) -4030 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) +(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -4007 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) @@ -2808,21 +2808,21 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) -((($ $) -4030 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) -((($ $) -4030 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1| |#1|) . 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T) (($) -4007 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) +((($) -4007 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) @@ -3109,7 +3109,7 @@ ((((-859)) . T) (((-1175)) . T)) ((((-859)) . T) (((-1175)) . T)) ((((-859)) . T) (((-1175)) . T)) -((((-641 |#1|)) . T) (((-859)) -4030 (|has| |#1| (-611 (-859))) (|has| |#1| (-847)) (|has| |#1| (-1094)))) +((((-641 |#1|)) . T) (((-859)) -4007 (|has| |#1| (-611 (-859))) (|has| |#1| (-847)) (|has| |#1| (-1094)))) ((((-1175)) . T)) ((((-1175)) . T)) ((((-1175)) . T)) @@ -3122,23 +3122,23 @@ ((((-1208)) . T) (((-859)) . T) (((-1175)) . T)) ((((-1175)) . T)) ((((-1175)) . 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T)) -(-4030 (|has| |#2| (-172)) (|has| |#2| (-723)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4007 (|has| |#2| (-172)) (|has| |#2| (-723)) (|has| |#2| (-845)) (|has| |#2| (-1046))) ((((-1170)) -12 (|has| |#2| (-897 (-1170))) (|has| |#2| (-1046)))) -(-4030 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-723)) (|has| |#2| (-723)))) +(-4007 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-723)) (|has| |#2| (-723)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-363)) @@ -3345,7 +3345,7 @@ (((|#1| |#2|) . T)) ((((-564)) . T) ((|#2|) |has| |#2| (-172))) ((((-114)) . T) ((|#1|) . T) (((-564)) . T)) -(-4030 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-4007 (|has| |#1| (-349)) (|has| |#1| (-368))) (((|#1| |#2|) . T)) ((((-225)) . T)) ((((-407 (-564))) . T) (($) . T) (((-564)) . T)) @@ -3357,7 +3357,7 @@ (((|#1|) . T)) (((|#1|) . 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T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -(((|#2|) . T) (((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) -((((-2 (|:| -1327 (-1170)) (|:| -2423 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -1354 (-1170)) (|:| -2577 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1019)) -(((|#2|) . T) (((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) ((((-859)) . T)) ((((-536)) |has| |#2| (-612 (-536))) (((-889 (-564))) |has| |#2| (-612 (-889 (-564)))) (((-889 (-379))) |has| |#2| (-612 (-889 (-379)))) (((-379)) . #0=(|has| |#2| (-1019))) (((-225)) . #0#)) ((((-294 |#3|)) . T)) @@ -3434,15 +3434,15 @@ ((((-1168 |#1| |#2| |#3|)) . T)) ((((-1168 |#1| |#2| |#3|)) . T) (((-1161 |#1| |#2| |#3|)) . T)) ((((-859)) . T)) -((((-859)) -4030 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4007 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) ((((-564) |#1|) . 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T)) -((((-859)) -4030 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4007 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) ((((-129)) . T) (((-859)) . T)) ((((-564) |#1|) . T)) ((((-129)) . T)) @@ -3466,13 +3466,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-363)) (|has| |#2| (-286 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-4030 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-906))) -(-4030 (|has| |#1| (-847)) (|has| |#1| (-1094))) +(-4007 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-906))) +(-4007 (|has| |#1| (-847)) (|has| |#1| (-1094))) ((((-859)) . T)) ((((-859)) . T)) ((((-859)) . T)) (((|#1| (-531 |#2|)) . T)) -((((-2 (|:| -1327 (-1170)) (|:| -2423 (-52)))) . T)) +((((-2 (|:| -1354 (-1170)) (|:| -2577 (-52)))) . T)) ((((-564) (-129)) . T)) (((|#1| (-564)) . T)) (((|#1| (-407 (-564))) . T)) @@ -3486,8 +3486,8 @@ ((((-1175)) . T)) ((((-859)) . T) (((-1175)) . T)) ((((-859)) . T) (((-1175)) . T)) -(-4030 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) -(-4030 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4007 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4007 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((($) . T)) (((|#2| (-531 (-861 |#1|))) . T)) ((((-1175)) . T)) @@ -3502,13 +3502,13 @@ ((((-1175)) . T)) ((((-859)) . T) (((-1175)) . T)) ((((-1175)) . T)) -((((-859)) -4030 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4007 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (((|#1|) . T)) (((|#2| (-768)) . T)) (((|#1| |#2|) . T)) ((((-1152) |#1|) . T)) ((((-407 |#2|)) . T)) -((((-2 (|:| -1327 |#1|) (|:| -2423 |#2|))) . T)) +((((-2 (|:| -1354 |#1|) (|:| -2577 |#2|))) . T)) (|has| |#1| (-556)) (|has| |#1| (-556)) ((($) . T) ((|#2|) . T)) @@ -3517,14 +3517,14 @@ ((((-564)) . T) (($) . 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151413) ((-108 . -556) T) ((-654 . -714) 151383) ((-1161 . -1019) NIL) ((-218 . -614) 151364) ((-319 . -23) T) ((-67 . -1209) T) ((-997 . -611) 151296) ((-690 . -231) 151278) ((-711 . -111) 151243) ((-641 . -34) T) ((-245 . -489) 151227) ((-1096 . -1092) 151211) ((-171 . -1094) T) ((-949 . -906) 151190) ((-515 . -614) 151174) ((-1287 . -1145) T) ((-1283 . -21) T) ((-481 . -906) 151153) ((-1283 . -25) T) ((-1281 . -131) T) ((-1279 . -131) T) ((-1272 . -102) T) ((-1255 . -611) 151119) ((-1244 . -1035) 151054) ((-1081 . -714) 150903) ((-1057 . -644) 150890) ((-949 . -644) 150815) ((-779 . -714) 150644) ((-536 . -611) 150626) ((-536 . -612) 150607) ((-777 . -714) 150456) ((-1223 . -1209) 150435) ((-1071 . -102) T) ((-381 . -25) T) ((-381 . -21) T) ((-481 . -644) 150360) ((-461 . -714) 150331) ((-454 . -714) 150180) ((-984 . -102) T) ((-1223 . -883) NIL) ((-1223 . -881) 150132) ((-1182 . -612) NIL) ((-734 . -102) T) ((-1182 . -611) 150114) ((-603 . -614) 150096) ((-1136 . -1117) 150041) 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. -349) NIL) ((-519 . -611) 148851) ((-379 . -792) T) ((-223 . -1094) T) ((-379 . -789) T) ((-225 . -791) T) ((-225 . -788) T) ((-59 . -612) 148812) ((-59 . -611) 148724) ((-225 . -723) T) ((-516 . -612) 148685) ((-516 . -611) 148597) ((-497 . -611) 148529) ((-496 . -612) 148490) ((-496 . -611) 148402) ((-1074 . -363) 148353) ((-40 . -411) 148330) ((-77 . -1209) T) ((-868 . -906) NIL) ((-359 . -329) 148314) ((-359 . -363) T) ((-353 . -329) 148298) ((-353 . -363) T) ((-345 . -329) 148282) ((-345 . -363) T) ((-316 . -284) 148261) ((-108 . -363) T) ((-70 . -1209) T) ((-1223 . -338) 148213) ((-868 . -644) 148158) ((-1223 . -377) 148110) ((-961 . -131) 147965) ((-812 . -131) 147835) ((-955 . -647) 147819) ((-1081 . -172) 147730) ((-955 . -373) 147714) ((-1057 . -791) T) ((-1057 . -788) T) ((-869 . -614) 147612) ((-779 . -172) 147503) ((-777 . -172) 147414) ((-813 . -47) 147376) ((-1057 . -723) T) ((-327 . -489) 147360) ((-949 . -723) T) ((-454 . -172) 147271) ((-245 . -286) 147248) ((-1272 . -309) 147186) ((-1251 . -897) 147099) ((-481 . -723) T) ((-1244 . -897) 147005) ((-1243 . -1052) 146840) ((-1223 . -897) 146673) ((-1222 . -1052) 146481) ((-1203 . -290) 146460) ((-1179 . -1209) T) ((-1177 . -368) T) ((-1176 . -368) T) ((-1140 . -151) 146444) ((-1114 . -102) T) ((-1112 . -1094) T) ((-1074 . -23) T) ((-1069 . -102) T) ((-924 . -952) T) ((-734 . -309) 146382) ((-75 . -1209) T) ((-30 . -952) T) ((-169 . -906) 146335) ((-660 . -382) 146307) ((-112 . -841) T) ((-1 . -611) 146289) ((-1074 . -1106) T) ((-128 . -647) 146271) ((-50 . -618) 146255) ((-1000 . -409) 146227) ((-594 . -897) 146140) ((-438 . -102) T) ((-141 . -309) NIL) ((-128 . -373) 146122) ((-869 . -1046) T) ((-830 . -847) 146101) ((-81 . -1209) T) ((-708 . -290) T) ((-40 . -1053) T) ((-581 . -172) T) ((-518 . -172) T) ((-511 . -611) 146083) ((-169 . -644) 145993) ((-507 . -611) 145975) ((-351 . -147) 145957) ((-351 . -145) T) ((-359 . -1106) T) ((-353 . -1106) T) ((-345 . -1106) T) ((-1001 . -307) T) ((-911 . -307) T) ((-869 . -243) T) ((-108 . -1106) T) ((-869 . -233) 145936) ((-1243 . -111) 145757) ((-1222 . -111) 145546) ((-245 . -1247) 145530) ((-564 . -845) T) ((-359 . -23) T) ((-354 . -349) T) ((-316 . -309) 145517) ((-313 . -309) 145458) ((-353 . -23) T) ((-319 . -131) T) ((-345 . -23) T) ((-1001 . -1019) T) ((-31 . -614) 145439) ((-108 . -23) T) ((-245 . -602) 145416) ((-1245 . -38) 145308) ((-1232 . -906) 145287) ((-112 . -1094) T) ((-1032 . -102) T) ((-1232 . -644) 145212) ((-868 . -791) NIL) ((-852 . -644) 145186) ((-868 . -788) NIL) ((-813 . -883) NIL) ((-868 . -723) T) ((-1081 . -514) 145059) ((-779 . -514) 145006) ((-777 . -514) 144958) ((-571 . -644) 144945) ((-813 . -1035) 144773) ((-454 . -514) 144716) ((-388 . -389) T) ((-1243 . -614) 144529) ((-1222 . -614) 144277) ((-60 . -1209) T) ((-619 . -847) 144256) ((-500 . -657) T) ((-1140 . -973) 144225) ((-1000 . -452) T) ((-695 . -845) T) ((-510 . -789) T) ((-474 . -1052) 144060) ((-343 . -1094) T) ((-313 . -1145) NIL) ((-289 . -131) T) ((-394 . -1094) T) ((-690 . -370) 144027) ((-867 . -1053) T) ((-223 . -618) 144004) ((-327 . -286) 143981) ((-474 . -111) 143802) ((-1243 . -1046) T) ((-1222 . -1046) T) ((-813 . -377) 143786) ((-169 . -723) T) ((-650 . -102) T) ((-1243 . -243) 143765) ((-1243 . -233) 143717) ((-1222 . -233) 143622) ((-1222 . -243) 143601) ((-1000 . -402) NIL) ((-666 . -637) 143549) ((-316 . -38) 143459) ((-313 . -38) 143388) ((-69 . -611) 143370) ((-319 . -493) 143336) ((-1182 . -288) 143315) ((-1217 . -847) T) ((-1107 . -1106) 143225) ((-83 . -1209) T) ((-61 . -611) 143207) ((-479 . -288) 143186) ((-1274 . -1035) 143163) ((-1158 . -1094) T) ((-1107 . -23) 143033) ((-813 . -897) 142969) ((-1232 . -723) T) ((-1096 . -1209) T) ((-474 . -614) 142795) ((-1081 . -290) 142726) ((-963 . -1094) T) ((-890 . -102) T) ((-779 . -290) 142637) ((-327 . -19) 142621) ((-59 . -288) 142598) ((-777 . -290) 142529) ((-852 . -723) T) ((-117 . -845) NIL) ((-516 . -288) 142506) ((-327 . -602) 142483) ((-496 . -288) 142460) ((-454 . -290) 142391) ((-1032 . -309) 142242) ((-677 . -490) 142223) ((-571 . -723) T) ((-672 . -490) 142204) ((-677 . -611) 142154) ((-672 . -611) 142120) ((-658 . -611) 142102) ((-478 . -490) 142083) ((-478 . -611) 142049) ((-245 . -612) 142010) ((-245 . -490) 141987) ((-138 . -490) 141968) ((-137 . -490) 141949) ((-133 . -490) 141930) ((-245 . -611) 141822) ((-213 . -102) T) ((-138 . -611) 141788) ((-137 . -611) 141754) ((-133 . -611) 141720) ((-1141 . -34) T) ((-940 . -1209) T) ((-343 . -714) 141665) ((-666 . -25) T) ((-666 . -21) T) ((-1170 . -614) 141646) ((-474 . -1046) T) ((-633 . -417) 141611) ((-605 . -417) 141576) ((-1114 . -1145) T) ((-581 . -290) T) ((-518 . -290) T) ((-1244 . -307) 141555) ((-474 . -233) 141507) ((-474 . -243) 141486) ((-1223 . -307) 141465) ((-1223 . -1019) NIL) ((-1074 . -131) T) ((-869 . -792) 141444) ((-144 . -102) T) ((-40 . -1094) T) ((-869 . -789) 141423) ((-641 . -1007) 141407) ((-580 . -1053) T) ((-564 . -1053) T) ((-495 . -1053) T) ((-407 . -452) T) ((-359 . -131) T) ((-316 . -400) 141391) ((-313 . -400) 141352) ((-353 . -131) T) ((-345 . -131) T) ((-1175 . -1094) T) ((-1114 . -38) 141339) ((-1088 . -611) 141306) ((-108 . -131) T) ((-951 . -1094) T) ((-918 . -1094) T) ((-768 . -1094) T) ((-668 . -1094) T) ((-697 . -147) T) ((-116 . -147) T) ((-1281 . -21) T) ((-1281 . -25) T) ((-1279 . -21) T) ((-1279 . -25) T) ((-660 . -1052) 141290) ((-531 . -847) T) ((-500 . -847) T) ((-355 . -1052) 141242) ((-352 . -1052) 141194) ((-344 . -1052) 141146) ((-251 . -1209) T) ((-250 . -1209) T) ((-264 . -1052) 140989) ((-247 . -1052) 140832) ((-660 . -111) 140811) ((-547 . -841) T) ((-355 . -111) 140749) ((-352 . -111) 140687) ((-344 . -111) 140625) ((-264 . -111) 140454) ((-247 . -111) 140283) ((-814 . -1213) 140262) ((-621 . -411) 140246) ((-44 . -21) T) ((-44 . -25) T) ((-812 . -637) 140152) ((-814 . -556) 140131) ((-251 . -1035) 139958) ((-250 . -1035) 139785) ((-126 . -119) 139769) ((-907 . -1052) 139734) ((-709 . -102) T) ((-695 . -1053) T) ((-536 . -616) 139637) ((-343 . -172) T) ((-88 . -611) 139619) ((-152 . -21) T) ((-152 . -25) T) ((-907 . -111) 139575) ((-40 . -714) 139520) ((-867 . -1094) T) ((-660 . -614) 139497) ((-642 . -614) 139478) ((-355 . -614) 139415) ((-352 . -614) 139352) ((-547 . -1094) T) ((-344 . -614) 139289) ((-327 . -612) 139250) ((-327 . -611) 139162) ((-264 . -614) 138915) ((-247 . -614) 138700) ((-1222 . -789) 138653) ((-1222 . -792) 138606) ((-251 . -377) 138575) ((-250 . -377) 138544) ((-650 . -38) 138514) ((-606 . -34) T) ((-482 . -1106) 138424) ((-475 . -34) T) ((-1107 . -131) 138294) ((-961 . -25) 138105) ((-907 . -614) 138055) ((-871 . -611) 138037) ((-961 . -21) 137992) ((-812 . -21) 137902) ((-812 . -25) 137753) ((-1215 . -368) T) ((-621 . -1053) T) ((-1172 . -556) 137732) ((-1166 . -47) 137709) ((-355 . -1046) T) ((-352 . -1046) T) ((-482 . -23) 137579) ((-344 . -1046) T) ((-247 . -1046) T) ((-264 . -1046) T) ((-1119 . -47) 137551) ((-117 . -1053) T) ((-1031 . -644) 137525) ((-955 . -34) T) ((-355 . -233) 137504) ((-355 . -243) T) ((-352 . -233) 137483) ((-352 . -243) T) ((-344 . -233) 137462) ((-344 . -243) T) ((-247 . -326) 137419) ((-264 . -326) 137391) ((-264 . -233) 137370) ((-1150 . -151) 137354) ((-251 . -897) 137286) ((-250 . -897) 137218) ((-1076 . -847) T) ((-414 . -1106) T) ((-1050 . -23) T) ((-907 . -1046) T) ((-322 . -644) 137200) ((-1021 . -845) T) ((-1203 . -999) 137166) ((-1167 . -917) 137145) ((-1161 . -917) 137124) ((-1161 . -817) NIL) ((-907 . -243) T) ((-814 . -363) 137103) ((-385 . -23) T) ((-127 . -1094) 137081) ((-121 . -1094) 137059) ((-907 . -233) T) ((-128 . -34) T) ((-379 . -644) 137024) ((-867 . -714) 137011) ((-1043 . -151) 136976) ((-40 . -172) T) ((-690 . -411) 136958) ((-709 . -309) 136945) ((-833 . -644) 136905) ((-824 . -644) 136879) ((-319 . -25) T) ((-319 . -21) T) ((-654 . -286) 136858) ((-580 . -1094) T) ((-564 . -1094) T) ((-495 . -1094) T) ((-245 . -288) 136835) ((-313 . -231) 136796) ((-1166 . -883) NIL) ((-55 . -1094) T) ((-1119 . -883) 136655) ((-129 . -847) T) ((-1166 . -1035) 136535) ((-1119 . -1035) 136418) ((-183 . -611) 136400) ((-851 . -1035) 136296) ((-779 . -286) 136223) ((-814 . -1106) T) ((-1031 . -723) T) ((-600 . -647) 136207) ((-1043 . -973) 136136) ((-996 . -102) T) ((-814 . -23) T) ((-709 . -1145) 136114) ((-690 . -1053) T) ((-600 . -373) 136098) ((-351 . -452) T) ((-343 . -290) T) ((-1260 . -1094) T) ((-248 . -1094) T) ((-399 . -102) T) ((-289 . -21) T) ((-289 . -25) T) ((-361 . -723) T) ((-707 . -1094) T) ((-695 . -1094) T) ((-361 . -473) T) ((-1203 . -611) 136080) ((-1166 . -377) 136064) ((-1119 . -377) 136048) ((-1021 . -411) 136010) ((-141 . -229) 135992) ((-379 . -791) T) ((-379 . -788) T) ((-867 . -172) T) ((-379 . -723) T) ((-708 . -611) 135974) ((-709 . -38) 135803) ((-1259 . -1257) 135787) ((-351 . -402) T) ((-1259 . -1094) 135737) ((-580 . -714) 135724) ((-564 . -714) 135711) ((-495 . -714) 135676) ((-316 . -627) 135655) ((-833 . -723) T) ((-824 . -723) T) ((-641 . -1209) T) ((-1074 . -637) 135603) ((-1166 . -897) 135546) ((-1119 . -897) 135530) ((-658 . -1052) 135514) ((-108 . -637) 135496) ((-482 . -131) 135366) ((-1172 . -1106) T) ((-949 . -47) 135335) ((-621 . -1094) T) ((-658 . -111) 135314) ((-491 . -611) 135280) ((-327 . -288) 135257) ((-481 . -47) 135214) ((-1172 . -23) T) ((-117 . -1094) T) ((-103 . -102) 135192) ((-1271 . -1106) T) ((-548 . -847) T) ((-1050 . -131) T) ((-1021 . -1053) T) ((-816 . -1035) 135176) ((-1000 . -721) 135148) ((-1271 . -23) T) ((-695 . -714) 135113) ((-585 . -611) 135095) ((-386 . -1035) 135079) ((-354 . -1053) T) ((-385 . -131) T) ((-324 . -1035) 135063) ((-225 . -883) 135045) ((-1001 . -917) T) ((-91 . -34) T) ((-1001 . -817) T) ((-911 . -917) T) ((-1189 . -611) 135027) ((-1114 . -825) T) ((-487 . -1213) T) ((-1099 . -1094) T) ((-1074 . -21) T) ((-1074 . -25) T) ((-217 . -1213) T) ((-996 . -309) 134992) ((-225 . -1035) 134952) ((-40 . -290) T) ((-711 . -644) 134912) ((-677 . -614) 134893) ((-672 . -614) 134874) ((-487 . -556) T) ((-478 . -614) 134855) ((-359 . -25) T) ((-359 . -21) T) ((-353 . -25) T) ((-217 . -556) T) ((-353 . -21) T) ((-345 . -25) T) ((-345 . -21) T) ((-245 . -614) 134832) ((-138 . -614) 134813) ((-137 . -614) 134794) ((-133 . -614) 134775) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1053) T) ((-580 . -172) T) ((-564 . -172) T) ((-495 . -172) T) ((-654 . -611) 134757) ((-734 . -733) 134741) ((-336 . -611) 134723) ((-68 . -383) T) ((-68 . -395) T) ((-1096 . -107) 134707) ((-1057 . -883) 134689) ((-949 . -883) 134614) ((-649 . -1106) T) ((-621 . -714) 134601) ((-481 . -883) NIL) ((-1140 . -102) T) ((-1088 . -616) 134585) ((-1057 . -1035) 134567) ((-97 . -611) 134549) ((-477 . -147) T) ((-949 . -1035) 134429) ((-117 . -714) 134374) ((-649 . -23) T) ((-481 . -1035) 134250) ((-1081 . -612) NIL) ((-1081 . -611) 134232) ((-779 . -612) NIL) ((-779 . -611) 134193) ((-777 . -612) 133827) ((-777 . -611) 133741) ((-1107 . -637) 133647) ((-461 . -611) 133629) ((-454 . -611) 133611) ((-454 . -612) 133472) ((-1032 . -229) 133418) ((-869 . -906) 133397) ((-126 . -34) T) ((-814 . -131) T) ((-645 . -611) 133379) ((-578 . -102) T) ((-355 . -1278) 133363) ((-352 . -1278) 133347) ((-344 . -1278) 133331) ((-127 . -514) 133264) ((-121 . -514) 133197) ((-511 . -789) T) ((-511 . -792) T) ((-510 . -791) T) ((-103 . -309) 133135) ((-222 . -102) 133113) ((-690 . -1094) T) ((-695 . -172) T) ((-869 . -644) 133065) ((-65 . -384) T) ((-275 . -611) 133047) ((-65 . -395) T) ((-949 . -377) 133031) ((-867 . -290) T) ((-50 . -611) 133013) ((-996 . -38) 132961) ((-581 . -611) 132943) ((-481 . -377) 132927) ((-581 . -612) 132909) ((-518 . -611) 132891) ((-907 . -1278) 132878) ((-868 . -1209) T) ((-697 . -452) T) ((-495 . -514) 132844) ((-487 . -363) T) ((-355 . -368) 132823) ((-352 . -368) 132802) ((-344 . -368) 132781) ((-711 . -723) T) ((-217 . -363) T) ((-116 . -452) T) ((-1282 . -1273) 132765) ((-868 . -881) 132742) ((-868 . -883) NIL) ((-961 . -847) 132641) ((-812 . -847) 132592) ((-1216 . -102) T) ((-650 . -652) 132576) ((-1195 . -34) T) ((-171 . -611) 132558) ((-1107 . -21) 132468) ((-1107 . -25) 132319) ((-868 . -1035) 132296) ((-949 . -897) 132277) ((-1232 . -47) 132254) ((-907 . -368) T) ((-59 . -647) 132238) ((-516 . -647) 132222) ((-481 . -897) 132199) ((-71 . -441) T) ((-71 . -395) T) ((-496 . -647) 132183) ((-59 . -373) 132167) ((-621 . -172) T) ((-516 . -373) 132151) ((-496 . -373) 132135) ((-824 . -705) 132119) ((-1166 . -307) 132098) ((-1172 . -131) T) ((-117 . -172) T) ((-1140 . -309) 132036) ((-169 . -1209) T) ((-633 . -741) 132020) ((-605 . -741) 132004) ((-1271 . -131) T) ((-1244 . -917) 131983) ((-1223 . -917) 131962) ((-1223 . -817) NIL) ((-690 . -714) 131912) ((-1222 . -906) 131865) ((-1021 . -1094) T) ((-868 . -377) 131842) ((-868 . -338) 131819) ((-902 . -1106) T) ((-169 . -881) 131803) ((-169 . -883) 131728) ((-487 . -1106) T) ((-354 . -1094) T) ((-217 . -1106) T) ((-76 . -441) T) ((-76 . -395) T) ((-169 . -1035) 131624) ((-319 . -847) T) ((-1259 . -514) 131557) ((-1243 . -644) 131454) ((-1222 . -644) 131324) ((-869 . -791) 131303) ((-869 . -788) 131282) ((-869 . -723) T) ((-487 . -23) T) ((-223 . -611) 131264) ((-174 . -452) T) ((-222 . -309) 131202) ((-86 . -441) T) ((-86 . -395) T) ((-217 . -23) T) ((-1283 . -1276) 131181) ((-580 . -290) T) ((-564 . -290) T) ((-673 . -1035) 131165) ((-495 . -290) T) ((-136 . -470) 131120) ((-48 . -1094) T) ((-709 . -231) 131104) ((-868 . -897) NIL) ((-1232 . -883) NIL) ((-886 . -102) T) ((-882 . -102) T) ((-388 . -1094) T) ((-169 . -377) 131088) ((-169 . -338) 131072) ((-1232 . -1035) 130952) ((-852 . -1035) 130848) ((-1136 . -102) T) ((-649 . -131) T) ((-117 . -514) 130756) ((-658 . -789) 130735) ((-658 . -792) 130714) ((-571 . -1035) 130696) ((-294 . -1266) 130666) ((-863 . -102) T) ((-960 . -556) 130645) ((-1203 . -1052) 130528) ((-482 . -637) 130434) ((-901 . -1094) T) ((-1021 . -714) 130371) ((-708 . -1052) 130336) ((-615 . -102) T) ((-600 . -34) T) ((-1141 . -1209) T) 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121771) ((-898 . -514) 121704) ((-343 . -1046) T) ((-117 . -612) NIL) ((-117 . -611) 121686) ((-869 . -1209) T) ((-666 . -417) 121670) ((-666 . -1117) 121615) ((-500 . -151) 121597) ((-343 . -233) T) ((-343 . -243) T) ((-40 . -1052) 121542) ((-869 . -881) 121526) ((-869 . -883) 121451) ((-709 . -1053) T) ((-690 . -999) NIL) ((-3 . |UnionCategory|) T) ((-1243 . -47) 121421) ((-1222 . -47) 121398) ((-1135 . -1007) 121369) ((-225 . -917) T) ((-40 . -111) 121298) ((-869 . -1035) 121162) ((-1114 . -714) 121149) ((-1099 . -611) 121131) ((-1074 . -147) 121110) ((-1074 . -145) 121061) ((-1001 . -363) T) ((-319 . -1197) 121027) ((-379 . -307) T) ((-319 . -1194) 120993) ((-316 . -172) 120972) ((-313 . -172) T) ((-1000 . -231) 120949) ((-911 . -363) T) ((-581 . -1278) 120936) ((-518 . -1278) 120913) ((-359 . -147) 120892) ((-359 . -145) 120843) ((-353 . -147) 120822) ((-353 . -145) 120773) ((-606 . -1185) 120749) ((-345 . -147) 120728) ((-345 . -145) 120679) ((-319 . -35) 120645) ((-475 . -1185) 120624) ((0 . |EnumerationCategory|) T) ((-319 . -95) 120590) ((-379 . -1019) T) ((-108 . -147) T) ((-108 . -145) NIL) ((-45 . -235) 120540) ((-650 . -1094) T) ((-606 . -107) 120487) ((-485 . -131) T) ((-475 . -107) 120437) ((-240 . -1106) 120347) ((-869 . -377) 120331) ((-869 . -338) 120315) ((-240 . -23) 120185) ((-40 . -614) 120115) ((-1057 . -917) T) ((-1057 . -817) T) ((-581 . -368) T) ((-518 . -368) T) ((-351 . -1145) T) ((-327 . -34) T) ((-44 . -417) 120099) ((-1175 . -614) 120034) ((-870 . -1209) T) ((-390 . -741) 120018) ((-1272 . -514) 119951) ((-728 . -131) T) ((-668 . -614) 119935) ((-1251 . -556) 119914) ((-1244 . -1213) 119893) ((-1244 . -556) 119844) ((-1223 . -1213) 119823) ((-311 . -1077) T) ((-1223 . -556) 119774) ((-734 . -514) 119707) ((-1222 . -1209) 119686) ((-1222 . -883) 119559) ((-890 . -1094) T) ((-144 . -841) T) ((-1222 . -881) 119529) ((-687 . -611) 119511) ((-1168 . -131) T) ((-523 . -309) 119449) ((-1167 . -131) T) ((-141 . -514) NIL) ((-1161 . -131) T) 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((-1203 . -644) 118431) ((-960 . -21) T) ((-960 . -25) T) ((-732 . -21) T) ((-732 . -25) T) ((-712 . -21) T) ((-712 . -25) T) ((-708 . -644) 118396) ((-453 . -21) T) ((-453 . -25) T) ((-339 . -102) T) ((-174 . -102) T) ((-996 . -1053) T) ((-867 . -1046) T) ((-771 . -102) T) ((-1244 . -363) 118375) ((-1243 . -897) 118281) ((-1223 . -363) 118260) ((-1222 . -897) 118111) ((-1021 . -611) 118093) ((-407 . -825) 118046) ((-1168 . -493) 118012) ((-169 . -917) 117943) ((-1167 . -493) 117909) ((-1161 . -493) 117875) ((-709 . -1094) T) ((-1120 . -493) 117841) ((-580 . -1052) 117828) ((-564 . -1052) 117815) ((-495 . -1052) 117780) ((-316 . -290) 117759) ((-313 . -290) T) ((-354 . -611) 117741) ((-418 . -25) T) ((-418 . -21) T) ((-99 . -286) 117720) ((-580 . -111) 117705) ((-564 . -111) 117690) ((-495 . -111) 117646) ((-1170 . -883) 117613) ((-898 . -489) 117597) ((-48 . -611) 117579) ((-48 . -612) 117524) ((-240 . -131) 117394) ((-1232 . -917) 117373) ((-813 . -1213) 117352) ((-388 . -490) 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. -131) T) ((-654 . -644) 116276) ((-245 . -1007) 116260) ((-869 . -307) T) ((-1283 . -1273) 116244) ((-768 . -789) T) ((-768 . -792) T) ((-697 . -38) 116231) ((-564 . -233) T) ((-495 . -243) T) ((-495 . -233) T) ((-1144 . -235) 116181) ((-1081 . -906) 116160) ((-116 . -38) 116147) ((-209 . -797) T) ((-208 . -797) T) ((-207 . -797) T) ((-206 . -797) T) ((-869 . -1019) 116125) ((-1272 . -489) 116109) ((-779 . -906) 116088) ((-777 . -906) 116067) ((-1182 . -1209) T) ((-454 . -906) 116046) ((-734 . -489) 116030) ((-1081 . -644) 115955) ((-695 . -614) 115890) ((-779 . -644) 115815) ((-621 . -1052) 115802) ((-479 . -1209) T) ((-343 . -368) T) ((-141 . -489) 115784) ((-777 . -644) 115709) ((-1135 . -1209) T) ((-549 . -847) T) ((-461 . -644) 115680) ((-264 . -883) 115539) ((-247 . -883) NIL) ((-117 . -1052) 115484) ((-454 . -644) 115409) ((-660 . -1035) 115386) ((-621 . -111) 115371) ((-355 . -1035) 115355) ((-352 . -1035) 115339) ((-344 . -1035) 115323) ((-264 . -1035) 115167) ((-247 . 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. -243) T) ((-48 . -233) T) ((-650 . -286) 110052) ((-550 . -235) 110002) ((-139 . -611) 109969) ((-136 . -611) 109951) ((-114 . -611) 109933) ((-477 . -38) 109898) ((-1283 . -1280) 109877) ((-1274 . -131) T) ((-1282 . -1053) T) ((-1076 . -102) T) ((-88 . -1209) T) ((-500 . -309) NIL) ((-997 . -107) 109861) ((-886 . -1094) T) ((-882 . -1094) T) ((-1259 . -647) 109845) ((-1259 . -373) 109829) ((-327 . -1209) T) ((-592 . -847) T) ((-1136 . -1094) T) ((-1136 . -1049) 109769) ((-103 . -514) 109702) ((-924 . -611) 109684) ((-343 . -723) T) ((-30 . -611) 109666) ((-863 . -1094) T) ((-840 . -1053) 109645) ((-40 . -644) 109590) ((-225 . -1213) T) ((-407 . -1053) T) ((-1152 . -151) 109572) ((-996 . -290) 109523) ((-615 . -1094) T) ((-225 . -556) T) ((-319 . -1240) 109507) ((-319 . -1237) 109477) ((-1182 . -1185) 109456) ((-1069 . -611) 109438) ((-643 . -151) 109422) ((-630 . -151) 109368) ((-1182 . -107) 109318) ((-479 . -1185) 109297) ((-487 . -147) T) ((-487 . -145) NIL) ((-1114 . -612) 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-883) NIL) ((-868 . -1106) T) ((-117 . -906) NIL) ((-1281 . -1280) 105428) ((-1279 . -1280) 105407) ((-779 . -883) NIL) ((-777 . -883) 105266) ((-1274 . -25) T) ((-1274 . -21) T) ((-1206 . -102) 105244) ((-1100 . -395) T) ((-621 . -644) 105231) ((-454 . -883) NIL) ((-671 . -102) 105209) ((-1081 . -1035) 105036) ((-868 . -23) T) ((-779 . -1035) 104895) ((-777 . -1035) 104752) ((-117 . -644) 104697) ((-454 . -1035) 104573) ((-316 . -614) 104137) ((-313 . -614) 104020) ((-645 . -1035) 104004) ((-625 . -102) T) ((-222 . -489) 103988) ((-1259 . -34) T) ((-136 . -614) 103972) ((-633 . -714) 103956) ((-605 . -714) 103940) ((-666 . -38) 103900) ((-319 . -102) T) ((-85 . -611) 103882) ((-50 . -1035) 103866) ((-1114 . -1052) 103853) ((-1081 . -377) 103837) ((-779 . -377) 103821) ((-695 . -723) T) ((-695 . -791) T) ((-695 . -788) T) ((-581 . -1035) 103808) ((-518 . -1035) 103785) ((-60 . -57) 103747) ((-324 . -131) T) ((-316 . -1046) 103637) ((-313 . -1046) T) ((-169 . -1106) T) ((-777 . -377) 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101735) ((-1021 . -644) 101672) ((-523 . -1094) 101650) ((-359 . -102) T) ((-353 . -102) T) ((-345 . -102) T) ((-108 . -102) T) ((-504 . -1094) T) ((-354 . -644) 101595) ((-1166 . -637) 101543) ((-1119 . -637) 101491) ((-385 . -509) 101470) ((-830 . -845) 101449) ((-379 . -1213) T) ((-690 . -723) T) ((-339 . -1053) T) ((-1223 . -989) 101401) ((-174 . -1053) T) ((-103 . -611) 101333) ((-1168 . -145) 101312) ((-1168 . -147) 101291) ((-379 . -556) T) ((-1167 . -147) 101270) ((-1167 . -145) 101249) ((-1161 . -145) 101156) ((-407 . -290) T) ((-1161 . -147) 101063) ((-1120 . -147) 101042) ((-1120 . -145) 101021) ((-319 . -38) 100862) ((-169 . -131) T) ((-313 . -792) NIL) ((-313 . -789) NIL) ((-650 . -1046) T) ((-48 . -644) 100827) ((-890 . -614) 100804) ((-1160 . -102) T) ((-991 . -102) T) ((-990 . -21) T) ((-127 . -1007) 100788) ((-121 . -1007) 100772) ((-990 . -25) T) ((-898 . -119) 100756) ((-1152 . -102) T) ((-813 . -847) 100735) ((-1232 . -131) T) ((-1166 . -25) T) ((-1166 . -21) T) 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95219) ((-1243 . -556) 95170) ((-711 . -1106) T) ((-1222 . -556) 95121) ((-564 . -1035) 95103) ((-594 . -147) 95082) ((-594 . -145) 95061) ((-495 . -1035) 95004) ((-1129 . -1131) T) ((-87 . -384) T) ((-87 . -395) T) ((-869 . -363) T) ((-833 . -131) T) ((-824 . -131) T) ((-711 . -23) T) ((-506 . -611) 94970) ((-502 . -611) 94952) ((-1283 . -1053) T) ((-379 . -1055) T) ((-1023 . -1094) 94930) ((-55 . -1035) 94912) ((-898 . -34) T) ((-482 . -309) 94850) ((-591 . -102) T) ((-1150 . -612) 94811) ((-1150 . -611) 94743) ((-1166 . -847) 94722) ((-45 . -102) T) ((-1119 . -847) 94701) ((-814 . -102) T) ((-1232 . -25) T) ((-1232 . -21) T) ((-852 . -25) T) ((-44 . -367) 94685) ((-852 . -21) T) ((-728 . -452) 94636) ((-1282 . -611) 94618) ((-1050 . -309) 94556) ((-667 . -1077) T) ((-604 . -1077) T) ((-390 . -1094) T) ((-571 . -25) T) ((-571 . -21) T) ((-180 . -1077) T) ((-161 . -1077) T) ((-156 . -1077) T) ((-154 . -1077) T) ((-619 . -1094) T) ((-695 . -883) 94538) ((-1259 . -1209) T) ((-227 . -309) 94476) ((-144 . -368) T) ((-1043 . -612) 94418) ((-1043 . -611) 94361) ((-313 . -906) NIL) ((-1217 . -841) T) ((-695 . -1035) 94306) ((-708 . -917) T) ((-474 . -1213) 94285) ((-1167 . -452) 94264) ((-1161 . -452) 94243) ((-330 . -102) T) ((-869 . -1106) T) ((-316 . -644) 94064) ((-313 . -644) 93993) ((-474 . -556) 93944) ((-339 . -514) 93910) ((-550 . -151) 93860) ((-40 . -307) T) ((-840 . -611) 93842) ((-697 . -290) T) ((-869 . -23) T) ((-379 . -493) T) ((-1074 . -231) 93812) ((-512 . -102) T) ((-407 . -612) 93619) ((-407 . -611) 93601) ((-263 . -611) 93583) ((-116 . -290) T) ((-1245 . -723) T) ((-1243 . -363) 93562) ((-1222 . -363) 93541) ((-1272 . -34) T) ((-1217 . -1094) T) ((-117 . -1209) T) ((-108 . -231) 93523) ((-1172 . -102) T) ((-477 . -1094) T) ((-523 . -489) 93507) ((-734 . -34) T) ((-482 . -38) 93477) ((-141 . -34) T) ((-117 . -881) 93454) ((-117 . -883) NIL) ((-621 . -1035) 93337) ((-641 . -847) 93316) ((-1271 . -102) T) ((-295 . -102) T) ((-709 . -368) 93295) 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-23) T) ((-715 . -1106) T) ((-711 . -131) T) ((-649 . -102) T) ((-477 . -714) 92048) ((-45 . -282) 91998) ((-105 . -1094) T) ((-68 . -611) 91980) ((-967 . -102) T) ((-861 . -102) T) ((-621 . -897) 91939) ((-1283 . -1094) T) ((-381 . -1094) T) ((-1208 . -1094) T) ((-1107 . -231) 91908) ((-82 . -1209) T) ((-1057 . -847) T) ((-949 . -847) 91887) ((-117 . -897) NIL) ((-779 . -917) 91866) ((-710 . -847) T) ((-531 . -1094) T) ((-500 . -1094) T) ((-355 . -1213) T) ((-352 . -1213) T) ((-344 . -1213) T) ((-264 . -1213) 91845) ((-247 . -1213) 91824) ((-533 . -857) T) ((-481 . -847) 91803) ((-1152 . -825) T) ((-1136 . -1052) 91787) ((-390 . -758) T) ((-690 . -1209) T) ((-687 . -1035) 91771) ((-355 . -556) T) ((-352 . -556) T) ((-344 . -556) T) ((-264 . -556) 91702) ((-247 . -556) 91633) ((-525 . -1077) T) ((-1136 . -111) 91612) ((-453 . -741) 91582) ((-863 . -1052) 91552) ((-814 . -38) 91494) ((-690 . -881) 91476) ((-690 . -883) 91458) ((-295 . -309) 91262) ((-907 . -1213) T) ((-666 . -411) 91246) ((-863 . -111) 91211) ((-690 . -1035) 91156) ((-1001 . -452) T) ((-907 . -556) T) ((-533 . -611) 91138) ((-581 . -917) T) ((-474 . -1106) T) ((-518 . -917) T) ((-1150 . -288) 91115) ((-911 . -452) T) ((-65 . -611) 91097) ((-630 . -229) 91043) ((-474 . -23) T) ((-1114 . -791) T) ((-869 . -131) T) ((-1114 . -788) T) ((-1274 . -1276) 91022) ((-1114 . -723) T) ((-650 . -644) 90996) ((-294 . -611) 90737) ((-1136 . -614) 90655) ((-1032 . -34) T) ((-812 . -845) 90634) ((-580 . -307) T) ((-564 . -307) T) ((-495 . -307) T) ((-1283 . -714) 90604) ((-690 . -377) 90586) ((-690 . -338) 90568) ((-477 . -172) T) ((-381 . -714) 90538) ((-863 . -614) 90473) ((-868 . -847) NIL) ((-564 . -1019) T) ((-495 . -1019) T) ((-1127 . -611) 90455) ((-1107 . -238) 90434) ((-214 . -102) T) ((-1144 . -102) T) ((-71 . -611) 90416) ((-1136 . -1046) T) ((-1172 . -38) 90313) ((-855 . -611) 90295) ((-564 . -545) T) ((-666 . -1053) T) ((-728 . -946) 90248) ((-1136 . -233) 90227) ((-1076 . -1094) T) ((-1031 . -25) T) ((-1031 . -21) T) ((-1000 . -1052) 90172) ((-902 . -102) T) ((-863 . -1046) T) ((-690 . -897) NIL) ((-355 . -329) 90156) ((-355 . -363) T) ((-352 . -329) 90140) ((-352 . -363) T) ((-344 . -329) 90124) ((-344 . -363) T) ((-487 . -102) T) ((-1271 . -38) 90094) ((-546 . -847) T) ((-523 . -683) 90044) ((-217 . -102) T) ((-1021 . -1035) 89924) ((-1000 . -111) 89853) ((-1168 . -970) 89822) ((-1167 . -970) 89784) ((-520 . -151) 89768) ((-1074 . -370) 89747) ((-351 . -611) 89729) ((-322 . -21) T) ((-354 . -1035) 89706) ((-322 . -25) T) ((-1161 . -970) 89675) ((-1120 . -970) 89642) ((-76 . -611) 89624) ((-695 . -307) T) ((-169 . -847) 89603) ((-129 . -841) T) ((-907 . -363) T) ((-379 . -25) T) ((-379 . -21) T) ((-907 . -329) 89590) ((-86 . -611) 89572) ((-695 . -1019) T) ((-673 . -847) T) ((-1243 . -131) T) ((-1222 . -131) T) ((-898 . -1007) 89556) ((-833 . -21) T) ((-48 . -1035) 89499) ((-833 . -25) T) ((-824 . -25) T) ((-824 . -21) T) ((-1281 . -1053) T) ((-549 . -102) T) ((-1279 . -1053) T) ((-650 . -723) T) ((-1098 . -616) 89402) ((-1000 . -614) 89332) ((-1282 . -1052) 89316) ((-1232 . -847) 89295) ((-812 . -411) 89264) ((-103 . -119) 89248) ((-129 . -1094) T) ((-52 . -1094) T) ((-923 . -611) 89230) ((-868 . -989) 89207) ((-820 . -102) T) ((-1282 . -111) 89186) ((-649 . -38) 89156) ((-571 . -847) T) ((-355 . -1106) T) ((-352 . -1106) T) ((-344 . -1106) T) ((-264 . -1106) T) ((-247 . -1106) T) ((-621 . -307) 89135) ((-1144 . -309) 88939) ((-524 . -1077) T) ((-311 . -1094) T) ((-660 . -23) T) ((-482 . -231) 88908) ((-152 . -1053) T) ((-355 . -23) T) ((-352 . -23) T) ((-344 . -23) T) ((-117 . -307) T) ((-264 . -23) T) ((-247 . -23) T) ((-1000 . -1046) T) ((-709 . -906) 88887) ((-1150 . -614) 88864) ((-1000 . -233) 88836) ((-1000 . -243) T) ((-117 . -1019) NIL) ((-907 . -1106) T) ((-1244 . -452) 88815) ((-1223 . -452) 88794) ((-523 . -611) 88726) ((-709 . -644) 88651) ((-407 . -1052) 88603) ((-504 . -611) 88585) ((-907 . -23) T) ((-487 . -309) NIL) ((-1282 . -614) 88541) 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-1219) 87595) ((-407 . -1046) T) ((-319 . -1053) T) ((-690 . -307) T) ((-108 . -845) T) ((-709 . -723) T) ((-407 . -243) T) ((-407 . -233) 87574) ((-487 . -38) 87524) ((-217 . -38) 87474) ((-474 . -493) 87440) ((-1216 . -368) T) ((-1152 . -1138) T) ((-1095 . -102) T) ((-697 . -611) 87422) ((-697 . -612) 87337) ((-711 . -21) T) ((-711 . -25) T) ((-1129 . -102) T) ((-134 . -611) 87319) ((-116 . -611) 87301) ((-157 . -25) T) ((-1281 . -1094) T) ((-869 . -637) 87249) ((-1279 . -1094) T) ((-960 . -102) T) ((-732 . -102) T) ((-712 . -102) T) ((-453 . -102) T) ((-813 . -452) 87200) ((-44 . -1094) T) ((-1082 . -847) T) ((-660 . -131) T) ((-1058 . -309) 87051) ((-666 . -714) 87035) ((-289 . -1053) T) ((-355 . -131) T) ((-352 . -131) T) ((-344 . -131) T) ((-264 . -131) T) ((-247 . -131) T) ((-418 . -102) T) ((-152 . -1094) T) ((-45 . -229) 86985) ((-955 . -847) 86964) ((-996 . -644) 86902) ((-240 . -1266) 86872) ((-1021 . -307) T) ((-294 . -1052) 86793) ((-907 . -131) T) ((-40 . -917) T) ((-487 . -400) 86775) ((-354 . -307) T) ((-217 . -400) 86757) ((-1074 . -411) 86741) ((-294 . -111) 86657) ((-1177 . -847) T) ((-1176 . -847) T) ((-869 . -25) T) ((-869 . -21) T) ((-339 . -611) 86639) ((-1245 . -47) 86583) ((-225 . -147) T) ((-174 . -611) 86565) ((-1107 . -845) 86544) ((-771 . -611) 86526) ((-128 . -847) T) ((-606 . -235) 86473) ((-475 . -235) 86423) ((-1281 . -714) 86393) ((-48 . -307) T) ((-1279 . -714) 86363) ((-65 . -614) 86292) ((-961 . -1094) T) ((-812 . -1094) 86082) ((-312 . -102) T) ((-898 . -1209) T) ((-48 . -1019) T) ((-1222 . -637) 85990) ((-685 . -102) 85968) ((-44 . -714) 85952) ((-550 . -102) T) ((-294 . -614) 85883) ((-67 . -383) T) ((-67 . -395) T) ((-658 . -23) T) ((-666 . -758) T) ((-1206 . -1094) 85861) ((-351 . -1052) 85806) ((-671 . -1094) 85784) ((-1057 . -147) T) ((-949 . -147) 85763) ((-949 . -145) 85742) ((-796 . -102) T) ((-152 . -714) 85726) ((-481 . -147) 85705) ((-481 . -145) 85684) ((-351 . -111) 85613) ((-1074 . -1053) T) ((-322 . -847) 85592) 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NIL) ((-1208 . -93) T) ((-351 . -1046) T) ((-70 . -383) T) ((-70 . -395) T) ((-1159 . -102) T) ((-666 . -514) 84914) ((-685 . -309) 84852) ((-960 . -38) 84749) ((-732 . -38) 84719) ((-550 . -309) 84523) ((-316 . -1209) T) ((-351 . -233) T) ((-351 . -243) T) ((-313 . -1209) T) ((-289 . -1094) T) ((-1174 . -611) 84505) ((-708 . -1213) T) ((-1150 . -647) 84489) ((-1203 . -556) 84468) ((-708 . -556) T) ((-316 . -881) 84452) ((-316 . -883) 84377) ((-313 . -881) 84338) ((-313 . -883) NIL) ((-796 . -309) 84303) ((-319 . -714) 84144) ((-324 . -323) 84121) ((-485 . -102) T) ((-474 . -25) T) ((-474 . -21) T) ((-418 . -38) 84095) ((-316 . -1035) 83758) ((-225 . -1194) T) ((-225 . -1197) T) ((-3 . -611) 83740) ((-313 . -1035) 83670) ((-2 . -1094) T) ((-2 . |RecordCategory|) T) ((-830 . -611) 83652) ((-1107 . -1053) 83582) ((-580 . -917) T) ((-564 . -817) T) ((-564 . -917) T) ((-495 . -917) T) ((-136 . -1035) 83566) ((-225 . -95) T) ((-75 . -441) T) ((-75 . -395) T) ((0 . -611) 83548) ((-169 . -147) 83527) ((-169 . -145) 83478) ((-225 . -35) T) ((-49 . -611) 83460) ((-477 . -1053) T) ((-487 . -231) 83442) ((-484 . -965) 83426) ((-482 . -845) 83405) ((-217 . -231) 83387) ((-81 . -441) T) ((-81 . -395) T) ((-1140 . -34) T) ((-812 . -172) 83366) ((-728 . -102) T) ((-1023 . -611) 83333) ((-500 . -286) 83308) ((-316 . -377) 83277) ((-313 . -377) 83238) ((-313 . -338) 83199) ((-1079 . -611) 83181) ((-813 . -946) 83128) ((-658 . -131) T) ((-1232 . -145) 83107) ((-1232 . -147) 83086) ((-1168 . -102) T) ((-1167 . -102) T) ((-1161 . -102) T) ((-1153 . -1094) T) ((-1120 . -102) T) ((-222 . -34) T) ((-289 . -714) 83073) ((-1153 . -608) 83049) ((-592 . -309) NIL) ((-484 . -1094) 83027) ((-390 . -611) 83009) ((-510 . -847) T) ((-1144 . -229) 82959) ((-1251 . -1250) 82943) ((-1251 . -1237) 82920) ((-1244 . -1242) 82881) ((-1244 . -1237) 82851) ((-1244 . -1240) 82835) ((-1223 . -1221) 82796) ((-1223 . -1237) 82773) ((-619 . -611) 82755) ((-1223 . -1219) 82739) ((-695 . -917) T) ((-1168 . -284) 82705) ((-1167 . -284) 82671) ((-1161 . -284) 82637) ((-1074 . -1094) T) ((-1056 . -1094) T) ((-48 . -302) T) ((-316 . -897) 82603) ((-313 . -897) NIL) ((-1056 . -1063) 82582) ((-1114 . -883) 82564) ((-796 . -38) 82548) ((-264 . -637) 82496) ((-247 . -637) 82444) ((-697 . -1052) 82431) ((-594 . -1237) 82408) ((-1120 . -284) 82374) ((-319 . -172) 82305) ((-359 . -1094) T) ((-353 . -1094) T) ((-345 . -1094) T) ((-500 . -19) 82287) ((-1114 . -1035) 82269) ((-1096 . -151) 82253) ((-108 . -1094) T) ((-116 . -1052) 82240) ((-708 . -363) T) ((-500 . -602) 82215) ((-697 . -111) 82200) ((-436 . -102) T) ((-45 . -1143) 82150) ((-116 . -111) 82135) ((-633 . -717) T) ((-605 . -717) T) ((-812 . -514) 82068) ((-1032 . -1209) T) ((-940 . -151) 82052) ((-1217 . -611) 82034) ((-1166 . -452) 81965) ((-1160 . -1094) T) ((-1152 . -1094) T) ((-525 . -102) T) ((-520 . -102) 81915) ((-1136 . -644) 81889) ((-1119 . -452) 81840) ((-1081 . -1213) 81819) ((-779 . -1213) 81798) ((-777 . -1213) 81777) ((-62 . -1209) T) ((-477 . -611) 81729) ((-477 . -612) 81651) ((-1081 . -556) 81582) ((-991 . -1094) T) ((-779 . -556) 81493) ((-777 . -556) 81424) ((-482 . -411) 81393) ((-621 . -917) 81372) ((-454 . -1213) 81351) ((-728 . -309) 81338) ((-697 . -614) 81310) ((-398 . -611) 81292) ((-671 . -514) 81225) ((-660 . -25) T) ((-660 . -21) T) ((-454 . -556) 81156) ((-355 . -25) T) ((-355 . -21) T) ((-117 . -917) T) ((-117 . -817) NIL) ((-352 . -25) T) ((-352 . -21) T) ((-344 . -25) T) ((-344 . -21) T) ((-264 . -25) T) ((-264 . -21) T) ((-247 . -25) T) ((-247 . -21) T) ((-83 . -384) T) ((-83 . -395) T) ((-134 . -614) 81138) ((-116 . -614) 81110) ((-1261 . -611) 81092) ((-1215 . -847) T) ((-1203 . -1106) T) ((-1203 . -23) T) ((-1161 . -309) 80977) ((-1120 . -309) 80964) ((-1074 . -714) 80832) ((-863 . -644) 80792) ((-940 . -977) 80776) ((-907 . -21) T) ((-289 . -172) T) ((-907 . -25) T) ((-311 . -93) T) ((-869 . -847) 80727) ((-708 . -1106) T) ((-708 . -23) T) ((-697 . -1046) T) ((-643 . -1094) 80705) 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. -611) 77339) ((-1076 . -612) 77320) ((-407 . -906) 77299) ((-50 . -1106) T) ((-1021 . -917) T) ((-1000 . -723) T) ((-709 . -883) NIL) ((-581 . -1106) T) ((-518 . -1106) T) ((-840 . -644) 77272) ((-1203 . -131) T) ((-1161 . -400) 77224) ((-1001 . -309) NIL) ((-812 . -489) 77208) ((-354 . -917) T) ((-1150 . -34) T) ((-407 . -644) 77160) ((-50 . -23) T) ((-708 . -131) T) ((-709 . -1035) 77040) ((-581 . -23) T) ((-108 . -514) NIL) ((-518 . -23) T) ((-169 . -409) 77011) ((-1134 . -1094) T) ((-1274 . -1273) 76995) ((-697 . -792) T) ((-697 . -789) T) ((-1114 . -307) T) ((-379 . -147) T) ((-280 . -611) 76977) ((-1222 . -989) 76947) ((-48 . -917) T) ((-671 . -489) 76931) ((-251 . -1266) 76901) ((-250 . -1266) 76871) ((-1170 . -847) T) ((-1107 . -172) 76850) ((-1114 . -1019) T) ((-1043 . -34) T) ((-833 . -147) 76829) ((-833 . -145) 76808) ((-734 . -107) 76792) ((-610 . -132) T) ((-482 . -1094) 76582) ((-1172 . -1053) T) ((-868 . -452) T) ((-85 . -1209) T) ((-240 . -38) 76552) ((-141 . -107) 76534) ((-709 . -377) 76518) ((-830 . -614) 76386) ((-1114 . -545) T) ((-579 . -102) T) ((-129 . -490) 76368) ((-390 . -1052) 76352) ((-1282 . -723) T) ((-1166 . -946) 76321) ((-129 . -611) 76288) ((-52 . -611) 76270) ((-1119 . -946) 76237) ((-649 . -411) 76221) ((-1271 . -1053) T) ((-619 . -1052) 76205) ((-658 . -25) T) ((-658 . -21) T) ((-1152 . -514) NIL) ((-1251 . -102) T) ((-1244 . -102) T) ((-390 . -111) 76184) ((-222 . -254) 76168) ((-1223 . -102) T) ((-1050 . -1094) T) ((-1001 . -1145) T) ((-1050 . -1049) 76108) ((-815 . -1094) T) ((-343 . -1213) T) ((-633 . -644) 76092) ((-619 . -111) 76071) ((-605 . -644) 76055) ((-595 . -102) T) ((-311 . -490) 76036) ((-585 . -131) T) ((-594 . -102) T) ((-414 . -1094) T) ((-385 . -1094) T) ((-311 . -611) 76002) ((-227 . -1094) 75980) ((-643 . -514) 75913) ((-630 . -514) 75757) ((-830 . -1046) 75736) ((-641 . -151) 75720) ((-343 . -556) T) ((-709 . -897) 75663) ((-550 . -229) 75613) ((-1251 . -284) 75579) ((-1074 . -290) 75530) ((-487 . -845) T) ((-223 . -1106) T) ((-1244 . -284) 75496) ((-1223 . -284) 75462) ((-1001 . -38) 75412) ((-217 . -845) T) ((-1203 . -493) 75378) ((-911 . -38) 75330) ((-840 . -791) 75309) ((-840 . -788) 75288) ((-840 . -723) 75267) ((-359 . -290) T) ((-353 . -290) T) ((-345 . -290) T) ((-169 . -452) 75198) ((-427 . -38) 75182) ((-108 . -290) T) ((-223 . -23) T) ((-407 . -791) 75161) ((-407 . -788) 75140) ((-407 . -723) T) ((-500 . -288) 75115) ((-477 . -1052) 75080) ((-654 . -131) T) ((-619 . -614) 75049) ((-1107 . -514) 74982) ((-336 . -131) T) ((-169 . -402) 74961) ((-482 . -714) 74903) ((-812 . -286) 74880) ((-477 . -111) 74836) ((-649 . -1053) T) ((-1232 . -452) 74767) ((-1270 . -1077) T) ((-1269 . -1077) T) ((-1081 . -131) T) ((-1050 . -714) 74709) ((-264 . -847) 74688) ((-247 . -847) 74667) ((-779 . -131) T) ((-777 . -131) T) ((-571 . -452) T) ((-1024 . -514) 74600) ((-619 . -1046) T) ((-591 . -1094) T) ((-533 . -173) T) ((-461 . -131) T) ((-454 . -131) T) ((-45 . -1094) T) ((-385 . -714) 74570) ((-814 . -1094) T) ((-476 . -514) 74503) ((-463 . -514) 74436) ((-453 . -367) 74406) ((-45 . -608) 74385) ((-316 . -302) T) ((-477 . -614) 74335) ((-666 . -611) 74297) ((-59 . -847) 74276) ((-1223 . -309) 74161) ((-548 . -611) 74143) ((-1001 . -400) 74125) ((-812 . -602) 74102) ((-516 . -847) 74081) ((-496 . -847) 74060) ((-40 . -1213) T) ((-996 . -1035) 73956) ((-50 . -131) T) ((-581 . -131) T) ((-518 . -131) T) ((-294 . -644) 73816) ((-343 . -329) 73793) ((-343 . -363) T) ((-322 . -323) 73770) ((-319 . -286) 73755) ((-40 . -556) T) ((-379 . -1194) T) ((-379 . -1197) T) ((-1032 . -1185) 73730) ((-1182 . -235) 73680) ((-1161 . -231) 73632) ((-330 . -1094) T) ((-379 . -95) T) ((-379 . -35) T) ((-1032 . -107) 73578) ((-477 . -1046) T) ((-479 . -235) 73528) ((-1153 . -489) 73462) ((-1283 . -1052) 73446) ((-381 . -1052) 73430) ((-477 . -243) T) ((-813 . -102) T) ((-711 . -147) 73409) ((-711 . -145) 73388) ((-484 . -489) 73372) ((-485 . -335) 73341) ((-1283 . -111) 73320) ((-512 . -1094) T) ((-482 . -172) 73299) ((-996 . -377) 73283) ((-413 . -102) T) ((-381 . -111) 73262) ((-996 . -338) 73246) ((-279 . -980) 73230) ((-278 . -980) 73214) ((-1281 . -611) 73196) ((-1279 . -611) 73178) ((-110 . -514) NIL) ((-1166 . -1235) 73162) ((-851 . -849) 73146) ((-1172 . -1094) T) ((-103 . -1209) T) ((-949 . -946) 73107) ((-814 . -714) 73049) ((-1223 . -1145) NIL) ((-481 . -946) 72994) ((-1057 . -143) T) ((-60 . -102) 72972) ((-44 . -611) 72954) ((-78 . -611) 72936) ((-351 . -644) 72881) ((-1271 . -1094) T) ((-511 . -847) T) ((-343 . -1106) T) ((-295 . -1094) T) ((-996 . -897) 72840) ((-295 . -608) 72819) ((-1283 . -614) 72768) ((-1251 . -38) 72665) ((-1244 . -38) 72506) ((-1223 . -38) 72302) ((-487 . -1053) T) ((-381 . -614) 72286) ((-217 . -1053) T) ((-343 . -23) T) ((-152 . -611) 72268) ((-830 . -792) 72247) ((-830 . -789) 72226) ((-1208 . -614) 72207) ((-595 . -38) 72180) ((-594 . -38) 72077) ((-867 . -556) T) ((-223 . -131) T) ((-319 . -999) 72043) ((-79 . -611) 72025) 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-1094) T) ((-1081 . -25) T) ((-1081 . -21) T) ((-531 . -789) T) ((-531 . -792) T) ((-117 . -1213) T) ((-960 . -1053) T) ((-621 . -556) T) ((-779 . -25) T) ((-779 . -21) T) ((-777 . -21) T) ((-777 . -25) T) ((-732 . -1053) T) ((-712 . -1053) T) ((-666 . -1052) 68869) ((-517 . -1077) T) ((-461 . -25) T) ((-117 . -556) T) ((-461 . -21) T) ((-454 . -25) T) ((-454 . -21) T) ((-1281 . -1052) 68853) ((-1136 . -1035) 68749) ((-814 . -290) 68728) ((-1279 . -1052) 68712) ((-820 . -1094) T) ((-1243 . -1194) 68678) ((-963 . -964) T) ((-666 . -111) 68657) ((-295 . -514) 68449) ((-1243 . -1197) 68415) ((-1243 . -95) 68381) ((-1226 . -102) 68359) ((-251 . -309) 68297) ((-250 . -309) 68235) ((-1223 . -231) 68187) ((-1153 . -612) NIL) ((-1153 . -611) 68169) ((-1222 . -1194) 68135) ((-1222 . -1197) 68101) ((-1217 . -368) T) ((-96 . -93) T) ((-1214 . -841) T) ((-1136 . -377) 68085) ((-1114 . -817) T) ((-1114 . -917) T) ((-1107 . -602) 68062) ((-1074 . -612) 68046) ((-484 . -611) 67978) ((-812 . -288) 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. -102) T) ((-1119 . -102) T) ((-851 . -102) T) ((-227 . -489) 67106) ((-1281 . -111) 67085) ((-1279 . -111) 67064) ((-44 . -1052) 67048) ((-1232 . -1235) 67032) ((-852 . -849) 67016) ((-1281 . -614) 66962) ((-1172 . -290) 66941) ((-110 . -286) 66916) ((-1214 . -1094) T) ((-128 . -151) 66898) ((-1136 . -897) 66857) ((-44 . -111) 66836) ((-1175 . -1254) T) ((-1160 . -490) 66817) ((-1160 . -611) 66783) ((-1152 . -612) NIL) ((-666 . -1046) T) ((-1152 . -611) 66765) ((-1058 . -608) 66740) ((-1058 . -1094) T) ((-991 . -490) 66721) ((-991 . -611) 66687) ((-74 . -441) T) ((-74 . -395) T) ((-699 . -1094) T) ((-152 . -1052) 66671) ((-666 . -233) 66650) ((-571 . -554) 66634) ((-355 . -147) 66613) ((-355 . -145) 66564) ((-352 . -147) 66543) ((-352 . -145) 66494) ((-344 . -147) 66473) ((-344 . -145) 66424) ((-264 . -145) 66403) ((-264 . -147) 66382) ((-251 . -38) 66352) ((-247 . -147) 66331) ((-117 . -363) T) ((-247 . -145) 66310) ((-250 . -38) 66280) ((-152 . -111) 66259) ((-1000 . -1035) 66147) 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-1053) T) ((-495 . -1053) T) ((-407 . -452) T) ((-359 . -131) T) ((-316 . -400) 141389) ((-313 . -400) 141350) ((-353 . -131) T) ((-345 . -131) T) ((-1175 . -1094) T) ((-1114 . -38) 141337) ((-1088 . -611) 141304) ((-108 . -131) T) ((-951 . -1094) T) ((-918 . -1094) T) ((-768 . -1094) T) ((-668 . -1094) T) ((-697 . -147) T) ((-116 . -147) T) ((-1281 . -21) T) ((-1281 . -25) T) ((-1279 . -21) T) ((-1279 . -25) T) ((-660 . -1052) 141288) ((-531 . -847) T) ((-500 . -847) T) ((-355 . -1052) 141240) ((-352 . -1052) 141192) ((-344 . -1052) 141144) ((-251 . -1209) T) ((-250 . -1209) T) ((-264 . -1052) 140987) ((-247 . -1052) 140830) ((-660 . -111) 140809) ((-547 . -841) T) ((-355 . -111) 140747) ((-352 . -111) 140685) ((-344 . -111) 140623) ((-264 . -111) 140452) ((-247 . -111) 140281) ((-814 . -1213) 140260) ((-621 . -411) 140244) ((-44 . -21) T) ((-44 . -25) T) ((-812 . -637) 140150) ((-814 . -556) 140129) ((-251 . -1035) 139956) ((-250 . -1035) 139783) ((-126 . -119) 139767) ((-907 . -1052) 139732) ((-709 . -102) T) ((-695 . -1053) T) ((-536 . -616) 139635) ((-343 . -172) T) ((-88 . -611) 139617) ((-152 . -21) T) ((-152 . -25) T) ((-907 . -111) 139573) ((-40 . -714) 139518) ((-867 . -1094) T) ((-660 . -614) 139495) ((-642 . -614) 139476) ((-355 . -614) 139413) ((-352 . -614) 139350) ((-547 . -1094) T) ((-344 . -614) 139287) ((-327 . -612) 139248) ((-327 . -611) 139160) ((-264 . -614) 138913) ((-247 . -614) 138698) ((-1222 . -789) 138651) ((-1222 . -792) 138604) ((-251 . -377) 138573) ((-250 . -377) 138542) ((-650 . -38) 138512) ((-606 . -34) T) ((-482 . -1106) 138422) ((-475 . -34) T) ((-1107 . -131) 138292) ((-961 . -25) 138103) ((-907 . -614) 138053) ((-871 . -611) 138035) ((-961 . -21) 137990) ((-812 . -21) 137900) ((-812 . -25) 137751) ((-1215 . -368) T) ((-621 . -1053) T) ((-1172 . -556) 137730) ((-1166 . -47) 137707) ((-355 . -1046) T) ((-352 . -1046) T) ((-482 . -23) 137577) ((-344 . -1046) T) ((-247 . -1046) T) ((-264 . -1046) T) ((-1119 . -47) 137549) 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-231) 136794) ((-1166 . -883) NIL) ((-55 . -1094) T) ((-1119 . -883) 136653) ((-129 . -847) T) ((-1166 . -1035) 136533) ((-1119 . -1035) 136416) ((-183 . -611) 136398) ((-851 . -1035) 136294) ((-779 . -286) 136221) ((-814 . -1106) T) ((-1031 . -723) T) ((-600 . -647) 136205) ((-1043 . -973) 136134) ((-996 . -102) T) ((-814 . -23) T) ((-709 . -1145) 136112) ((-690 . -1053) T) ((-600 . -373) 136096) ((-351 . -452) T) ((-343 . -290) T) ((-1260 . -1094) T) ((-248 . -1094) T) ((-399 . -102) T) ((-289 . -21) T) ((-289 . -25) T) ((-361 . -723) T) ((-707 . -1094) T) ((-695 . -1094) T) ((-361 . -473) T) ((-1203 . -611) 136078) ((-1166 . -377) 136062) ((-1119 . -377) 136046) ((-1021 . -411) 136008) ((-141 . -229) 135990) ((-379 . -791) T) ((-379 . -788) T) ((-867 . -172) T) ((-379 . -723) T) ((-708 . -611) 135972) ((-709 . -38) 135801) ((-1259 . -1257) 135785) ((-351 . -402) T) ((-1259 . -1094) 135735) ((-580 . -714) 135722) ((-564 . -714) 135709) ((-495 . -714) 135674) ((-316 . -627) 135653) 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134910) ((-677 . -614) 134891) ((-672 . -614) 134872) ((-487 . -556) T) ((-478 . -614) 134853) ((-359 . -25) T) ((-359 . -21) T) ((-353 . -25) T) ((-217 . -556) T) ((-353 . -21) T) ((-345 . -25) T) ((-345 . -21) T) ((-245 . -614) 134830) ((-138 . -614) 134811) ((-137 . -614) 134792) ((-133 . -614) 134773) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1053) T) ((-580 . -172) T) ((-564 . -172) T) ((-495 . -172) T) ((-654 . -611) 134755) ((-734 . -733) 134739) ((-336 . -611) 134721) ((-68 . -383) T) ((-68 . -395) T) ((-1096 . -107) 134705) ((-1057 . -883) 134687) ((-949 . -883) 134612) ((-649 . -1106) T) ((-621 . -714) 134599) ((-481 . -883) NIL) ((-1140 . -102) T) ((-1088 . -616) 134583) ((-1057 . -1035) 134565) ((-97 . -611) 134547) ((-477 . -147) T) ((-949 . -1035) 134427) ((-117 . -714) 134372) ((-649 . -23) T) ((-481 . -1035) 134248) ((-1081 . -612) NIL) ((-1081 . -611) 134230) ((-779 . -612) NIL) ((-779 . -611) 134191) ((-777 . -612) 133825) ((-777 . -611) 133739) ((-1107 . -637) 133645) ((-461 . -611) 133627) ((-454 . -611) 133609) ((-454 . -612) 133470) ((-1032 . -229) 133416) ((-869 . -906) 133395) ((-126 . -34) T) ((-814 . -131) T) ((-645 . -611) 133377) ((-578 . -102) T) ((-355 . -1278) 133361) ((-352 . -1278) 133345) ((-344 . -1278) 133329) ((-127 . -514) 133262) ((-121 . -514) 133195) ((-511 . -789) T) ((-511 . -792) T) ((-510 . -791) T) ((-103 . -309) 133133) ((-222 . -102) 133111) ((-690 . -1094) T) ((-695 . -172) T) ((-869 . -644) 133063) ((-65 . -384) T) ((-275 . -611) 133045) ((-65 . -395) T) ((-949 . -377) 133029) ((-867 . -290) T) ((-50 . -611) 133011) ((-996 . -38) 132959) ((-581 . -611) 132941) ((-481 . -377) 132925) ((-581 . -612) 132907) ((-518 . -611) 132889) ((-907 . -1278) 132876) ((-868 . -1209) T) ((-697 . -452) T) ((-495 . -514) 132842) ((-487 . -363) T) ((-355 . -368) 132821) ((-352 . -368) 132800) ((-344 . -368) 132779) ((-711 . -723) T) ((-217 . -363) T) ((-116 . -452) T) ((-1282 . -1273) 132763) ((-868 . -881) 132740) ((-868 . -883) NIL) ((-961 . -847) 132639) ((-812 . -847) 132590) ((-1216 . -102) T) ((-650 . -652) 132574) ((-1195 . -34) T) ((-171 . -611) 132556) ((-1107 . -21) 132466) ((-1107 . -25) 132317) ((-868 . -1035) 132294) ((-949 . -897) 132275) ((-1232 . -47) 132252) ((-907 . -368) T) ((-59 . -647) 132236) ((-516 . -647) 132220) ((-481 . -897) 132197) ((-71 . -441) T) ((-71 . -395) T) ((-496 . -647) 132181) ((-59 . -373) 132165) ((-621 . -172) T) ((-516 . -373) 132149) ((-496 . -373) 132133) ((-824 . -705) 132117) ((-1166 . -307) 132096) ((-1172 . -131) T) ((-117 . -172) T) ((-1140 . -309) 132034) ((-169 . -1209) T) ((-633 . -741) 132018) ((-605 . -741) 132002) ((-1271 . -131) T) ((-1244 . -917) 131981) ((-1223 . -917) 131960) ((-1223 . -817) NIL) ((-690 . -714) 131910) ((-1222 . -906) 131863) ((-1021 . -1094) T) ((-868 . -377) 131840) ((-868 . -338) 131817) ((-902 . -1106) T) ((-169 . -881) 131801) ((-169 . -883) 131726) ((-487 . -1106) T) ((-354 . -1094) T) ((-217 . -1106) T) ((-76 . -441) T) ((-76 . -395) T) ((-169 . -1035) 131622) ((-319 . -847) T) ((-1259 . -514) 131555) ((-1243 . -644) 131452) ((-1222 . -644) 131322) ((-869 . -791) 131301) ((-869 . -788) 131280) ((-869 . -723) T) ((-487 . -23) T) ((-223 . -611) 131262) ((-174 . -452) T) ((-222 . -309) 131200) ((-86 . -441) T) ((-86 . -395) T) ((-217 . -23) T) ((-1283 . -1276) 131179) ((-580 . -290) T) ((-564 . -290) T) ((-673 . -1035) 131163) ((-495 . -290) T) ((-136 . -470) 131118) ((-48 . -1094) T) ((-709 . -231) 131102) ((-868 . -897) NIL) ((-1232 . -883) NIL) ((-886 . -102) T) ((-882 . -102) T) ((-388 . -1094) T) ((-169 . -377) 131086) ((-169 . -338) 131070) ((-1232 . -1035) 130950) ((-852 . -1035) 130846) ((-1136 . -102) T) ((-649 . -131) T) ((-117 . -514) 130754) ((-658 . -789) 130733) ((-658 . -792) 130712) ((-571 . -1035) 130694) ((-294 . -1266) 130664) ((-863 . -102) T) ((-960 . -556) 130643) ((-1203 . -1052) 130526) ((-482 . -637) 130432) ((-901 . -1094) T) ((-1021 . -714) 130369) ((-708 . -1052) 130334) ((-615 . -102) T) ((-600 . -34) T) ((-1141 . -1209) T) ((-1203 . -111) 130203) ((-474 . -644) 130100) ((-354 . -714) 130045) ((-169 . -897) 130004) ((-695 . -290) T) ((-690 . -172) T) ((-708 . -111) 129960) ((-1287 . -1053) T) ((-1232 . -377) 129944) ((-418 . -1213) 129922) ((-1112 . -611) 129904) ((-313 . -845) NIL) ((-418 . -556) T) ((-225 . -307) T) ((-1222 . -788) 129857) ((-1222 . -791) 129810) ((-1243 . -723) T) ((-1222 . -723) T) ((-48 . -714) 129775) ((-225 . -1019) T) ((-351 . -1266) 129752) ((-1245 . -411) 129718) ((-715 . -723) T) ((-1232 . -897) 129661) ((-1203 . -614) 129543) ((-112 . -611) 129525) ((-112 . -612) 129507) ((-715 . -473) T) ((-708 . -614) 129457) ((-482 . -21) 129367) ((-127 . -489) 129351) ((-121 . -489) 129335) ((-482 . -25) 129186) ((-621 . -290) T) ((-585 . -1052) 129161) ((-437 . -1094) T) ((-1057 . -307) T) ((-117 . -290) T) ((-1098 . -102) T) ((-1000 . -102) T) ((-585 . -111) 129129) ((-1136 . -309) 129067) ((-1203 . -1046) T) ((-1057 . -1019) T) ((-66 . -1209) T) ((-1050 . -25) T) ((-1050 . -21) T) ((-708 . -1046) T) ((-385 . -21) T) ((-385 . -25) T) ((-690 . -514) NIL) ((-1021 . -172) T) ((-708 . -243) T) ((-1057 . -545) T) ((-506 . -102) T) ((-502 . -102) T) ((-354 . -172) T) ((-343 . -611) 129049) ((-394 . -611) 129031) ((-474 . -723) T) ((-1114 . -845) T) ((-889 . -1035) 128999) ((-108 . -847) T) ((-654 . -1052) 128983) ((-487 . -131) T) ((-1245 . -1053) T) ((-217 . -131) T) ((-1150 . -102) 128961) ((-99 . -1094) T) ((-245 . -662) 128945) ((-245 . -647) 128929) ((-654 . -111) 128908) ((-585 . -614) 128892) ((-316 . -411) 128876) ((-245 . -373) 128860) ((-1153 . -235) 128807) ((-996 . -231) 128791) ((-74 . -1209) T) ((-48 . -172) T) ((-697 . -387) T) ((-697 . -143) T) ((-1282 . -102) T) ((-1189 . -614) 128773) ((-1081 . -1052) 128616) ((-264 . -906) 128595) ((-247 . -906) 128574) ((-779 . -1052) 128397) ((-777 . -1052) 128240) ((-606 . -1209) T) ((-1158 . -611) 128222) ((-1081 . -111) 128051) ((-1043 . -102) T) ((-475 . -1209) T) 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-1106) T) ((-316 . -1053) 126086) ((-313 . -1053) T) ((-128 . -1209) T) ((-779 . -614) 125834) ((-777 . -614) 125600) ((-654 . -1046) T) ((-1287 . -1094) T) ((-454 . -614) 125385) ((-169 . -307) 125316) ((-418 . -23) T) ((-40 . -611) 125298) ((-40 . -612) 125282) ((-108 . -989) 125264) ((-116 . -866) 125248) ((-645 . -614) 125232) ((-48 . -514) 125198) ((-1195 . -1007) 125182) ((-1175 . -611) 125149) ((-1182 . -34) T) ((-951 . -611) 125115) ((-918 . -611) 125097) ((-1107 . -847) 125048) ((-768 . -611) 125030) ((-668 . -611) 125012) ((-1150 . -309) 124950) ((-479 . -34) T) ((-1086 . -1209) T) ((-477 . -452) T) ((-1135 . -34) T) ((-1081 . -1046) T) ((-50 . -614) 124919) ((-779 . -1046) T) ((-777 . -1046) T) ((-643 . -235) 124903) ((-630 . -235) 124849) ((-581 . -614) 124799) ((-518 . -614) 124729) ((-1232 . -307) 124708) ((-1081 . -326) 124669) ((-454 . -1046) T) ((-1172 . -21) T) ((-1081 . -233) 124648) ((-779 . -326) 124625) ((-779 . -233) T) ((-777 . -326) 124597) ((-728 . -1213) 124576) ((-327 . -647) 124560) ((-1172 . -25) T) ((-59 . -34) T) ((-519 . -34) T) ((-516 . -34) T) ((-454 . -326) 124539) ((-327 . -373) 124523) ((-497 . -34) T) ((-496 . -34) T) ((-1000 . -1145) NIL) ((-728 . -556) 124454) ((-633 . -102) T) ((-605 . -102) T) ((-355 . -723) T) ((-352 . -723) T) ((-344 . -723) T) ((-264 . -723) T) ((-247 . -723) T) ((-1043 . -309) 124362) ((-898 . -1094) 124340) ((-50 . -1046) T) ((-1271 . -21) T) ((-1271 . -25) T) ((-1168 . -556) 124319) ((-1167 . -1213) 124298) ((-581 . -1046) T) ((-518 . -1046) T) ((-1161 . -1213) 124277) ((-361 . -1035) 124261) ((-322 . -1035) 124245) ((-1021 . -290) T) ((-379 . -883) 124227) ((-1167 . -556) 124178) ((-1161 . -556) 124129) ((-1000 . -38) 124074) ((-796 . -1106) T) ((-907 . -723) T) ((-581 . -243) T) ((-581 . -233) T) ((-518 . -233) T) ((-518 . -243) T) ((-1120 . -556) 124053) ((-354 . -290) T) ((-643 . -691) 124037) ((-379 . -1035) 123997) ((-1114 . -1053) T) ((-103 . -125) 123981) ((-796 . -23) T) ((-1281 . -1276) 123957) ((-1259 . -286) 123934) ((-407 . -309) 123899) ((-1279 . -1276) 123878) ((-1245 . -1094) T) ((-867 . -611) 123860) ((-833 . -1035) 123829) ((-203 . -784) T) ((-202 . -784) T) ((-201 . -784) T) ((-200 . -784) T) ((-199 . -784) T) ((-198 . -784) T) ((-197 . -784) T) ((-196 . -784) T) ((-195 . -784) T) ((-194 . -784) T) ((-547 . -611) 123811) ((-495 . -999) T) ((-274 . -836) T) ((-273 . -836) T) ((-272 . -836) T) ((-271 . -836) T) ((-48 . -290) T) ((-270 . -836) T) ((-269 . -836) T) ((-268 . -836) T) ((-193 . -784) T) ((-610 . -847) T) ((-650 . -411) 123795) ((-223 . -614) 123757) ((-110 . -847) T) ((-649 . -21) T) ((-649 . -25) T) ((-1282 . -38) 123727) ((-117 . -286) 123678) ((-1259 . -19) 123662) ((-1259 . -602) 123639) ((-1272 . -1094) T) ((-1071 . -1094) T) ((-984 . -1094) T) ((-960 . -131) T) ((-734 . -1094) T) ((-732 . -131) T) ((-712 . -131) T) ((-511 . -790) T) ((-407 . -1145) 123617) ((-453 . -131) T) ((-511 . -791) T) ((-223 . -1046) T) ((-294 . -102) 123399) ((-141 . -1094) T) ((-695 . -999) T) ((-91 . -1209) T) ((-127 . -611) 123331) ((-121 . -611) 123263) ((-1287 . -172) T) ((-1167 . -363) 123242) ((-1161 . -363) 123221) ((-316 . -1094) T) ((-418 . -131) T) ((-313 . -1094) T) ((-407 . -38) 123173) ((-1127 . -102) T) ((-1245 . -714) 123065) ((-650 . -1053) T) ((-1129 . -1254) T) ((-319 . -145) 123044) ((-319 . -147) 123023) ((-139 . -1094) T) ((-136 . -1094) T) ((-114 . -1094) T) ((-855 . -102) T) ((-580 . -611) 123005) ((-564 . -612) 122904) ((-564 . -611) 122886) ((-495 . -611) 122868) ((-495 . -612) 122813) ((-485 . -23) T) ((-482 . -847) 122764) ((-487 . -637) 122746) ((-962 . -611) 122728) ((-217 . -637) 122710) ((-225 . -404) T) ((-658 . -644) 122694) ((-55 . -611) 122676) ((-1166 . -917) 122655) ((-728 . -1106) T) ((-351 . -102) T) ((-1208 . -1077) T) ((-1114 . -841) T) ((-815 . -847) T) ((-728 . -23) T) ((-343 . -1052) 122600) ((-1152 . -1151) T) ((-1141 . -107) 122584) ((-1168 . -1106) T) ((-1167 . -1106) T) ((-515 . -1035) 122568) 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. -1035) 115322) ((-264 . -1035) 115166) ((-247 . -1035) 115042) ((-117 . -111) 114971) ((-59 . -1209) T) ((-519 . -1209) T) ((-516 . -1209) T) ((-497 . -1209) T) ((-496 . -1209) T) ((-437 . -611) 114953) ((-434 . -611) 114935) ((-3 . -102) T) ((-1024 . -1202) 114904) ((-830 . -102) T) ((-685 . -57) 114862) ((-695 . -1046) T) ((-50 . -644) 114836) ((-289 . -452) T) ((-476 . -1202) 114805) ((0 . -102) T) ((-581 . -644) 114770) ((-518 . -644) 114715) ((-49 . -102) T) ((-907 . -1035) 114702) ((-695 . -243) T) ((-1074 . -409) 114681) ((-728 . -637) 114629) ((-996 . -1094) T) ((-709 . -172) 114520) ((-621 . -614) 114415) ((-487 . -989) 114397) ((-264 . -377) 114381) ((-247 . -377) 114365) ((-399 . -1094) T) ((-1023 . -102) 114343) ((-339 . -38) 114327) ((-217 . -989) 114309) ((-117 . -614) 114239) ((-174 . -38) 114171) ((-1243 . -307) 114150) ((-1222 . -307) 114129) ((-654 . -723) T) ((-99 . -611) 114111) ((-1161 . -637) 114063) ((-485 . -25) T) ((-485 . -21) T) ((-1222 . -1019) 114015) 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112296) ((-690 . -243) T) ((-690 . -233) NIL) ((-840 . -845) 112275) ((-695 . -792) T) ((-695 . -789) T) ((-1000 . -411) 112252) ((-354 . -111) 112181) ((-379 . -917) T) ((-407 . -845) 112160) ((-709 . -290) 112071) ((-223 . -723) T) ((-1251 . -493) 112037) ((-1244 . -493) 112003) ((-1223 . -493) 111969) ((-578 . -1094) T) ((-316 . -999) 111948) ((-222 . -1094) 111926) ((-1216 . -841) T) ((-319 . -970) 111888) ((-105 . -102) T) ((-48 . -1052) 111853) ((-1283 . -102) T) ((-381 . -102) T) ((-48 . -111) 111809) ((-1001 . -637) 111791) ((-1245 . -611) 111773) ((-531 . -102) T) ((-500 . -102) T) ((-1127 . -1128) 111757) ((-152 . -1266) 111741) ((-245 . -1209) T) ((-1208 . -102) T) ((-1021 . -614) 111678) ((-1166 . -1213) 111657) ((-354 . -614) 111587) ((-1119 . -1213) 111566) ((-240 . -21) 111476) ((-240 . -25) 111327) ((-127 . -119) 111311) ((-121 . -119) 111295) ((-44 . -741) 111279) ((-1166 . -556) 111190) ((-1119 . -556) 111121) ((-1216 . -1094) T) ((-1032 . -286) 111096) ((-1160 . 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-721) 107922) ((-1287 . -1046) T) ((-813 . -637) 107870) ((-294 . -1053) 107812) ((-169 . -1213) 107717) ((-225 . -1106) T) ((-324 . -23) T) ((-1161 . -989) 107669) ((-840 . -1094) T) ((-1245 . -1052) 107574) ((-1120 . -737) 107553) ((-1243 . -917) 107532) ((-1222 . -917) 107511) ((-867 . -723) T) ((-169 . -556) 107422) ((-580 . -644) 107409) ((-564 . -644) 107396) ((-407 . -1094) T) ((-263 . -1094) T) ((-213 . -611) 107378) ((-495 . -644) 107343) ((-225 . -23) T) ((-1222 . -817) 107296) ((-1281 . -102) T) ((-354 . -1278) 107273) ((-1279 . -102) T) ((-1245 . -111) 107165) ((-144 . -611) 107147) ((-990 . -131) T) ((-44 . -102) T) ((-240 . -847) 107098) ((-1232 . -1213) 107077) ((-103 . -489) 107061) ((-1282 . -714) 107031) ((-1081 . -47) 106992) ((-1057 . -1106) T) ((-949 . -1106) T) ((-127 . -34) T) ((-121 . -34) T) ((-779 . -47) 106969) ((-777 . -47) 106941) ((-1232 . -556) 106852) ((-354 . -368) T) ((-481 . -1106) T) ((-1166 . -131) T) ((-1119 . -131) T) ((-454 . -47) 106831) ((-868 . -363) T) ((-851 . -131) T) ((-152 . -102) T) ((-1057 . -23) T) ((-949 . -23) T) ((-571 . -556) T) ((-813 . -25) T) ((-813 . -21) T) ((-1136 . -514) 106764) ((-591 . -1077) T) ((-585 . -1035) 106748) ((-1245 . -614) 106622) ((-481 . -23) T) ((-351 . -1053) T) ((-1203 . -897) 106603) ((-666 . -309) 106541) ((-1107 . -1266) 106511) ((-695 . -644) 106476) ((-1000 . -172) T) ((-960 . -145) 106455) ((-633 . -1094) T) ((-605 . -1094) T) ((-960 . -147) 106434) ((-1001 . -847) T) ((-732 . -147) 106413) ((-732 . -145) 106392) ((-968 . -847) T) ((-474 . -917) 106371) ((-316 . -1052) 106281) ((-313 . -1052) 106210) ((-996 . -286) 106168) ((-407 . -714) 106120) ((-697 . -845) T) ((-1245 . -1046) T) ((-316 . -111) 106016) ((-313 . -111) 105929) ((-961 . -102) T) ((-812 . -102) 105719) ((-709 . -612) NIL) ((-709 . -611) 105701) ((-654 . -1035) 105597) ((-1245 . -326) 105541) ((-1032 . -288) 105516) ((-580 . -723) T) ((-564 . -791) T) ((-169 . -363) 105467) ((-564 . -788) T) ((-564 . -723) T) ((-495 . -723) T) ((-1140 . -489) 105451) ((-1081 . -883) NIL) ((-868 . -1106) T) ((-117 . -906) NIL) ((-1281 . -1280) 105427) ((-1279 . -1280) 105406) ((-779 . -883) NIL) ((-777 . -883) 105265) ((-1274 . -25) T) ((-1274 . -21) T) ((-1206 . -102) 105243) ((-1100 . -395) T) ((-621 . -644) 105230) ((-454 . -883) NIL) ((-671 . -102) 105208) ((-1081 . -1035) 105035) ((-868 . -23) T) ((-779 . -1035) 104894) ((-777 . -1035) 104751) ((-117 . -644) 104696) ((-454 . -1035) 104572) ((-316 . -614) 104136) ((-313 . -614) 104019) ((-645 . -1035) 104003) ((-625 . -102) T) ((-222 . -489) 103987) ((-1259 . -34) T) ((-136 . -614) 103971) ((-633 . -714) 103955) ((-605 . -714) 103939) ((-666 . -38) 103899) ((-319 . -102) T) ((-85 . -611) 103881) ((-50 . -1035) 103865) ((-1114 . -1052) 103852) ((-1081 . -377) 103836) ((-779 . -377) 103820) ((-695 . -723) T) ((-695 . -791) T) ((-695 . -788) T) ((-581 . -1035) 103807) ((-518 . -1035) 103784) ((-60 . -57) 103746) ((-324 . -131) T) ((-316 . -1046) 103636) ((-313 . -1046) T) ((-169 . -1106) T) ((-777 . -377) 103620) ((-45 . -151) 103570) ((-1001 . -989) 103552) ((-454 . -377) 103536) ((-407 . -172) T) ((-316 . -243) 103515) ((-313 . -243) T) ((-313 . -233) NIL) ((-294 . -1094) 103297) ((-225 . -131) T) ((-1114 . -111) 103282) ((-169 . -23) T) ((-796 . -147) 103261) ((-796 . -145) 103240) ((-251 . -637) 103146) ((-250 . -637) 103052) ((-319 . -284) 103018) ((-1150 . -514) 102951) ((-1127 . -1094) T) ((-225 . -1055) T) ((-812 . -309) 102889) ((-1081 . -897) 102824) ((-779 . -897) 102767) ((-777 . -897) 102751) ((-1281 . -38) 102721) ((-1279 . -38) 102691) ((-1232 . -1106) T) ((-852 . -1106) T) ((-454 . -897) 102668) ((-855 . -1094) T) ((-1232 . -23) T) ((-1114 . -614) 102640) ((-571 . -1106) T) ((-852 . -23) T) ((-621 . -723) T) ((-355 . -917) T) ((-352 . -917) T) ((-289 . -102) T) ((-344 . -917) T) ((-1057 . -131) T) ((-967 . -1077) T) ((-949 . -131) T) ((-117 . -791) NIL) ((-117 . -788) NIL) ((-117 . -723) T) ((-690 . -906) NIL) ((-1043 . -514) 102541) ((-481 . -131) T) ((-571 . -23) T) ((-671 . -309) 102479) ((-633 . -758) T) ((-605 . -758) T) ((-1223 . -847) NIL) ((-1000 . -290) T) ((-251 . -21) T) ((-690 . -644) 102429) ((-351 . -1094) T) ((-251 . -25) T) ((-250 . -21) T) ((-250 . -25) T) ((-152 . -38) 102413) ((-2 . -102) T) ((-907 . -917) T) ((-482 . -1266) 102383) ((-223 . -1035) 102360) ((-1114 . -1046) T) ((-708 . -307) T) ((-294 . -714) 102302) ((-697 . -1053) T) ((-487 . -452) T) ((-407 . -514) 102214) ((-217 . -452) T) ((-1114 . -233) T) ((-295 . -151) 102164) ((-996 . -612) 102125) ((-996 . -611) 102107) ((-986 . -611) 102089) ((-116 . -1053) T) ((-650 . -1052) 102073) ((-225 . -493) T) ((-399 . -611) 102055) ((-399 . -612) 102032) ((-1050 . -1266) 102002) ((-650 . -111) 101981) ((-1136 . -489) 101965) ((-812 . -38) 101935) ((-63 . -441) T) ((-63 . -395) T) ((-1153 . -102) T) ((-868 . -131) T) ((-484 . -102) 101913) ((-1287 . -368) T) ((-1074 . -102) T) ((-1056 . -102) T) ((-351 . -714) 101858) ((-728 . -147) 101837) ((-728 . -145) 101816) ((-650 . -614) 101734) ((-1021 . -644) 101671) ((-523 . -1094) 101649) ((-359 . -102) T) ((-353 . -102) T) ((-345 . -102) T) ((-108 . -102) T) ((-504 . -1094) T) ((-354 . -644) 101594) ((-1166 . -637) 101542) ((-1119 . -637) 101490) ((-385 . -509) 101469) ((-830 . -845) 101448) ((-379 . -1213) T) ((-690 . -723) T) ((-339 . -1053) T) ((-1223 . -989) 101400) ((-174 . -1053) T) ((-103 . -611) 101332) ((-1168 . -145) 101311) ((-1168 . -147) 101290) ((-379 . -556) T) ((-1167 . -147) 101269) ((-1167 . -145) 101248) ((-1161 . -145) 101155) ((-407 . -290) T) ((-1161 . -147) 101062) ((-1120 . -147) 101041) ((-1120 . -145) 101020) ((-319 . -38) 100861) ((-169 . -131) T) ((-313 . -792) NIL) ((-313 . -789) NIL) ((-650 . -1046) T) ((-48 . -644) 100826) ((-890 . -614) 100803) ((-1160 . -102) T) ((-991 . -102) T) ((-990 . -21) T) ((-127 . -1007) 100787) ((-121 . -1007) 100771) ((-990 . -25) T) ((-898 . -119) 100755) ((-1152 . -102) T) ((-813 . -847) 100734) ((-1232 . 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-883) 94538) ((-1259 . -1209) T) ((-227 . -309) 94476) ((-144 . -368) T) ((-1043 . -612) 94418) ((-1043 . -611) 94361) ((-313 . -906) NIL) ((-1217 . -841) T) ((-695 . -1035) 94306) ((-708 . -917) T) ((-474 . -1213) 94285) ((-1167 . -452) 94264) ((-1161 . -452) 94243) ((-330 . -102) T) ((-869 . -1106) T) ((-316 . -644) 94064) ((-313 . -644) 93993) ((-474 . -556) 93944) ((-339 . -514) 93910) ((-550 . -151) 93860) ((-40 . -307) T) ((-840 . -611) 93842) ((-697 . -290) T) ((-869 . -23) T) ((-379 . -493) T) ((-1074 . -231) 93812) ((-512 . -102) T) ((-407 . -612) 93619) ((-407 . -611) 93601) ((-263 . -611) 93583) ((-116 . -290) T) ((-1245 . -723) T) ((-1243 . -363) 93562) ((-1222 . -363) 93541) ((-1272 . -34) T) ((-1217 . -1094) T) ((-117 . -1209) T) ((-108 . -231) 93523) ((-1172 . -102) T) ((-477 . -1094) T) ((-523 . -489) 93507) ((-734 . -34) T) ((-482 . -38) 93477) ((-141 . -34) T) ((-117 . -881) 93454) ((-117 . -883) NIL) ((-621 . -1035) 93337) ((-641 . -847) 93316) ((-1271 . -102) T) 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91262) ((-907 . -1213) T) ((-666 . -411) 91246) ((-863 . -111) 91211) ((-690 . -1035) 91156) ((-1001 . -452) T) ((-907 . -556) T) ((-533 . -611) 91138) ((-581 . -917) T) ((-474 . -1106) T) ((-518 . -917) T) ((-1150 . -288) 91115) ((-911 . -452) T) ((-65 . -611) 91097) ((-630 . -229) 91043) ((-474 . -23) T) ((-1114 . -791) T) ((-869 . -131) T) ((-1114 . -788) T) ((-1274 . -1276) 91022) ((-1114 . -723) T) ((-650 . -644) 90996) ((-294 . -611) 90737) ((-1136 . -614) 90655) ((-1032 . -34) T) ((-812 . -845) 90634) ((-580 . -307) T) ((-564 . -307) T) ((-495 . -307) T) ((-1283 . -714) 90604) ((-690 . -377) 90586) ((-690 . -338) 90568) ((-477 . -172) T) ((-381 . -714) 90538) ((-863 . -614) 90473) ((-868 . -847) NIL) ((-564 . -1019) T) ((-495 . -1019) T) ((-1127 . -611) 90455) ((-1107 . -238) 90434) ((-214 . -102) T) ((-1144 . -102) T) ((-71 . -611) 90416) ((-1136 . -1046) T) ((-1172 . -38) 90313) ((-855 . -611) 90295) ((-564 . -545) T) ((-666 . -1053) T) ((-728 . -946) 90248) ((-1136 . -233) 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. -23) T) ((-697 . -1046) T) ((-643 . -1094) 80705) ((-630 . -1094) T) ((-581 . -1213) T) ((-518 . -1213) T) ((-697 . -233) T) ((-630 . -608) 80680) ((-581 . -556) T) ((-518 . -556) T) ((-359 . -714) 80632) ((-339 . -1052) 80616) ((-353 . -714) 80568) ((-345 . -714) 80520) ((-174 . -1052) 80452) ((-174 . -111) 80363) ((-108 . -714) 80313) ((-339 . -111) 80292) ((-274 . -1094) T) ((-273 . -1094) T) ((-272 . -1094) T) ((-271 . -1094) T) ((-270 . -1094) T) ((-269 . -1094) T) ((-268 . -1094) T) ((-212 . -1094) T) ((-211 . -1094) T) ((-169 . -1197) 80270) ((-169 . -1194) 80248) ((-209 . -1094) T) ((-208 . -1094) T) ((-116 . -1046) T) ((-207 . -1094) T) ((-206 . -1094) T) ((-203 . -1094) T) ((-202 . -1094) T) ((-201 . -1094) T) ((-200 . -1094) T) ((-199 . -1094) T) ((-198 . -1094) T) ((-197 . -1094) T) ((-196 . -1094) T) ((-195 . -1094) T) ((-194 . -1094) T) ((-193 . -1094) T) ((-240 . -102) 80038) ((-169 . -35) 80016) ((-169 . -95) 79994) ((-650 . -1035) 79890) ((-482 . -1053) 79820) 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-57) 78308) ((-497 . -57) 78258) ((-351 . -1278) 78235) ((-225 . -452) T) ((-319 . -290) 78186) ((-345 . -172) T) ((-174 . -243) T) ((-1222 . -847) 78085) ((-108 . -172) T) ((-869 . -989) 78069) ((-654 . -1106) T) ((-581 . -363) T) ((-581 . -329) 78056) ((-518 . -329) 78033) ((-518 . -363) T) ((-316 . -307) 78012) ((-313 . -307) T) ((-600 . -847) 77991) ((-1107 . -714) 77933) ((-520 . -282) 77917) ((-654 . -23) T) ((-418 . -231) 77901) ((-313 . -1019) NIL) ((-336 . -23) T) ((-103 . -1007) 77885) ((-45 . -36) 77864) ((-610 . -1094) T) ((-351 . -368) T) ((-524 . -102) T) ((-495 . -27) T) ((-240 . -309) 77802) ((-1081 . -1106) T) ((-1282 . -644) 77776) ((-779 . -1106) T) ((-777 . -1106) T) ((-454 . -1106) T) ((-1057 . -452) T) ((-949 . -452) 77727) ((-1109 . -1077) T) ((-110 . -1094) T) ((-1081 . -23) T) ((-814 . -1053) T) ((-779 . -23) T) ((-777 . -23) T) ((-481 . -452) 77678) ((-1153 . -514) 77461) ((-381 . -382) 77440) ((-1172 . -411) 77424) ((-461 . -23) T) ((-454 . -23) T) ((-96 . 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. -38) 66280) ((-152 . -111) 66259) ((-1000 . -1035) 66147) ((-1161 . -845) NIL) ((-690 . -1213) T) ((-796 . -1053) T) ((-695 . -1106) T) ((-1281 . -1046) T) ((-1279 . -614) 66076) ((-1279 . -1046) T) ((-1150 . -1209) T) ((-1000 . -377) 66053) ((-907 . -145) T) ((-907 . -147) 66035) ((-867 . -131) T) ((-812 . -1052) 65932) ((-690 . -556) T) ((-695 . -23) T) ((-643 . -611) 65864) ((-643 . -612) 65825) ((-630 . -612) NIL) ((-630 . -611) 65807) ((-487 . -172) T) ((-223 . -21) T) ((-217 . -172) T) ((-223 . -25) T) ((-474 . -1197) 65773) ((-474 . -1194) 65739) ((-274 . -611) 65721) ((-273 . -611) 65703) ((-272 . -611) 65685) ((-271 . -611) 65667) ((-270 . -611) 65649) ((-500 . -647) 65631) ((-269 . -611) 65613) ((-339 . -723) T) ((-268 . -611) 65595) ((-110 . -19) 65577) ((-174 . -723) T) ((-500 . -373) 65559) ((-212 . -611) 65541) ((-520 . -1143) 65525) ((-500 . -123) T) ((-110 . -602) 65500) ((-211 . -611) 65482) ((-474 . -35) 65448) ((-474 . -95) 65414) ((-209 . -611) 65396) ((-208 . 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. -1046) T) ((-180 . -1094) T) ((-161 . -1094) T) ((-156 . -1094) T) ((-154 . -1094) T) ((-453 . -758) T) ((-31 . -1077) T) ((-960 . -172) 60021) ((-967 . -93) T) ((-1074 . -1052) 59931) ((-619 . -791) 59910) ((-592 . -1094) T) ((-619 . -788) 59889) ((-619 . -723) T) ((-295 . -286) 59868) ((-294 . -1209) T) ((-1050 . -611) 59830) ((-1050 . -612) 59791) ((-1021 . -1106) T) ((-169 . -102) T) ((-275 . -847) T) ((-1159 . -1094) T) ((-815 . -611) 59773) ((-1107 . -288) 59750) ((-1096 . -229) 59734) ((-1000 . -307) T) ((-796 . -714) 59718) ((-359 . -1052) 59670) ((-354 . -1106) T) ((-353 . -1052) 59622) ((-414 . -611) 59604) ((-385 . -611) 59586) ((-345 . -1052) 59538) ((-227 . -611) 59470) ((-1074 . -111) 59366) ((-1021 . -23) T) ((-108 . -1052) 59316) ((-895 . -102) T) ((-838 . -102) T) ((-805 . -102) T) ((-766 . -102) T) ((-673 . -102) T) ((-474 . -452) 59295) ((-418 . -172) T) ((-359 . -111) 59233) ((-353 . -111) 59171) ((-345 . -111) 59109) ((-251 . -231) 59078) ((-250 . -231) 59047) 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. -845) 49361) ((-247 . -946) 49306) ((-250 . -845) 49285) ((-777 . -145) 49264) ((-777 . -147) 49243) ((-152 . -644) 49217) ((-579 . -1094) T) ((-454 . -147) 49196) ((-454 . -145) 49175) ((-666 . -723) T) ((-820 . -611) 49157) ((-1251 . -1094) T) ((-1244 . -1094) T) ((-1223 . -1094) T) ((-1203 . -1197) 49123) ((-1203 . -1194) 49089) ((-1168 . -290) 49068) ((-1167 . -290) 49019) ((-1161 . -290) 48970) ((-1120 . -290) 48949) ((-339 . -897) 48930) ((-1001 . -172) T) ((-911 . -172) T) ((-595 . -1094) T) ((-594 . -1094) T) ((-690 . -21) T) ((-690 . -25) T) ((-474 . -1240) 48914) ((-474 . -1237) 48884) ((-418 . -286) 48812) ((-547 . -847) T) ((-316 . -1106) 48661) ((-313 . -1106) T) ((-1203 . -35) 48627) ((-1203 . -95) 48593) ((-84 . -611) 48575) ((-91 . -102) 48553) ((-1287 . -131) T) ((-591 . -614) 48534) ((-581 . -145) T) ((-581 . -147) 48516) ((-518 . -147) 48498) ((-518 . -145) T) ((-316 . -23) 48350) ((-40 . -342) 48324) ((-313 . -23) T) ((-814 . -614) 48238) ((-1152 . -647) 48220) 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T))
\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 5c620e2b..9501ab40 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3449148015) +(30 . 3449227609) (4414 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -477,662 +477,663 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |extract!| |OMUnknownCD?| |expenseOfEvaluation| - |integralMatrix| |ground| |makeMulti| |c06fpf| |bombieriNorm| - |fillPascalTriangle| |lepol| |rightExactQuotient| - |functionIsContinuousAtEndPoints| |in?| |minRowIndex| |mainVariable| - |dmpToHdmp| |port| |leadingMonomial| |mainValue| |ScanArabic| - |vectorise| |primitive?| |light| |decreasePrecision| |setAdaptive3D| - |primextintfrac| |divide| |algintegrate| |leadingCoefficient| |exquo| - |close!| |child| |exprToXXP| |string?| |invmod| |key| |code| - |component| |cCsc| |tensorProduct| |f01rdf| |shuffle| - |primitiveMonomials| |t| |arg1| |div| |expandLog| |minimize| |limit| - |cyclicEntries| |basicSet| |cAtanh| |tab1| |removeSquaresIfCan| - |column| |printStats!| |reductum| |arg2| |quo| |extractBottom!| - |filename| |intersect| |axesColorDefault| |zeroDimPrimary?| - |fixedPointExquo| |indicialEquations| |genericLeftTrace| - |mainCharacterization| |SturmHabichtCoefficients| |radicalRoots| - |escape| |remainder| |pleskenSplit| |setMaxPoints| |trigs| |not?| - |critM| |getCurve| |duplicates| |makeViewport3D| |f01qef| |rem| - |conditions| |substring?| |zeroSquareMatrix| |makeTerm| |musserTrials| - |frobenius| |high| |parse| |measure2Result| |quadraticNorm| - |factorByRecursion| |f02axf| |members| |match| |horizConcat| - |tan2trig| |intensity| |semiSubResultantGcdEuclidean2| |minColIndex| - |setEpilogue!| |lyndon?| |OMgetApp| |mapExponents| |d02gbf| |suffix?| - |s18adf| |droot| |e02aef| |intcompBasis| |monomRDE| |revert| - |partialQuotients| |quote| |shellSort| |ScanFloatIgnoreSpacesIfCan| - |contours| |mainVariable?| |showAll?| |csc2sin| |viewDeltaXDefault| - |s21bcf| |primlimitedint| |variable?| |any?| - |standardBasisOfCyclicSubmodule| |prefix?| |decrease| - |intermediateResultsIF| |triangSolve| |summation| |factorSFBRlcUnit| - |showSummary| |karatsubaOnce| |perfectSqrt| |halfExtendedResultant2| - |idealiserMatrix| |divideExponents| |generalTwoFactor| |skewSFunction| - |option?| |c02aff| |subHeight| |upperCase?| |totolex| |fixPredicate| - |bezoutDiscriminant| |c06ekf| |euclideanNormalForm| |isOp| - |radicalEigenvalues| |reducedContinuedFraction| |sorted?| |derivative| - |lowerPolynomial| |removeRedundantFactorsInPols| |returnTypeOf| - |principal?| |showAttributes| |zeroOf| |slash| |zeroSetSplit| - |symmetricPower| |equiv| |merge!| |definingInequation| |cycleTail| - |exprex| |indicialEquationAtInfinity| |notelem| |complex?| - |identityMatrix| |factorOfDegree| |s19aaf| |parameters| |cCoth| - |iisin| |OMputString| |rdregime| |reset| |wholePart| - |constantOperator| |mindegTerm| |bernoulli| |sh| |identity| - |firstNumer| |removeZeroes| |orbits| |infix?| |makeGraphImage| - |areEquivalent?| |showTheFTable| |laplace| |solveInField| BY - |numberOfFactors| |e04mbf| |selectIntegrationRoutines| |minus!| - |write| |mask| |index| |digamma| |even?| |mainMonomials| - |topPredicate| |less?| |weakBiRank| |badValues| |bumptab1| |save| - |divergence| |extensionDegree| |reify| |critMTonD1| |redPol| - |invmultisect| |setCondition!| |showIntensityFunctions| |chiSquare| - |systemSizeIF| |zero| |prolateSpheroidal| |basisOfNucleus| - |alternative?| |multiset| |setref| |logical?| |nothing| |box| - |removeRoughlyRedundantFactorsInContents| |scan| |composite| - |setFormula!| |palgRDE0| |OMputFloat| |normal?| |e04ycf| - |absolutelyIrreducible?| |bindings| |connectTo| |upDateBranches| - |yellow| |And| |listRepresentation| |packageCall| |splitDenominator| - |times!| |toseSquareFreePart| |createPrimitiveElement| |rank| - |addPointLast| |sqfrFactor| |tanIfCan| |seriesToOutputForm| |Or| |sub| - |conditionsForIdempotents| LODO2FUN |compBound| |showArrayValues| - |logGamma| |asinhIfCan| |plusInfinity| |midpoints| |s13adf| |Not| - |flatten| |color| |backOldPos| |c06eaf| |algDsolve| |besselI| - |readInt32!| |minusInfinity| |errorInfo| |monicLeftDivide| |prem| - |quoByVar| |setleft!| |f02aff| |getProperty| |outputArgs| |null?| - |patternVariable| |startPolynomial| |bumprow| |e02def| |genus| - |generalizedEigenvectors| |child?| |conical| |rightFactorCandidate| - |smith| |c05adf| |lfextlimint| |imagE| |initiallyReduced?| - |viewWriteDefault| |ridHack1| |startTableGcd!| |rotatey| |outputForm| - |readable?| |nextPartition| |region| |showTheRoutinesTable| - |categoryFrame| |ratPoly| |se2rfi| |d01bbf| |movedPoints| |solveid| - |digit| |e01bef| |selectNonFiniteRoutines| |nextSubsetGray| |bothWays| - |dimensions| |semiResultantEuclideannaif| |invertible?| |lists| |type| - |rightGcd| |generic| |order| |tryFunctionalDecomposition| - |setsubMatrix!| |maxint| |wordsForStrongGenerators| |nthr| |numer| - |henselFact| |d01gaf| |leftUnit| |extractPoint| |groebnerIdeal| - |e02baf| |listBranches| |hostPlatform| |denom| |getMeasure| - |unrankImproperPartitions0| |boundOfCauchy| |OMencodingUnknown| - |evaluateInverse| |fortranDouble| |normalized?| |nary?| |coordinate| - |functionIsFracPolynomial?| |qualifier| |ref| |An| |replace| |rotate!| - |reflect| |tubePoints| |f02xef| |outerProduct| |orOperands| |pi| - |tubeRadiusDefault| |optional| |showTheSymbolTable| |imports| - |rationalFunction| |lllip| |mkPrim| |OMsupportsCD?| |s21bbf| - |setClosed| |infinity| |closeComponent| |dark| |interpretString| - |tanh2coth| |axes| |changeName| |setRow!| |tValues| - |fullPartialFraction| |e01saf| |alphabetic| |meshPar1Var| |lfunc| ~ - |stoseInvertibleSet| |duplicates?| |exponents| |yCoord| |figureUnits| - |lowerCase!| |lift| |categories| |f04arf| |curveColor| - |nextsousResultant2| |unknownEndian| |generator| |readBytes!| - |square?| |diagonal| |kernel| |e02daf| |reduce| |simplifyPower| - |coth2trigh| |open| |power| |setRealSteps| = |elementary| |sparsityIF| - |primextendedint| |draw| |replaceKthElement| |numericIfCan| - |elliptic?| |iiGamma| |mpsode| |OMputAtp| |setlast!| |eq?| |dequeue| - |float?| |complexSolve| |subPolSet?| |quoted?| < |s14baf| - |currentCategoryFrame| |iiasinh| |OMbindTCP| |nullary| |f02bjf| - |maxPoints3D| > |spherical| |e02zaf| |constantToUnaryFunction| - |asimpson| |stoseLastSubResultant| |operations| - |nextNormalPrimitivePoly| |extractIfCan| |changeNameToObjf| <= - |exportedOperators| |makeObject| |positiveRemainder| |tanQ| - |rightMult| |rroot| |schwerpunkt| |complexNormalize| - |integralCoordinates| >= |denominators| |vedf2vef| |leadingTerm| - |interReduce| |createThreeSpace| |pile| |mainMonomial| |c06gsf| - |corrPoly| |alternatingGroup| |coef| |mapMatrixIfCan| - |normalizedDivide| |ipow| |hMonic| |currentEnv| |writeByte!| |c05pbf| - UTS2UP |reducedQPowers| |LagrangeInterpolation| |clearCache| - |symmetricTensors| |basisOfRightNucloid| |coercePreimagesImages| - |isQuotient| |hdmpToP| |df2ef| + |setright!| |s21baf| - |removeSuperfluousQuasiComponents| |stoseInvertible?reg| |coordinates| - |blankSeparate| |getCode| |OMconnInDevice| |leftRegularRepresentation| - - |zeroVector| |minPoints3D| |numberOfDivisors| |sylvesterSequence| - |byte| |f07aef| |presub| |imaginary| / |iiasin| |odd?| |concat| - |increment| |constant?| |monicModulo| |colorFunction| |concat!| - |parseString| |bezoutMatrix| |rewriteIdealWithQuasiMonicGenerators| - |computeCycleEntry| |deriv| |outputMeasure| |makeSin| |lazyGintegrate| - |basisOfLeftNucleus| |split!| |unexpand| |relationsIdeal| - |newSubProgram| |someBasis| |int| |keys| |reducedForm| |iicot| - |dimensionsOf| |ratDenom| |Nul| |rk4qc| |iFTable| |subTriSet?| |unit?| - |SFunction| |mesh| |OMsend| |defineProperty| |numFunEvals3D| |iisec| - |autoReduced?| |bright| |Ci| |e02gaf| |surface| |objectOf| |expt| - |noKaratsuba| |fortranCarriageReturn| |sinhIfCan| |coHeight| |solid?| - |space| |besselY| |upperCase| |iidprod| |bubbleSort!| |reverse| - |mappingAst| |list| |kovacic| |pade| |leftZero| - |removeRoughlyRedundantFactorsInPol| |perspective| |checkForZero| - |groebSolve| |pomopo!| |car| |octon| |branchIfCan| |toroidal| - |iterationVar| |cSech| |genericPosition| |leastMonomial| |gradient| - |computeCycleLength| |cdr| |powerAssociative?| |antiCommutator| |rule| - |leaf?| |d03eef| |redPo| |lfintegrate| |tryFunctionalDecomposition?| - |declare| |setDifference| |inputOutputBinaryFile| |setEmpty!| - |initializeGroupForWordProblem| |resultantEuclideannaif| |oddintegers| - |basisOfLeftNucloid| |myDegree| |groebner?| |setIntersection| - |totalDifferential| |palglimint0| |iicsch| |seriesSolve| |dec| - |doubleRank| |leftRankPolynomial| |internalLastSubResultant| |subset?| - |lookup| |setUnion| |explogs2trigs| |clearDenominator| - |rewriteIdealWithHeadRemainder| |possiblyNewVariety?| |error| - |setleaves!| |setLabelValue| |matrix| |extractIndex| |lllp| |apply| - |makeSeries| |enterInCache| |realRoots| |cyclicEqual?| |assert| - |pastel| |innerSolve| |finite?| |diagonals| |distribute| - |symmetricRemainder| |OMencodingBinary| |elem?| |f02wef| |splitLinear| - |fortranLiteralLine| |quotient| |arrayStack| |morphism| |size| - |inverseIntegralMatrixAtInfinity| |node?| |fractionPart| - |tubePointsDefault| |nonSingularModel| |generalizedInverse| |front| - |sumOfKthPowerDivisors| |setColumn!| |unitCanonical| - |leastAffineMultiple| |OMgetFloat| |cschIfCan| - |rightRegularRepresentation| |redpps| |plus!| |twist| |coleman| - |outputBinaryFile| |polyPart| |primintfldpoly| |properties| - |rightCharacteristicPolynomial| |failed?| |Lazard2| - |selectMultiDimensionalRoutines| |consnewpol| |first| |xCoord| - |stronglyReduced?| |adaptive| |pToDmp| |relerror| |algebraicSort| - |nullSpace| |translate| |generic?| |say| |rest| |powerSum| - |genericRightMinimalPolynomial| |reorder| |e02bef| - |getMultiplicationMatrix| |modulus| |hasoln| |setMaxPoints3D| |failed| - |substitute| |pole?| |primitivePart| |moebiusMu| |OMconnectTCP| - |listConjugateBases| |compactFraction| |move| |quadratic?| - |removeDuplicates| |ef2edf| |characteristicSet| |copyInto!| |cSin| - |quotedOperators| |f02aaf| |generators| |delete| |monomial?| |edf2efi| - |semiResultantEuclidean1| |updateStatus!| |topFortranOutputStack| - |froot| |bitCoef| |df2fi| |simplifyLog| |integralRepresents| - |combineFeatureCompatibility| |physicalLength!| |open?| |OMgetAttr| - |loopPoints| |zeroDimensional?| |getBadValues| |clikeUniv| |pdf2df| - |edf2ef| |fractRadix| |leftMult| |exptMod| |rightExtendedGcd| - |minIndex| |pToHdmp| |collectUpper| |po| |usingTable?| - |particularSolution| |initTable!| |insertTop!| |s17adf| |andOperands| - |drawComplexVectorField| |imagI| |diagonal?| |lazy?| - |compiledFunction| |elRow2!| |double| |OMcloseConn| |writeInt8!| - |recoverAfterFail| |gcdcofactprim| |Ei| |lazyPseudoRemainder| - |principalIdeal| |datalist| |pushFortranOutputStack| |factor1| - |linears| |plot| |basisOfRightAnnihilator| |OMputApp| - |resultantReduit| |lazyIrreducibleFactors| |stoseInvertibleSetsqfreg| - |popFortranOutputStack| |s18dcf| |iisqrt3| |toseLastSubResultant| - |aspFilename| |select!| |mat| |match?| |maxrank| |roughSubIdeal?| - |mainExpression| |f02bbf| |zag| |eigenvalues| |cylindrical| - |purelyAlgebraic?| |top!| |currentSubProgram| - |semiLastSubResultantEuclidean| |d01amf| |d01apf| |tower| |interval| - |outputFixed| |sumSquares| |leadingCoefficientRicDE| |aromberg| - |denominator| |constant| |rischDE| |extendedResultant| |setfirst!| - |belong?| |fullDisplay| |checkRur| |padicallyExpand| |quatern| |bat1| - |precision| |cot2trig| |f01ref| |curve?| |cAcsc| |createNormalPoly| - |endOfFile?| |goto| |permutationRepresentation| |s15aef| - |retractIfCan| |declare!| |setScreenResolution| |debug| |returnType!| - |OMputEndError| |level| |ratpart| |oddlambert| |clipParametric| - |primitivePart!| |e04fdf| |scanOneDimSubspaces| D |qqq| - |innerEigenvectors| |s17def| |overlabel| |generateIrredPoly| |f07fef| - |repeating?| |callForm?| |equality| |mainSquareFreePart| |ode| - |external?| |red| |typeLists| |lazyPremWithDefault| |float| - |inconsistent?| |queue| |showTheIFTable| |completeSmith| |s19adf| - |att2Result| |internalIntegrate| |fixedDivisor| FG2F |outputAsFortran| - |ricDsolve| |e01bgf| |fractRagits| |remove!| |completeHensel| - |overlap| |OMputEndAttr| |collectQuasiMonic| |setOrder| - |perfectNthRoot| |componentUpperBound| |primintegrate| |rdHack1| - |merge| |inputBinaryFile| |OMReadError?| |setProperty| - |groebnerFactorize| |complexEigenvalues| |output| - |semiDiscriminantEuclidean| |cAtan| |acotIfCan| |explicitlyFinite?| - |mapmult| |minPoly| |segment| |ignore?| |nthFlag| |monomRDEsys| - |newLine| |cfirst| |nilFactor| |adaptive3D?| |lflimitedint| - |infiniteProduct| |map| |enumerate| |asechIfCan| - |createMultiplicationTable| |bandedHessian| |log| |s17agf| |karatsuba| - |besselJ| |f02ajf| |internalZeroSetSplit| |triangularSystems| - |useSingleFactorBound| |simpsono| |fortranComplex| |laguerreL| - |realElementary| |var2StepsDefault| |print| |closedCurve?| - |polarCoordinates| |alphanumeric?| |LyndonWordsList1| |check| |paren| - |center| GE |printStatement| |extendedint| |resolve| |latex| - |equivOperands| |key?| |ParCond| |shade| |rotate| GT |any| - |bipolarCylindrical| |pop!| |getGraph| |numberOfNormalPoly| |cTanh| - |characteristicPolynomial| |quasiMonicPolynomials| |graphStates| LE - |node| |convert| |internalInfRittWu?| |bracket| |makeYoungTableau| - |retract| |status| |airyBi| |biRank| |shallowExpand| |stronglyReduce| - |secIfCan| LT |root?| |localReal?| |squareFreePart| |mantissa| - |crushedSet| |addMatch| |mathieu12| |nil?| |laurentIfCan| |e02bdf| - |leftMinimalPolynomial| |extractProperty| |factorSquareFreePolynomial| - |nand| |goodnessOfFit| |symFunc| |erf| |fractionFreeGauss!| - |magnitude| |degree| |factors| |readUInt8!| |resetVariableOrder| - |jordanAlgebra?| |primes| |divideIfCan| |normalizeAtInfinity| - |logIfCan| |more?| |nil| |derivationCoordinates| |pushup| |exQuo| - |s21bdf| |ptree| |bivariatePolynomials| |Vectorise| |transpose| - |rightLcm| |iiacsch| |dilog| |predicates| |makeResult| |setPrologue!| - |sumOfSquares| |coshIfCan| |splitConstant| |scalarMatrix| - |kroneckerDelta| |linearMatrix| |sin| |signatureAst| |rationalPoints| - |SturmHabichtMultiple| |clip| |elseBranch| |simpson| |outputGeneral| - |approximate| |setchildren!| |hyperelliptic| |insert| |cos| - |enterPointData| |sechIfCan| |indices| |LiePolyIfCan| |imagk| - |complex| |ldf2vmf| |rombergo| |completeEval| |tan| |removeCoshSq| - |rightRank| |radicalOfLeftTraceForm| |mapDown!| |singularitiesOf| - |LyndonWordsList| |companionBlocks| |bringDown| |cot| |acoshIfCan| - |commutative?| |differentialVariables| |hasSolution?| |leaves| |hue| - |symmetric?| |Aleph| |toScale| |shift| |sec| |represents| |super| - |branchPointAtInfinity?| |squareMatrix| |complexZeros| |vertConcat| - |gcdcofact| |nthRoot| |csc| |OMserve| |rational| |supDimElseRittWu?| - |iiatan| |maxPoints| |f01mcf| |listexp| |complete| |tracePowMod| - |asin| |refine| |getOperator| |getRef| |weierstrass| |OMgetSymbol| - |integerIfCan| |difference| |remove| |acos| |OMgetEndObject| - |flexibleArray| |getStream| |varselect| |equation| |subscript| - |resetAttributeButtons| |cn| |denomRicDE| |sizeLess?| - |possiblyInfinite?| |atan| |loadNativeModule| |bitLength| - |clearFortranOutputStack| |expextendedint| |sech2cosh| - |irreducibleFactor| |resetNew| |closed?| |jacobi| |last| |function| - |acot| |inverseIntegralMatrix| |LyndonBasis| |normalizeIfCan| |length| - |localAbs| |Beta| |assoc| |comp| |irreducibleRepresentation| - |collectUnder| |sort!| |point?| |asec| |safeFloor| |leftLcm| - |semiResultantReduitEuclidean| |scripts| |hessian| |hermiteH| |qroot| - |OMwrite| |left| |monom| |acsc| |eval| |sizeMultiplication| - |multiEuclidean| |hdmpToDmp| |acothIfCan| |rationalPower| - |nextNormalPoly| |entry| |nlde| |evenlambert| |continuedFraction| - |right| |sinh| |vspace| |numerators| |member?| |bfKeys| |innerint| - |OMsetEncoding| |normal01| |returns| |scaleRoots| |cosh| |elRow1!| - |linearDependence| |rootDirectory| |addMatchRestricted| |solve| - |common| |atoms| |optimize| |overset?| |resultant| |minPoints| - |graphs| |tanh| |solveLinearlyOverQ| |exp1| |OMputBind| |just| - |minset| |binding| |prod| |selectAndPolynomials| |ran| |f07fdf| |coth| - |pushNewContour| |factorList| |rischNormalize| - |createPrimitiveNormalPoly| |mdeg| |ode2| |polar| |algebraicDecompose| - |lazyPseudoDivide| |multiplyExponents| |sech| - |semiIndiceSubResultantEuclidean| |tanAn| |rowEchLocal| |shiftLeft| - |s19acf| |expandTrigProducts| |addPoint| |lquo| |lieAlgebra?| |cCot| - |csch| |radicalSolve| |lastSubResultantEuclidean| |byteBuffer| |nodes| - |HermiteIntegrate| |startStats!| |graeffe| |atanIfCan| |makeFR| - |roughEqualIdeals?| |asinh| |leftGcd| |mainForm| |cyclePartition| - |imagJ| |decimal| |discriminantEuclidean| |iExquo| |dioSolve| |bits| - |integral?| |d03faf| |acosh| |completeHermite| |cosh2sech| |predicate| - |halfExtendedResultant1| |legendre| |curveColorPalette| |polyRDE| - |exponent| |OMputInteger| |epilogue| |rk4f| |top| |d02gaf| |atanh| - |paraboloidal| |pushucoef| |univariatePolynomialsGcds| |trunc| - |argument| |rightQuotient| |linearAssociatedOrder| |lcm| |s17dcf| - |rst| |removeSinSq| |ScanFloatIgnoreSpaces| |acoth| |dom| - |insertBottom!| |groebgen| |normalise| |OMgetEndBind| |qelt| - |leviCivitaSymbol| |dflist| |selectFiniteRoutines| |newTypeLists| - |plenaryPower| |ListOfTerms| |idealiser| |asech| |qsetelt| |leader| - |ceiling| |hclf| |parametersOf| |exactQuotient| |mkcomm| - |leadingSupport| |style| |beauzamyBound| |OMgetObject| |c06fuf| - |symbol| |append| |s17dlf| |palgLODE| |cAsin| |symmetricSquare| - |e02ajf| |xRange| |changeThreshhold| |symmetricDifference| |extension| - |entries| |multiple| |makeSUP| |expression| |insertionSort!| |gcd| - |Frobenius| |alphanumeric| |adaptive?| |exactQuotient!| |yRange| - |numberOfPrimitivePoly| |s17ajf| |iibinom| |trace2PowMod| - |finiteBasis| |HenselLift| |integer| |zoom| |applyQuote| |false| - |chvar| |genericLeftNorm| |unitVector| |zRange| |airyAi| - |viewPhiDefault| |tree| |numericalOptimization| |headReduce| - |degreePartition| |setStatus| |ratDsolve| |bezoutResultant| |map!| - |bandedJacobian| |polyRicDE| |e02ahf| |result| |prindINFO| |title| - |formula| |createZechTable| |iomode| |countable?| |curry| - |countRealRoots| |qsetelt!| |twoFactor| |rightOne| |singleFactorBound| - |variationOfParameters| |collect| |useSingleFactorBound?| |pointLists| - |leftCharacteristicPolynomial| |hasTopPredicate?| |sinh2csch| - |ruleset| |factorGroebnerBasis| |lyndon| |preprocess| |mulmod| - |largest| |readInt16!| |coerceS| |anticoord| |moreAlgebraic?| |iiacsc| - |#| |e| |lastSubResultant| |createLowComplexityNormalBasis| |swap!| - |rationalIfCan| |sec2cos| |insertRoot!| GF2FG |simpleBounds?| - |iteratedInitials| |atom?| |minimalPolynomial| |label| - |realEigenvectors| |rightFactorIfCan| |exprToGenUPS| |contract| - |nrows| |numberOfComponents| |hostByteOrder| |minGbasis| |bounds| - |findCycle| |suchThat| |stFunc1| |OMencodingXML| - |unprotectedRemoveRedundantFactors| |drawComplex| |complexIntegrate| - |ncols| |setClipValue| |lex| |algSplitSimple| |toseInvertibleSet| - |sqfree| |s18aff| |genericRightTraceForm| |midpoint| |normalElement| - |cyclotomic| |rightScalarTimes!| |minimumExponent| - |balancedBinaryTree| |signAround| |setMinPoints| |meatAxe| - |startTableInvSet!| |argumentListOf| |zerosOf| |rquo| |arguments| - |accuracyIF| |f04atf| |leftDivide| |seed| |dn| |fortranCharacter| - |rightMinimalPolynomial| |leftQuotient| |cap| - |solveLinearPolynomialEquationByFractions| |isList| - |LowTriBddDenomInv| |isMult| |zeroDimPrime?| |polCase| |bipolar| - |internalIntegrate0| |explimitedint| |numberOfHues| |components| - |point| |singular?| |f01maf| |bottom!| |leftFactor| |numberOfChildren| - |internal?| |rootProduct| |nthFractionalTerm| |multiEuclideanTree| - |conditionP| |constructor| |f02aef| |setPredicates| |elColumn2!| - |d01asf| |normalDeriv| |critT| |cycles| |normalDenom| - |selectOptimizationRoutines| |OMputEndObject| |stack| - |generalizedEigenvector| |lazyVariations| |matrixGcd| |maxColIndex| - |chineseRemainder| |width| |permutation| |option| |OMputSymbol| - |addBadValue| |chebyshevU| |superscript| |ellipticCylindrical| - |expandPower| |setelt!| |series| |rightPower| |rules| |ReduceOrder| - |algebraic?| |leftAlternative?| |primitiveElement| |pointColor| - |exponential| |messagePrint| |asinIfCan| |divisors| |test| |bitTruth| - |dmp2rfi| |conjugate| |findBinding| |viewDeltaYDefault| - |positiveSolve| |Gamma| |flagFactor| |entry?| |eigenvector| |solve1| - |hexDigit?| |distFact| |sort| |fglmIfCan| |RittWuCompare| |e04ucf| - |dim| |OMputBVar| |var1StepsDefault| |associatedSystem| |cycleRagits| - |npcoef| |integral| |critBonD| |mathieu11| |coth2tanh| - |localIntegralBasis| |abs| |permutations| |badNum| |decompose| - |deleteProperty!| |reverse!| |principalAncestors| |min| - |partialNumerators| |halfExtendedSubResultantGcd2| - |getMultiplicationTable| |rightTrim| |showFortranOutputStack| - |setLegalFortranSourceExtensions| |fixedPoint| |makingStats?| |fTable| - |solveRetract| |sizePascalTriangle| |binary| |leftTrim| |superHeight| - |term?| |commaSeparate| |clipPointsDefault| - |removeRedundantFactorsInContents| |sample| |discreteLog| |f01bsf| - |random| |d02bbf| |getExplanations| |eof?| |e01daf| |safetyMargin| - |e02bcf| |inspect| |idealSimplify| |fortranInteger| - |nativeModuleExtension| |basisOfMiddleNucleus| |FormatArabic| - |patternMatchTimes| |mightHaveRoots| |extendedIntegrate| - |exprHasAlgebraicWeight| |e01baf| |negative?| |outputSpacing| - |appendPoint| |leadingIdeal| |complexLimit| |screenResolution| - |elements| |rename| |tex| |max| |expPot| |sup| |bumptab| - |wordInStrongGenerators| |lazyIntegrate| |rootOf| - |SturmHabichtSequence| |coefficient| |cycleEntry| |taylorQuoByVar| - |OMunhandledSymbol| |modularGcdPrimitive| |quotientByP| - |squareFreePrim| |normFactors| |doubleComplex?| |diagonalProduct| - |iitan| |setProperty!| |rewriteIdealWithRemainder| |mapExpon| |radix| - |connect| |romberg| |arity| |tanintegrate| |aLinear| - |subResultantGcdEuclidean| |factorSquareFree| |weights| |c06frf| - |f2st| |push!| |expintegrate| |makeprod| |geometric| |colorDef| - |randomR| |rischDEsys| |swapRows!| |makeFloatFunction| |pattern| - |omError| |truncate| |cyclicSubmodule| |numberOfVariables| - |rootNormalize| |e02adf| |s14abf| |sPol| |second| |rationalPoint?| - |totalGroebner| |iipow| |rowEchelon| |ramified?| |monicDivide| - |leftUnits| |symbol?| |viewpoint| |symmetricProduct| |third| - |fortranTypeOf| |cyclic| |prime| |lifting1| |powers| - |permutationGroup| |generalInfiniteProduct| |numberOfMonomials| |diff| - |reduceByQuasiMonic| |listOfMonoms| |rootRadius| |viewPosDefault| |Is| - |subresultantSequence| |complement| |radicalEigenvector| |normalize| - |prevPrime| |linear?| |s18aef| |message| |hexDigit| |rightUnit| - |reindex| |wrregime| |implies?| |lineColorDefault| - |subQuasiComponent?| |stFuncN| |rowEchelonLocal| |semicolonSeparate| - |pow| |notOperand| |linearAssociatedLog| |e02ddf| |rotatez| |s18def| - |cosSinInfo| |sequences| |tan2cot| |dot| |laplacian| - |purelyAlgebraicLeadingMonomial?| |binaryTournament| |write!| - |prinpolINFO| |sum| |quasiRegular?| |coerceListOfPairs| |birth| - |central?| |heapSort| |cAcoth| |KrullNumber| |void| |pascalTriangle| - |OMclose| |size?| |removeConstantTerm| |enqueue!| |generalSqFr| - |intChoose| |insert!| |compose| |complexForm| |alphabetic?| - |genericLeftTraceForm| |PollardSmallFactor| |triangulate| |presuper| - |euclideanGroebner| |stiffnessAndStabilityOfODEIF| |read!| |exists?| - |matrixConcat3D| |cons| |subSet| |getOrder| |iprint| |fibonacci| - |separant| |rootBound| |rewriteSetByReducingWithParticularGenerators| - |pseudoQuotient| |testModulus| |OMgetType| |pmintegrate| - |invertibleSet| |round| |extractTop!| |operation| |subMatrix| |extend| - |transform| |c06gqf| |lp| |mr| |padecf| |UpTriBddDenomInv| |stirling2| - |symmetricGroup| |representationType| |floor| |capacity| |typeList| - |s13acf| |OMopenString| |phiCoord| |setImagSteps| |withPredicates| - |solveLinear| |setAdaptive| |reopen!| |monicRightFactorIfCan| - |universe| |pquo| |multiplyCoefficients| |sturmVariationsOf| - |deleteRoutine!| |pmComplexintegrate| |routines| - |isAbsolutelyIrreducible?| |double?| |getMatch| |leftScalarTimes!| - |s18acf| |stoseInvertible?| |reducedSystem| |ramifiedAtInfinity?| - |matrixDimensions| |retractable?| |term| |c06fqf| - |reciprocalPolynomial| |tube| |iiatanh| |squareFree| - |selectSumOfSquaresRoutines| |e01sef| |viewDefaults| |source| - |printTypes| |factorFraction| |graphCurves| |systemCommand| |increase| - |computePowers| |lighting| |showTypeInOutput| |linearPolynomials| - |character?| |doubleDisc| |getProperties| |lhs| |oblateSpheroidal| - |stopTableGcd!| |tanh2trigh| |modTree| |stopMusserTrials| - |reduceBasisAtInfinity| |GospersMethod| |ptFunc| |poisson| - |patternMatch| |rhs| |permanent| |rootPower| |comparison| - |clearTheFTable| |argscript| |primPartElseUnitCanonical!| - |dihedralGroup| |clearTable!| |iicos| |primeFactor| |normal| - |headRemainder| |range| |bytes| |e02dcf| |multisect| |e02akf| - |rangePascalTriangle| |mesh?| |rightZero| |monicRightDivide| - |OMsupportsSymbol?| |fill!| |rectangularMatrix| |choosemon| - |mergeDifference| |generalizedContinuumHypothesisAssumed?| - |zeroSetSplitIntoTriangularSystems| |genericLeftDiscriminant| - |controlPanel| |target| |cycleLength| |s14aaf| |coefficients| - 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|printInfo| |code| |boundOfCauchy| + |arg2| |stripCommentsAndBlanks| |semiResultantReduitEuclidean| |t| + |prime?| |reductum| |div| |degree| |d01gaf| |f01qcf| |zRange| + |denominator| |mesh?| |roughBase?| |critBonD| |zeroMatrix| + |virtualDegree| |integralBasis| |quo| |resultantReduitEuclidean| + |basisOfRightNucleus| |filename| |pole?| |airyBi| |map!| |removeZero| + |andOperands| |scopes| |getCurve| |antiAssociative?| |s18aff| + |maxIndex| |conditions| |solid| |qsetelt!| |not?| |showArrayValues| + |prem| |startTable!| |subQuasiComponent?| |distdfact| |gcdprim| + |univcase| |antisymmetricTensors| |concat!| |rem| |match| |iicoth| + |vertConcat| |squareFreeFactors| |parse| |setStatus| |rational?| + |bernoulli| |ignore?| |cyclePartition| |frobenius| + |variationOfParameters| |substring?| |csc2sin| |extractBottom!| + |space| |OMputFloat| |mainExpression| |fixedDivisor| |yCoord| + |idealSimplify| |backOldPos| |iiacoth| |squareMatrix| |summation| + |lieAlgebra?| |setProperties| |resultantEuclidean| + |integralDerivationMatrix| |divideIfCan| |compBound| |limitedint| + |UnVectorise| |symmetricSquare| |measure| |suffix?| |superscript| + |fortranCharacter| |minimumDegree| |stronglyReduce| |iisinh| + |completeHensel| |mathieu23| |semiDegreeSubResultantEuclidean| + |adaptive| |LyndonWordsList| |rightUnits| |totolex| |prinshINFO| + |figureUnits| |imagJ| |routines| |positiveRemainder| |acsch| + |extractIfCan| |showSummary| |eulerPhi| |subPolSet?| |satisfy?| + |complete| |color| |prefix?| |factorGroebnerBasis| |OMlistSymbols| + |rowEchLocal| |f04jgf| |leadingTerm| |reducedSystem| + |halfExtendedResultant2| |quasiMonic?| |singular?| + |internalSubPolSet?| |rename!| UP2UTS |leftFactor| |selectfirst| + |LazardQuotient| |mapBivariate| |showAttributes| |extractClosed| + |factorset| |taylorRep| |rightRank| |chebyshevT| |stopTableGcd!| + |lllp| |f07adf| |Ei| |overset?| |lazyPremWithDefault| |reset| + |reducedQPowers| |monomial?| |cAcsch| |bracket| BY |redPol| |listexp| + |null?| |in?| |replaceKthElement| |unitsColorDefault| |minColIndex| + |removeSinhSq| |mainPrimitivePart| |getOperator| |qPot| + |lineColorDefault| |redmat| |invertibleSet| |nonLinearPart| + |pointPlot| |write| |socf2socdf| |normalElement| |charpol| + |viewWriteDefault| |sample| |leftTrace| |badValues| |save| + |divideIfCan!| |approxSqrt| |removeDuplicates!| |errorKind| |infix?| + |divisor| |bindings| |f01mcf| |expint| |graphState| + |lazyPseudoQuotient| |transcendentalDecompose| |extendedEuclidean| + |zero| |OMmakeConn| |term| |mask| |mapGen| |jordanAdmissible?| + |colorFunction| |uniform01| |primintegrate| |f04qaf| |untab| + |unexpand| |plus!| |vector| |fintegrate| |modulus| |tanAn| |qinterval| + |f2df| |d02ejf| |wholeRadix| |front| |sort!| + |basisOfCommutingElements| |nothing| |And| |expintfldpoly| + |loopPoints| |rotate!| |alphanumeric?| |sn| |multiEuclidean| + |LyndonWordsList1| |reducedDiscriminant| |pushuconst| |nary?| + |removeRoughlyRedundantFactorsInContents| |Or| |imagE| + |lastSubResultant| |s17adf| |monomialIntPoly| |operator| |nodes| + |countRealRoots| |complexIntegrate| |e04ucf| |outputSpacing| |updatF| + |Not| |fracPart| |e02bdf| |OMputApp| |exteriorDifferential| |vedf2vef| + |heap| |diagonalProduct| |lexTriangular| |symbolTableOf| + |plusInfinity| |hdmpToDmp| |rewriteIdealWithRemainder| |elseBranch| + |pushucoef| |intPatternMatch| |diag| |ratDsolve| |anticoord| + |basisOfLeftAnnihilator| |decreasePrecision| |minusInfinity| + |stosePrepareSubResAlgo| |minIndex| |key?| |flatten| |maxPoints| + |processTemplate| |pushup| |OMputInteger| |internalDecompose| + |getBadValues| |log2| |critM| |zoom| |/\\| |bsolve| |realSolve| + |width| |mindegTerm| |halfExtendedSubResultantGcd2| |maxdeg| |s20adf| + |asinIfCan| |viewport3D| |polCase| |corrPoly| |trapezoidalo| |\\/| + |listRepresentation| |clikeUniv| |operators| |rootBound| + |symmetricProduct| |merge| |createGenericMatrix| |birth| + |leastMonomial| |OMputError| |nonSingularModel| |nextItem| |entry?| + |subResultantsChain| |normalized?| |argscript| + |numberOfComputedEntries| |triangulate| |argumentList!| + |indiceSubResultant| |OMclose| |pdct| |lazyEvaluate| |abs| |logGamma| + |cCosh| |numer| |node?| |returnType!| |squareFreePart| |permutations| + |nor| |linearPart| |type| |e02bbf| |e02ahf| |sincos| |leftUnit| + |denom| |powers| |lllip| |factorOfDegree| |linearlyDependent?| + |repeating| |writeLine!| |certainlySubVariety?| |outputForm| + |mergeDifference| |laguerre| |degreeSubResultantEuclidean| |isobaric?| + |bumptab| |constantLeft| |f04arf| |numberOfIrreduciblePoly| |iidsum| + |readBytes!| |find| |multiset| |combineFeatureCompatibility| + |branchPointAtInfinity?| |cot2trig| |setLegalFortranSourceExtensions| + |pi| |nextNormalPrimitivePoly| |middle| |headRemainder| |e04mbf| + |nextsubResultant2| |nand| |relationsIdeal| |iisec| + |rangePascalTriangle| |algintegrate| |infinity| |optional| + |semiLastSubResultantEuclidean| |mainKernel| |contours| + |useSingleFactorBound| |terms| |addBadValue| |htrigs| |chiSquare| + |differentiate| |outerProduct| |reduceBasisAtInfinity| + |semiSubResultantGcdEuclidean2| |conjugate| |uniform| |anfactor| + |goodnessOfFit| |bringDown| |wordInStrongGenerators| |cCos| ~ + |readUInt16!| |bitLength| |constantToUnaryFunction| |readable?| + |makeFloatFunction| |roman| |hspace| |RemainderList| |expPot| + |primextendedint| |categories| |remainder| |more?| |generator| + |point?| = |stirling1| |kernel| |pack!| |withPredicates| |insert!| + |stirling2| |addMatchRestricted| |basisOfCenter| |getCode| |open| + |removeRoughlyRedundantFactorsInPols| |constantCoefficientRicDE| + |cosh2sech| |draw| |elliptic| |s18def| |genus| |po| + |lazyPseudoRemainder| |chebyshevU| |inGroundField?| |zeroSquareMatrix| + |setClosed| |polyPart| |infLex?| < |internalSubQuasiComponent?| + |nthFractionalTerm| |removeRedundantFactors| |pseudoDivide| + |radicalEigenvector| |solveRetract| |gradient| + |generalizedEigenvectors| |symmetricTensors| |alternating| |critT| > + |minimize| |padecf| |numberOfFactors| |FormatArabic| |fortranLiteral| + |twoFactor| |order| |exprHasWeightCosWXorSinWX| |mainMonomials| F2FG + |subSet| <= |getStream| |reseed| |complexElementary| |truncate| + |changeVar| |partialFraction| |operations| |coordinate| |superHeight| + |coth2trigh| |setLength!| |dimensions| >= + |stiffnessAndStabilityFactor| |makeObject| |primintfldpoly| + |diagonalMatrix| |OMsetEncoding| |scalarMatrix| |lquo| |lyndon?| + |external?| |removeCoshSq| |iitan| |binomial| |universe| + |constantIfCan| |commutativeEquality| |permutationGroup| |d01bbf| + |opeval| |term?| |c05nbf| |autoReduced?| |skewSFunction| |critB| + |bezoutResultant| |has?| |s21baf| |coef| |cfirst| |dimensionsOf| + |hcrf| |currentEnv| |selectOrPolynomials| |diagonal| |intensity| + |cAcsc| |f04maf| + |fortranComplex| |OMbindTCP| |eulerE| + |mainVariable?| |credPol| |drawStyle| |getMultiplicationMatrix| + |outputFixed| |cCsch| |isQuotient| |rischDE| |rangeIsFinite| + |argumentListOf| - |setProperty| |linearAssociatedOrder| |debug3D| + |clearCache| |selectMultiDimensionalRoutines| |contains?| + |trigs2explogs| |bivariateSLPEBR| |selectFiniteRoutines| |iibinom| + |e02bcf| |torsionIfCan| |makeSUP| / |printCode| |OMlistCDs| + |OMputEndObject| |cotIfCan| |modularFactor| |definingPolynomial| + |OMgetEndAttr| |purelyAlgebraicLeadingMonomial?| |d03faf| + |createThreeSpace| |c02agf| |setMinPoints| |clipParametric| |quoted?| + |lfextlimint| |normalizedAssociate| |e02baf| |s01eaf| |setClipValue| + |showRegion| |increase| |stFunc2| |d03eef| |createRandomElement| + |goodPoint| |floor| |concat| |constantKernel| |setPoly| |iifact| + |drawComplex| |integralAtInfinity?| |contract| |fortranTypeOf| |isOp| + |whitePoint| |computeInt| |unitNormalize| |f02bbf| |numberOfCycles| + |clip| |prinb| |super| |resetNew| |doubleRank| |getButtonValue| + |leftLcm| |sechIfCan| |ord| |hessian| |iiacos| |complement| + |listConjugateBases| |smith| |modifyPoint| |subCase?| |aCubic| |light| + |sinhcosh| |iidprod| |testDim| |normalForm| |getOrder| |implies| + |showAll?| |keys| |constantOpIfCan| |bottom!| |getOperands| + |outputFloating| |returnTypeOf| |denominators| |imagK| |gbasis| + |addPoint2| |components| |deepCopy| |unravel| |edf2ef| |bright| + |outputAsScript| |specialTrigs| |baseRDE| |minPoly| |minus!| + |critMonD1| |makeCrit| |rst| |lowerCase!| |genericLeftTraceForm| + |reverse| |top!| |rewriteSetByReducingWithParticularGenerators| + |generalPosition| |limitPlus| |list| |inverseIntegralMatrix| + |isAbsolutelyIrreducible?| |iiGamma| |recur| |f01rdf| |s17agf| + |endOfFile?| |unitCanonical| |quoByVar| |irreducible?| |increment| + |car| |functionIsOscillatory| |nextSublist| |s17dgf| |mvar| + |hasPredicate?| |expandPower| |mathieu11| |genericRightDiscriminant| + |cAtanh| |Nul| |viewDeltaYDefault| |cdr| + |rewriteIdealWithHeadRemainder| |rule| |iilog| + |stoseIntegralLastSubResultant| |OMcloseConn| |rootPower| |lookup| + |f01rcf| |leftExtendedGcd| |plotPolar| |setDifference| |declare| + |monic?| |f02wef| |pToDmp| |collect| |exprToGenUPS| |imaginary| + |integral?| |sizePascalTriangle| |mpsode| |setIntersection| + |unvectorise| |fortranCompilerName| |zero?| |integralMatrix| + |lastSubResultantElseSplit| |s21bdf| |mainVariables| |reducedForm| + |slash| |setUnion| |randomR| |Gamma| |unitVector| |is?| |BumInSepFFE| + |createPrimitiveElement| |randomLC| |updatD| |mirror| |apply| |error| + |dec| |elements| |quote| |basicSet| |outputGeneral| + |internalLastSubResultant| |dn| |d02bbf| |quadraticNorm| |maxPoints3D| + |interval| |psolve| |integerIfCan| |assert| |fill!| |rischDEsys| + |lflimitedint| |integers| |toseInvertible?| |recip| |size| |mdeg| + |d02kef| |pointColorDefault| |iiatanh| |addMatch| |compdegd| + |generic?| |createPrimitivePoly| |subspace| |df2fi| + |powerAssociative?| |zCoord| |ddFact| |dimension| |orbits| |wrregime| + |cartesian| |presuper| |e04fdf| |kmax| |just| |infieldint| + |properties| |characteristicPolynomial| |rootOf| |sign| |critpOrder| + |algebraic?| |first| |setAttributeButtonStep| |factorAndSplit| + |showTheIFTable| |symmetric?| |toroidal| |queue| |translate| + |perfectSquare?| |partitions| |failed| |quasiComponent| |rest| + |mappingAst| |hostPlatform| |toScale| |simplifyLog| |clipWithRanges| + |iipow| |symmetricPower| |f04axf| |minRowIndex| |move| |substitute| + |c02aff| |doubleResultant| |inRadical?| |rombergo| |normalDeriv| |say| + |f01ref| |realEigenvectors| |cyclicEqual?| |stoseSquareFreePart| + |parametric?| |viewSizeDefault| |removeDuplicates| |transpose| + |f02xef| |acotIfCan| |laurentIfCan| |fortranInteger| |interpolate| + |repSq| |normalDenom| |inputBinaryFile| |cycleRagits| |f01qdf| + |nextIrreduciblePoly| |npcoef| |readInt8!| |setRow!| + |setVariableOrder| |delete| |leftRemainder| + |removeRoughlyRedundantFactorsInPol| |create3Space| + |solveLinearPolynomialEquationByRecursion| |iiacot| |roughUnitIdeal?| + |squareTop| |s17ahf| |invmultisect| |e01saf| |oddInfiniteProduct| + |partialNumerators| |createMultiplicationTable| |patternMatch| + |mathieu12| |bounds| |distribute| |infieldIntegrate| |radPoly| + |setOfMinN| |refine| |reducedContinuedFraction| |Lazard| + |expenseOfEvaluationIF| |meatAxe| |flagFactor| |writeUInt8!| |decimal| + |powern| |minimumExponent| |polar| |viewDefaults| |normFactors| + |selectSumOfSquaresRoutines| |choosemon| |rarrow| |alphabetic?| + |exprHasAlgebraicWeight| |numberOfNormalPoly| |content| |laplace| + |insertRoot!| |s17dhf| |isTimes| |outputMeasure| |secIfCan| |prologue| + |s14baf| |child| |unrankImproperPartitions1| |nsqfree| |double| + |useEisensteinCriterion| |hconcat| |extendedint| |cAcoth| + |basisOfRightAnnihilator| |pushFortranOutputStack| |binary| + |OMgetEndAtp| |complexLimit| |leftUnits| |createPrimitiveNormalPoly| + |oddintegers| |binaryTournament| |rationalFunction| |changeBase| + |match?| |popFortranOutputStack| |s19abf| |lighting| + |getVariableOrder| |resultantReduit| |generalizedInverse| |poisson| + |systemSizeIF| |rewriteIdealWithQuasiMonicGenerators| + |pointSizeDefault| |belong?| |infiniteProduct| |rotatex| + |leftScalarTimes!| |arrayStack| |basis| |rightMult| |c05adf| + |wholePart| |getProperties| |shufflein| |knownInfBasis| |mix| + |tracePowMod| |var2Steps| |scaleRoots| |possiblyNewVariety?| + |acschIfCan| |interpretString| |constant| |iiatan| + |degreeSubResultant| |readInt32!| |retractIfCan| |cAcos| |f04atf| + |stoseInvertible?| |exactQuotient!| |rowEch| |and?| + |structuralConstants| |debug| |binaryTree| |oblateSpheroidal| |eof?| + |assign| |outputAsFortran| |makeViewport2D| |iisin| |freeOf?| |d02gaf| + |declare!| |leftCharacteristicPolynomial| D |regularRepresentation| + |wronskianMatrix| |level| |wreath| |dictionary| |increasePrecision| + |makingStats?| |irreducibleFactor| |associatorDependence| + |groebnerFactorize| |lyndonIfCan| |janko2| |derivative| |atanhIfCan| + |coord| |float| |coerceP| |triangular?| |leftDiscriminant| |subscript| + |antiCommutative?| |charClass| |genericPosition| |column| |lowerCase| + |weight| |asechIfCan| |iiacsc| |number?| |makeGraphImage| |rightTrace| + |factorSquareFreePolynomial| |someBasis| |sinh2csch| |ocf2ocdf| + |multMonom| |regime| |setchildren!| |separant| |conical| + |setProperty!| |currentScope| |iiperm| |expintegrate| + |modifyPointData| |applyRules| |infinite?| |singularitiesOf| |pow| + |simpsono| |binaryFunction| |OMputString| |usingTable?| |map| |fTable| + |supRittWu?| |getGoodPrime| |coleman| |tan2trig| |insertMatch| + |resultantnaif| |segment| |OMencodingUnknown| |scale| + |bezoutDiscriminant| |write!| |alternatingGroup| |log| |double?| + |leftFactorIfCan| |useSingleFactorBound?| |eyeDistance| |lepol| + |overlap| |diff| |OMgetEndError| |extendedResultant| |nodeOf?| |rquo| + |mkPrim| |domainOf| |resetAttributeButtons| + |genericRightMinimalPolynomial| |print| |tubePoints| |initials| + |OMgetEndObject| |blankSeparate| |sturmVariationsOf| GE |OMgetEndApp| + |palgextint0| |e02dcf| |resolve| |mainForm| |makeSin| |tRange| + |center| |readLine!| |contractSolve| GT |parametersOf| + |palginfieldint| |node| |push| |complex?| |polygon| |exactQuotient| + |convert| |vspace| |retract| |e02def| |internalIntegrate| + |radicalEigenvalues| |rectangularMatrix| LE |generalInfiniteProduct| + |balancedBinaryTree| |limit| |mantissa| |readIfCan!| |rename| + |graphCurves| |youngGroup| |frst| |hasTopPredicate?| |ScanArabic| LT + |critMTonD1| |eigenvalues| |sizeLess?| |identitySquareMatrix| + |integrate| |swapRows!| |status| |divergence| |minimalPolynomial| + |curryRight| |solveid| |ridHack1| |pomopo!| |palgLODE0| + |viewThetaDefault| |sh| |numberOfComponents| |bernoulliB| + |setPredicates| |pdf2ef| |extensionDegree| |numerators| LODO2FUN + |arbitrary| |positive?| |newLine| |associative?| |erf| |directSum| + |enterPointData| |OMreadStr| |groebSolve| |RittWuCompare| |position!| + |minPoints| |nil| |eigenMatrix| |notOperand| |recoverAfterFail| + |selectODEIVPRoutines| |splitNodeOf!| |createIrreduciblePoly| |curve?| + |thenBranch| |perspective| |componentUpperBound| |exists?| |readByte!| + |listOfMonoms| |ptree| |transform| |central?| |rightRemainder| + |B1solve| |setValue!| |minGbasis| |subNode?| |packageCall| |dilog| + |maximumExponent| |llprop| |subresultantVector| |inf| |minset| |pade| + |cosIfCan| |rootPoly| |approximate| |insert| |removeSinSq| |varselect| + |sin| |isMult| |cyclicCopy| |alphabetic| |heapSort| |replace| + |ParCond| |besselY| |complex| |quartic| |qualifier| |cos| |revert| + |pushdown| |flexibleArray| |complexExpand| |viewWriteAvailable| + |child?| |upDateBranches| |basisOfRightNucloid| |exportedOperators| + |restorePrecision| |tan| |selectOptimizationRoutines| |getRef| + |computeCycleEntry| |makeViewport3D| |scanOneDimSubspaces| + |initiallyReduced?| |unknownEndian| |beauzamyBound| |palglimint| + |shift| |cot| |innerEigenvectors| |exprHasLogarithmicWeights| + |showIntensityFunctions| |rightScalarTimes!| |repeating?| |leastPower| + |leaves| |SFunction| |cLog| |definingEquations| |sec| |gcdPrimitive| + |mat| |showTypeInOutput| |setleaves!| |elRow2!| |parent| + |problemPoints| |cAsinh| |s18acf| |times| |loadNativeModule| |csc| + |newReduc| |neglist| |c06ecf| |numberOfMonomials| |putGraph| + |equation| |var1StepsDefault| |var1Steps| |nthFactor| |remove| + |quadratic| |asin| |compose| |equivOperands| |meshPar2Var| |atom?| + |tensorProduct| |symbol?| |rootKerSimp| |atrapezoidal| |sub| |acos| + |transcendenceDegree| |inspect| |selectPDERoutines| |maxRowIndex| + |quasiRegular| |d02raf| |rubiksGroup| |cn| |comp| |logical?| |generic| + |function| |last| |ricDsolve| |atan| |cSinh| |localAbs| |iExquo| + |OMgetBind| RF2UTS |linearDependenceOverZ| |assoc| |headAst| |monom| + |makeprod| |stoseInvertible?sqfreg| |acot| |fractionPart| |s14abf| + |ScanRoman| |asimpson| |modTree| |irreducibleRepresentation| + |nextSubsetGray| |entry| |rightLcm| |left| |slex| |asec| |eval| + |mainMonomial| |lazyGintegrate| |doubleFloatFormat| |aQuartic| + |inHallBasis?| |e02akf| |optimize| |multiple?| |right| |even?| |acsc| + |ode1| |yellow| |reduceByQuasiMonic| |singularAtInfinity?| |e01bgf| + |multiEuclideanTree| |ODESolve| |common| |shiftRoots| |round| + |digamma| |sinh| |orOperands| |bits| |OMunhandledSymbol| |shuffle| + |prod| |mainCharacterization| |hostByteOrder| |setProperties!| + |largest| |primaryDecomp| |cosh| |invertIfCan| |basisOfNucleus| + |indiceSubResultantEuclidean| |nullary?| |genericLeftTrace| |rroot| + |nextPrime| |delete!| |primeFactor| |tanh| |rationalPower| |exQuo| + |univariatePolynomials| |shanksDiscLogAlgorithm| |denomRicDE| |d02bhf| + |laurentRep| |dark| |mainCoefficients| |square?| |coth| + |brillhartTrials| |setOrder| |leftOne| |lexico| |pointColor| |addiag| + |dflist| |showTheFTable| |box| |legendre| |sech| |bandedJacobian| + |algebraicCoefficients?| |eigenvector| |HermiteIntegrate| + |SturmHabichtMultiple| |crest| |lowerPolynomial| |factorSFBRlcUnit| + |shade| |csch| |parents| |module| |setEmpty!| |cyclicSubmodule| + |setEpilogue!| |cExp| |rCoord| |bezoutMatrix| |block| |top| + |hyperelliptic| |asinh| |printStatement| |prolateSpheroidal| + |genericRightTraceForm| |enumerate| |nextLatticePermutation| + |simplifyExp| |bag| |e02ajf| |hasoln| |acosh| |ceiling| |c06eaf| + |generalizedContinuumHypothesisAssumed?| |divisors| |padicFraction| + |showTheRoutinesTable| |extract!| |principalAncestors| + |clearTheIFTable| |lcm| |atanh| |userOrdered?| |dom| |morphism| + |expIfCan| |imagI| |stoseInvertibleSetsqfreg| |printHeader| + |totalDifferential| |startStats!| |submod| |acoth| |rationalPoints| + |zeroSetSplitIntoTriangularSystems| |getMultiplicationTable| + |symbolIfCan| |lifting| |f02adf| |inverseIntegralMatrixAtInfinity| + |append| |firstUncouplingMatrix| |symbol| |split| |asech| + |viewZoomDefault| |leader| |subst| |nextPartition| |fglmIfCan| + |sturmSequence| |rootRadius| |lSpaceBasis| |zerosOf| |duplicates| + |expression| |mainContent| |gcd| |hexDigit?| |rationalApproximation| + |generalTwoFactor| |c06fpf| |sinIfCan| |rightQuotient| |tree| + |basisOfLeftNucloid| |relerror| |false| |integer| |multiple| |curve| + |factorFraction| |genericLeftMinimalPolynomial| |palglimint0| |result| + |qroot| |moduloP| |delta| |OMUnknownCD?| |decrease| |palgintegrate| + |applyQuote| |leadingIdeal| |tanh2trigh| |zag| |fixedPointExquo| + |title| |s21bcf| |se2rfi| |lists| |expandLog| |setImagSteps| + |movedPoints| |triangSolve| |perfectNthPower?| |orbit| + |nextPrimitiveNormalPoly| |cyclicParents| |eisensteinIrreducible?| + |solve1| |list?| |incrementKthElement| |tanQ| |fractionFreeGauss!| + |unitNormal| |e02gaf| |rotatey| |clearTheFTable| |expt| |ruleset| |#| + |LyndonCoordinates| |e| |Vectorise| |objects| |OMgetString| + |expressIdealMember| |part?| |const| |lazyPseudoDivide| |OMputEndBind| + |label| |one?| |base| |viewPosDefault| |supersub| |chiSquare1| + |reorder| |getIdentifier| |head| |minordet| |changeNameToObjf| + |nthFlag| |computePowers| |real?| |makeEq| |redpps| |suchThat| + |typeLists| |spherical| |deleteProperty!| |setMaxPoints3D| |lazyPrem| + |lambda| |OMsupportsSymbol?| |radicalOfLeftTraceForm| |setright!| + |mainVariable| |minPoints3D| |ipow| |totalGroebner| |character?| + |startPolynomial| |notelem| |graeffe| |roughBasicSet| |csubst| + |arguments| |read!| |expandTrigProducts| |splitConstant| + |differentialVariables| |leftGcd| |primitive?| |topPredicate| + |printStats!| |genericLeftDiscriminant| |OMputEndAttr| |cubic| + |ratpart| |f04faf| |makeCos| |c06gqf| |primitiveElement| |stack| + |inputOutputBinaryFile| |outputArgs| |constructor| |any?| |reflect| + |bivariate?| |multisect| |coercePreimagesImages| |shallowCopy| |rules| + |coefficient| |copies| |cSec| |degreePartition| |option| + |inconsistent?| |univariatePolynomialsGcds| |rootSimp| |safeCeiling| + |test| |sumOfDivisors| |LyndonBasis| |baseRDEsys| |zeroDimPrimary?| + |rootNormalize| |algebraicOf| |homogeneous?| |s19adf| |maxColIndex| + |primitivePart| |setrest!| |algebraicVariables| |dim| |partition| + |stiffnessAndStabilityOfODEIF| |associates?| |isExpt| |point| |unary?| + |isConnected?| |bubbleSort!| |prepareDecompose| |f04asf| |previous| + |hex| |primextintfrac| |acoshIfCan| |writeInt8!| |prefix| |sort| + |rightExactQuotient| |ScanFloatIgnoreSpaces| |UpTriBddDenomInv| + |stopTableInvSet!| |f01brf| |subResultantGcd| + |generalizedContinuumHypothesisAssumed| |infix| |rootsOf| + |wordInGenerators| |hypergeometric0F1| |rightTrim| |numFunEvals| |max| + |e02ddf| |findCycle| |realRoots| |overbar| |series| |binding| + |complexNumericIfCan| |rightExtendedGcd| |leftTrim| |sPol| + |stoseInvertibleSet| |curryLeft| |leftDivide| |elem?| |indices| + |leftExactQuotient| |hexDigit| |script| |uncouplingMatrices| |f02bjf| + |cAcosh| |f01bsf| |random| |identityMatrix| |mainDefiningPolynomial| + |toseLastSubResultant| |iicosh| |palgextint| |hclf| |maxrow| + |complexNormalize| |divide| |stoseLastSubResultant| |quadratic?| + |OMgetInteger| |monicRightFactorIfCan| |biRank| |tablePow| |imagk| + |shellSort| |showTheSymbolTable| |min| |digits| |quotient| |s17akf| + |cAtan| |tex| |clearDenominator| |coefficients| |impliesOperands| + |lagrange| |definingInequation| |normal01| |over| + |linearlyDependentOverZ?| |minPol| |getZechTable| |internal?| + |semicolonSeparate| |setTex!| |localUnquote| |useEisensteinCriterion?| + |d01aqf| |primeFrobenius| |rowEchelonLocal| |radicalSolve| |merge!| + |interReduce| |rightOne| |explogs2trigs| |internalAugment| |second| + |addmod| |pattern| |red| |localIntegralBasis| |d01alf| + |semiResultantEuclidean1| |f02agf| |setlast!| |supDimElseRittWu?| + |third| |partialQuotients| |df2ef| |c06gcf| |euclideanGroebner| + |currentSubProgram| |cyclotomicDecomposition| |yCoordinates| |tan2cot| + |SturmHabichtSequence| |cyclic| |algDsolve| |deref| |points| + |rationalPoint?| |makeSketch| |singleFactorBound| |iisech| + |univariate?| |resetVariableOrder| |ran| |integralBasisAtInfinity| + |createMultiplicationMatrix| |primitivePart!| |gderiv| |predicates| + |message| |taylorQuoByVar| |pseudoQuotient| |inverseLaplace| + |OMconnOutDevice| |adjoint| |identity| |getSyntaxFormsFromFile| + |setnext!| |iprint| |identification| |lyndon| |quadraticForm| |rk4f| + |evaluateInverse| |printTypes| |entries| |complexRoots| |iiabs| + |setsubMatrix!| |monomials| |void| |axesColorDefault| |antiCommutator| + |evaluate| |fixedPoints| |ramified?| |leftRankPolynomial| + |insertionSort!| |newSubProgram| |multiplyExponents| |exponential| + |primPartElseUnitCanonical!| |sum| |LazardQuotient2| |idealiserMatrix| + |conjug| |subtractIfCan| |characteristicSerie| |colorDef| + |mainSquareFreePart| |numberOfChildren| |permanent| |fi2df| + |buildSyntax| |sumSquares| |nonQsign| |whatInfinity| |cons| + |changeName| |approxNthRoot| |row| |messagePrint| |Beta| |deepExpand| + |iterationVar| |c06ekf| |groebner| |explicitlyFinite?| + |basisOfLeftNucleus| |alternative?| |complexEigenvectors| |lambert| + |subresultantSequence| |mr| |generalLambert| |f02akf| |deleteRoutine!| + |d01amf| |cup| |rotatez| |elColumn2!| |imagi| |lp| |d01ajf| + |fractRagits| |allRootsOf| |f02axf| |radix| |mapmult| |d01apf| + |nthRootIfCan| |roughEqualIdeals?| |escape| |coerceS| |seed| + |zeroVector| |selectIntegrationRoutines| + |functionIsContinuousAtEndPoints| |clipBoolean| |exprToUPS| + |systemCommand| |possiblyInfinite?| |f07fdf| |s21bbf| + |integralCoordinates| |constantOperator| |halfExtendedResultant1| + |constantRight| |qqq| |create| |source| |root?| |lhs| |ParCondList| + |selectPolynomials| |tubeRadiusDefault| |ldf2lst| |numberOfComposites| + |e02zaf| |controlPanel| |OMconnectTCP| |rhs| |subscriptedVariables| + |dequeue| |accuracyIF| |findConstructor| |s14aaf| |e04dgf| + |radicalRoots| |raisePolynomial| |extend| |normal| |resize| + |dihedralGroup| |cothIfCan| |addPointLast| |Aleph| |lintgcd| |isPower| + |sin?| |adaptive3D?| |e01bff| |OMgetSymbol| |stFuncN| + |genericRightNorm| |s17dlf| |subset?| |matrixDimensions| |cyclotomic| + |removeRedundantFactorsInContents| |stop| |style| |duplicates?| + |commutative?| |cSin| |datalist| |setButtonValue| |target| |powerSum| + |totalLex| |zeroDim?| |scalarTypeOf| |extractSplittingLeaf| + |strongGenerators| |numFunEvals3D| |leastAffineMultiple| + |indicialEquation| |distance| |intcompBasis| |mapUnivariate| + |chineseRemainder| |reduced?| |changeMeasure| |tube| |sylvesterMatrix| + |rightMinimalPolynomial| |subResultantChain| |leftZero| + |binarySearchTree| |iicos| |pmComplexintegrate| |setRealSteps| + |cosSinInfo| |besselI| |numberOfOperations| |derivationCoordinates| + |represents| |optpair| |rationalIfCan| |swap| |intChoose| |power| + |permutation| |s17ajf| |lfintegrate| |cond| |discreteLog| |leftMult| + |compound?| |univariateSolve| |weakBiRank| |ravel| |precision| + |asecIfCan| |tubePointsDefault| |karatsubaOnce| |iitanh| |bumptab1| + |euclideanNormalForm| |product| |dioSolve| |linearAssociatedExp| + |PollardSmallFactor| |reshape| |e01daf| |listOfLists| |writeByte!| + |firstNumer| |lfinfieldint| |totalDegree| |screenResolution3D| + |flexible?| |prefixRagits| |quasiMonicPolynomials| |sparsityIF| + |extendedIntegrate| |halfExtendedSubResultantGcd1| |mesh| + |safetyMargin| |idealiser| |d01fcf| |e02adf| |rischNormalize| + |GospersMethod| |randnum| |distFact| |acothIfCan| |less?| + |solveLinear| |overlabel| |upperCase!| |saturate| |listYoungTableaus| + |separate| |stopTable!| |perfectNthRoot| |vconcat| + |integralMatrixAtInfinity| |tanintegrate| |difference| + |cRationalPower| |OMgetEndBVar| |currentCategoryFrame| + |tryFunctionalDecomposition| |tValues| |OMputEndAtp| + |chainSubResultants| |call| |listBranches| |patternMatchTimes| + |removeZeroes| |update| |unit?| |select!| |deepestTail| + |stopMusserTrials| |d01gbf| |setleft!| |doublyTransitive?| + |complexSolve| |linSolve| |phiCoord| |karatsubaDivide| ** + |bandedHessian| |linear?| |sayLength| |medialSet| |exprToXXP| |init| + |mapCoef| |exprex| |collectUpper| |xn| |OMReadError?| |mightHaveRoots| + |algint| |OMgetObject| |Is| |c06gbf| |multiplyCoefficients| + |rootProduct| |e04ycf| |dimensionOfIrreducibleRepresentation| EQ + |OMgetFloat| |generalizedEigenvector| |subResultantGcdEuclidean| + |positiveSolve| |cCoth| |wholeRagits| + |semiIndiceSubResultantEuclidean| |LiePoly| |position| + |numberOfVariables| |rightZero| |approximants| + |createLowComplexityTable| |factors| |formula| |dmp2rfi| |laplacian| + |leftRegularRepresentation| |explicitlyEmpty?| |associatedSystem| + |solveLinearPolynomialEquationByFractions| |prime| |leadingIndex| + |twist| |cycleSplit!| |any| |maxint| |indicialEquationAtInfinity| + |s18dcf| |exptMod| |e01bef| |symbolTable| |s17aef| |char| + |rightCharacteristicPolynomial| |linGenPos| |irreducibleFactors| + |whileLoop| |dmpToHdmp| |e01baf| |setMaxPoints| |checkPrecision| + |rational| |OMputEndBVar| |children| |pol| |index| |dmpToP| |nthRoot| + |rotate| |convergents| |reciprocalPolynomial| |nrows| + |factorByRecursion| |s13acf| |realEigenvalues| |fortranLinkerArgs| + |chvar| |nextNormalPoly| |purelyTranscendental?| |forLoop| |interpret| + |ncols| |monomRDEsys| |norm| |standardBasisOfCyclicSubmodule| + |computeCycleLength| |OMputSymbol| |rk4| |conditionP| + |separateDegrees| |fillPascalTriangle| |sts2stst| |direction| |iiexp| + |pair| |lazyIrreducibleFactors| |linear| |symmetricDifference| + |unmakeSUP| |bitTruth| |completeEval| |curry| |logpart| |innerSolve1| + |cyclicEntries| |lo| |droot| |extractTop!| |palgRDE0| |pair?| |value| + |shiftRight| |monicLeftDivide| |ramifiedAtInfinity?| |iFTable| + |polynomial| |incr| |kind| |lex| |lieAdmissible?| |polygon?| + |fixPredicate| |crushedSet| |float?| |extractIndex| |weierstrass| + |adaptive?| |op| |hdmpToP| |polygamma| |useNagFunctions| |factorials| + |cardinality| |balancedFactorisation| |physicalLength| |stFunc1| + |intermediateResultsIF| |s18aef| |normalise| |genericRightTrace| + |normalizedDivide| |reverse!| |nextsousResultant2| + |removeRedundantFactorsInPols| |cyclotomicFactorization| + |OMUnknownSymbol?| |removeIrreducibleRedundantFactors| |FormatRoman| + |besselK| |eigenvectors| |resultantEuclideannaif| |clipSurface| + |finiteBasis| |extendIfCan| |varList| |rewriteSetWithReduction| + |aQuadratic| |tanh2coth| |sqfrFactor| |cCsc| |rightDivide| + |KrullNumber| F |dfRange| |operation| |linears| |symFunc| + |nthExponent| |rdregime| |comment| |subNodeOf?| |karatsuba| + |coerceListOfPairs| |composites| |d01akf| |d02gbf| |getMeasure| + |mathieu24| |trunc| |createZechTable| |qfactor| |matrix| + |numberOfFractionalTerms| |upperCase| |firstSubsetGray| |OMputAttr| + |characteristic| |union| |s17aff| |stoseInternalLastSubResultant| + |bitCoef| |branchIfCan| |absolutelyIrreducible?| |musserTrials| + |tryFunctionalDecomposition?| |antisymmetric?| |coHeight| + |outlineRender| |jacobiIdentity?| |reverseLex| |ip4Address| |polyRDE| + |appendPoint| |vectorise| |hasSolution?| |UP2ifCan| |length| + |outputAsTex| |viewport2D| |viewpoint| |edf2efi| |kovacic| |close| + |evenInfiniteProduct| |rightFactorIfCan| |clearFortranOutputStack| + |purelyAlgebraic?| |zeroOf| |normalizeAtInfinity| |rightTraceMatrix| + |shrinkable| |scripts| |coth2tanh| |mapExponents| |inverseColeman| + |doubleComplex?| |lfunc| |arity| |factor1| |hi| |OMreadFile| + |dihedral| |pquo| |Frobenius| |readUInt8!| |e04jaf| |display| + |lexGroebner| |minrank| |divisorCascade| |realZeros| + |rightRankPolynomial| |invertible?| |ellipticCylindrical| |tanSum| + |associatedEquations| |lazyPquo| |cycleElt| |lazy?| |padicallyExpand| + |closedCurve| |defineProperty| |id| |determinant| |OMputEndApp| + |charthRoot| |OMencodingBinary| |initTable!| |commaSeparate| |deriv| + |linearMatrix| |createLowComplexityNormalBasis| |separateFactors| + |iicsch| |cAsech| |getMatch| |goto| |linearDependence| + |trailingCoefficient| |var2StepsDefault| |host| |invertibleElseSplit?| + |s13adf| |powmod| |mapExpon| |table| |iteratedInitials| |normDeriv2| + |principalIdeal| |setLabelValue| |c06frf| |numeric| |cPower| + |tanIfCan| |acscIfCan| |sizeMultiplication| |elRow1!| |totalfract| + |new| |palgint0| |showScalarValues| |input| |obj| + |rootOfIrreduciblePoly| |radical| |startTableInvSet!| |cTan| + |enqueue!| |quotedOperators| |expextendedint| |search| |makeop| |plus| + |trapezoidal| |f07aef| |startTableGcd!| |library| |sumOfSquares| + |ldf2vmf| |deepestInitial| |principal?| |cache| |ratDenom| + |toseInvertibleSet| |plenaryPower| |fractRadix| |monicModulo| |mindeg| + |binomThmExpt| |discriminant| |clipPointsDefault| |e02agf| |addPoint| + |pointColorPalette| |reindex| |rowEchelon| |screenResolution| + |monicCompleteDecompose| |checkRur| |numericIfCan| |repeatUntilLoop| + |nullSpace| |ReduceOrder| |safeFloor| |meshPar1Var| |OMgetApp| |bat1| + |fullDisplay| |getGraph| |iCompose| |finite?| |cSech| |s17dcf| + |completeSmith| |factorsOfCyclicGroupSize| |geometric| |parts| + |generators| |groebnerIdeal| |isOpen?| |set| |category| |s18adf| + |completeEchelonBasis| |simpleBounds?| |iisqrt2| |checkForZero| |inc| + |mainValue| |ptFunc| |tab| |outputBinaryFile| |linearPolynomials| + |domain| |sech2cosh| |composite| |finiteBound| |sup| |pop!| + |writeBytes!| |leftAlternative?| |lazyIntegrate| |byteBuffer| + |algebraicSort| |upperCase?| |package| |continuedFraction| + |OMconnInDevice| |subTriSet?| |leftRecip| |pile| |roughSubIdeal?| + |cot2tan| |resetBadValues| |trim| |fortranLiteralLine| |dot| |atoms| + |closeComponent| |selectNonFiniteRoutines| |conjugates| |gcdcofact| + |extractPoint| |sequences| |intersect| |makeTerm| |connectTo| |delay| + |initiallyReduce| |dominantTerm| |height| |green| |s17acf| + |externalList| |nthExpon| |transcendent?| |gcdcofactprim| |remove!| + |sortConstraints| |zeroDimensional?| |clearTheSymbolTable| + |printInfo!| |localReal?| |scripted?| |maxrank| |enterInCache| ~= + |integer?| |bat| |rightPower| |areEquivalent?| |sumOfKthPowerDivisors| + |tubePlot| |seriesSolve| |semiResultantEuclidean2| |schwerpunkt| + |SturmHabicht| |depth| |solid?| |factorList| |coerce| |palgRDE| + |rootDirectory| |midpoint| |eq?| |getPickedPoints| |makeYoungTableau| + |taylorIfCan| |stronglyReduced?| |quasiRegular?| |complexZeros| + |btwFact| |construct| |expenseOfEvaluation| |OMsupportsCD?| + |curveColorPalette| |rk4a| |SturmHabichtCoefficients| |decompose| + |cycle| |makeResult| |companionBlocks| |equiv| |typeList| + |integralRepresents| |rightFactorCandidate| |rightNorm| |bipolar| + |getDatabase| |complementaryBasis| |f02aaf| |close!| |subMatrix| + |show| |inrootof| |size?| |digit?| |element?| |magnitude| + |prinpolINFO| |internalIntegrate0| |getlo| |internalInfRittWu?| + |pascalTriangle| |region| |alphanumeric| |OMread| |explicitEntries?| + |surface| |monomialIntegrate| |aromberg| |computeBasis| + |collectQuasiMonic| |lowerCase?| |multinomial| |trace| |comparison| + |bigEndian| |output| |horizConcat| |permutationRepresentation| + |nextColeman| |OMputObject| |tubeRadius| |simplifyPower| |iiacosh| + |vark| |expr| |setprevious!| |e04gcf| |tail| |trace2PowMod| |isPlus| + |BasicMethod| |component| |f02ajf| |primPartElseUnitCanonical| + |rightRegularRepresentation| |monicRightDivide| |bfEntry| + |symmetricRemainder| |partialDenominators| |wordsForStrongGenerators| + |torsion?| UTS2UP |complexEigenvalues| |ksec| + |ScanFloatIgnoreSpacesIfCan| |mapUnivariateIfCan| + |countRealRootsMultiple| |leftTraceMatrix| |unknown| |low| + |elementary| |plot| |tab1| |graphs| |basisOfMiddleNucleus| + |dualSignature| |sncndn| |true| |OMgetEndBind| |diophantineSystem| + |jordanAlgebra?| |dAndcExp| |option?| |fortranCarriageReturn| + |littleEndian| |iiasec| |iiasin| |weighted| |factorial| |oddlambert| + |variable| |df2mf| |moebiusMu| |rightRecip| + |unprotectedRemoveRedundantFactors| |scan| |axes| |cap| |badNum| + |zeroDimPrime?| |pr2dmp| |iterators| |outputList| |insertTop!| + |readLineIfCan!| |makeMulti| |quatern| |imports| |OMsend| |weights| + |readUInt32!| |measure2Result| |compiledFunction| |hash| |matrixGcd| + |c06ebf| |iiasech| |viewPhiDefault| |copy!| |predicate| |bombieriNorm| + |rk4qc| |radicalSimplify| |fullPartialFraction| |ode| |count| |e04naf| + |hermite| |setelt| |interactiveEnv| |exp1| |postfix| |OMgetType| + |writable?| |extension| |generateIrredPoly| + |initializeGroupForWordProblem| |traceMatrix| |perfectSqrt| |cAsin| + |li| |paren| |constant?| |stoseInvertible?reg| |OMreceive| + |calcRanges| |coerceImages| |dequeue!| |times!| |setTopPredicate| + |copy| |pureLex| |mapSolve| |variable?| |open?| |ef2edf| |midpoints| + |f02abf| |ode2| |bipolarCylindrical| |parseString| |e01bhf| |fortran| + |graphStates| |integral| |next| |Hausdorff| |leadingBasisTerm| + |power!| |curveColor| |s19acf| |triangularSystems| |showClipRegion| + |parabolicCylindrical| |elliptic?| |OMgetAttr| |monomRDE| + |toseSquareFreePart| |noLinearFactor?| |firstDenom| |e02aef| |odd?| + |autoCoerce| |polynomialZeros| |cross| |failed?| |optional?| + |basisOfCentroid| |cycleEntry| |c06fqf| |equiv?| |options| |groebner?| + |findBinding| |asinhIfCan| |back| |createNormalPoly| |iomode| |f02aef| + |cscIfCan| |graphImage| |fmecg| |pToHdmp| |schema| + |numberOfPrimitivePoly| |indicialEquations| |parameters| + |relativeApprox| |ref| |OMputAtp| |evenlambert| |empty| |squareFree| + |nthr| |prevPrime| |conditionsForIdempotents| |f2st| |e02dff| + |tableau| |sdf2lst| |retractable?| |string| |polyRicDE| |monicDivide| + |rightUnit| |high| |sylvesterSequence| |lastSubResultantEuclidean| + |romberg| |subHeight| |physicalLength!| |OMputBind| |f04mbf| + |traverse| |leviCivitaSymbol| |cycleTail| |shallowExpand| |reify| + |quotientByP| |probablyZeroDim?| |pleskenSplit| |airyAi| |aspFilename| + |getExplanations| |every?| |coefChoose| |shiftLeft| |denomLODE| + |setColumn!| |removeCosSq| |mapUp!| |createNormalPrimitivePoly| + |iroot| |push!| |s20acf| |tower| |rightAlternative?| |squareFreePrim| + |splitDenominator| NOT |fibonacci| |newTypeLists| |setPrologue!| + |monicDecomposeIfCan| |genericLeftNorm| |d01asf| |df2st| |sqfree| + |functionIsFracPolynomial?| |iicsc| |decomposeFunc| OR |reduction| + |swapColumns!| |normalizeIfCan| |reduceLODE| |laguerreL| |gramschmidt| + |simplify| |LiePolyIfCan| |nullary| |swap!| |removeSquaresIfCan| AND + |Ci| |removeSuperfluousCases| |eq| |setErrorBound| |tanNa| |directory| + |closedCurve?| |closed?| |readInt16!| |endSubProgram| |coerceL| + |consnewpol| |iter| |numericalOptimization| |euler| |headReduced?| + |diagonals| |branchPoint?| |innerSolve| |csch2sinh| + |LowTriBddDenomInv| |condition| |d03edf| |string?| |invmod| + |sinhIfCan| |squareFreeLexTriangular| |leftPower| |log10| |e02bef| + |leadingExponent| |pushdterm| |complexNumeric| |coshIfCan| |s15adf| + |moreAlgebraic?| |bit?| |e01sef| |jacobi| |rightGcd| |generate| + |primlimintfrac| |rank| |euclideanSize| |constDsolve| |polyred| + |bitand| |makeVariable| |pointLists| |ideal| |LagrangeInterpolation| + |splitLinear| |continue| |makeSeries| |kernels| |limitedIntegrate| + |fixedPoint| |bitior| |Si| |OMencodingXML| |signAround| + |setCondition!| |negative?| |rur| |incrementBy| |preprocess| |iiacsch| + |thetaCoord| |univariate| |sec2cos| |makeUnit| |solveInField| + |exponentialOrder| |hitherPlane| |drawToScale| |f01maf| |expand| + |cycleLength| |OMParseError?| |f02awf| |factorSquareFreeByRecursion| + |OMputEndError| |omError| |OMgetAtp| |member?| |trigs| + |commonDenominator| |filterWhile| |errorInfo| |oneDimensionalArray| + |OMopenString| |kroneckerDelta| |coordinates| |exp| |equality| + |stoseInvertibleSetreg| |nilFactor| |doubleDisc| + |discriminantEuclidean| |filterUntil| |setFormula!| |hMonic| |setref| + |matrixConcat3D| |factor| |mulmod| * |empty?| |nlde| |imagj| + |clearTable!| |unit| |select| |iiasinh| + |solveLinearPolynomialEquation| |bothWays| |sqrt| + |drawComplexVectorField| |argument| |s19aaf| |besselJ| |iisqrt3| + |acosIfCan| |commutator| |myDegree| |setvalue!| |diagonal?| |real| + |leftNorm| |f04adf| |nullity| |connect| |implies?| |nil?| |f02aff| + |palgLODE| |tanhIfCan| |f07fef| |imag| |polarCoordinates| |sequence| + |returns| |octon| |mkIntegral| |callForm?| |semiDiscriminantEuclidean| + |directProduct| |moduleSum| |f04mcf| |s15aef| |setelt!| + |prepareSubResAlgo| |range| |quasiAlgebraicSet| + |extendedSubResultantGcd| |setStatus!| |signatureAst| |unaryFunction| + |HenselLift| |radicalEigenvectors| |explimitedint| |PDESolve| |An| + |normalize| |nativeModuleExtension| |simpson| |algebraicDecompose| + GF2FG |lift| |leadingSupport| |mathieu22| |brace| |changeWeightLevel| + |leftQuotient| |drawCurves| |infinityNorm| |prindINFO| |setFieldInfo| + Y |bivariatePolynomials| |zeroSetSplit| |makeRecord| |hasHi| |compile| + |reduce| |e01sff| |pushNewContour| |destruct| |sin2csc| |putColorInfo| + |members| |brillhartIrreducible?| |divideExponents| |objectOf| |redPo| + |categoryFrame| |factorsOfDegree| |orthonormalBasis| |aLinear| SEGMENT + |ratPoly| |completeHermite| |build| |solveLinearlyOverQ| + |semiResultantEuclideannaif| |cyclic?| |froot| |c05pbf| |isList| + |leaf?| |copyInto!| |mkAnswer| |paraboloidal| |cAcot| |mkcomm| + |linkToFortran| |semiSubResultantGcdEuclidean1| |null| |numberOfHues| + |innerint| |or?| |highCommonTerms| |setAdaptive| |exponents| + |pseudoRemainder| |mergeFactors| |OMopenFile| |OMgetError| |not| + |iflist2Result| |lfextendedint| |monomial| |augment| + |nextPrimitivePoly| |e01sbf| |s13aaf| |factorSquareFree| + |splitSquarefree| |primes| |henselFact| |and| |realElementary| + |legendreP| |normInvertible?| |multivariate| |associator| |OMserve| + |gethi| |meshFun2Var| |bfKeys| |modularGcdPrimitive| |hermiteH| |or| + |leadingCoefficientRicDE| |split!| |variables| |mapdiv| + |fortranDouble| |index?| |e02daf| |epilogue| |removeConstantTerm| + |lprop| |edf2df| |xor| |mapDown!| |nthCoef| |seriesToOutputForm| + |singRicDE| |Lazard2| |fortranLogical| |testModulus| + |numberOfImproperPartitions| |OMgetVariable| |signature| + |abelianGroup| |case| |countable?| |rootSplit| |harmonic| |c06fuf| + |setfirst!| |d02cjf| |setPosition| |removeSuperfluousQuasiComponents| + |palgint| |presub| |OMencodingSGML| |Zero| |exponent| |OMwrite| + |cschIfCan| |moebius| |f02fjf| |mapMatrixIfCan| |fprindINFO| + |gcdPolynomial| |edf2fi| |pastel| |characteristicSet| |One| |bumprow| + |d01anf| |exponential1| |s17def| |patternVariable| |modularGcd| + |setScreenResolution3D| |numberOfDivisors| |cycles| + |squareFreePolynomial| |byte| |recolor| |hue| |lazyResidueClass| + |taylor| |xCoord| |solve| |compactFraction| |setScreenResolution| + |groebgen| |rspace| |cyclicGroup| |ffactor| |name| |cos2sec| + |noKaratsuba| |laurent| |pointData| |complexForm| |fortranReal| + |numerator| |noncommutativeJordanAlgebra?| |jacobian| |initial| + |pmintegrate| |att2Result| |makeFR| |bytes| |property| |body| + |puiseux| |cylindrical| |inverse| |OMputBVar| |collectUnder| + |lazyVariations| |univariatePolynomial| |quickSort| |int| |latex| + |sorted?| |internalZeroSetSplit| FG2F |blue| |createNormalElement| + |selectsecond| |showFortranOutputStack| |primlimitedint| + |tableForDiscreteLogarithm| |elt| |inv| |listLoops| |root| |logIfCan| + |algSplitSimple| |updateStatus!| |unparse| |cAsec| |f01qef| + |generalSqFr| |normal?| |nil| |infinite| |arbitraryExponent| + |approximate| |complex| |shallowMutable| |canonical| |noetherian| + |central| |partiallyOrderedSet| |arbitraryPrecision| + |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| + |additiveValuation| |unitsKnown| |canonicalUnitNormal| + |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| + |commutative|)
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T) ((-102) |has| |#1| (-1094)) ((-611 (-859)) -4030 (|has| |#1| (-1094)) (|has| |#1| (-611 (-859)))) ((-309 |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) ((-489 |#1|) . T) ((-514 |#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) ((-1094) |has| |#1| (-1094)) ((-1209) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-407 (-564))) -4007 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-38 |#1|) . T) ((-38 $) -4007 (|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#) -4007 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-131) . T) ((-145) -4007 (|has| |#1| (-349)) (|has| |#1| (-145))) ((-147) |has| |#1| (-147)) ((-614 #0#) -4007 (|has| |#1| (-1035 (-407 (-564)))) (|has| |#1| (-349)) (|has| |#1| (-363))) ((-614 (-564)) . T) ((-614 |#1|) . T) ((-614 $) -4007 (|has| |#1| (-556)) (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-611 (-859)) . T) ((-172) . T) ((-612 (-169 (-225))) |has| |#1| (-1019)) ((-612 (-169 (-379))) |has| |#1| (-1019)) ((-612 (-536)) |has| |#1| (-612 (-536))) ((-612 (-889 (-379))) |has| |#1| (-612 (-889 (-379)))) ((-612 (-889 (-564))) |has| |#1| (-612 (-889 (-564)))) ((-612 #1=(-1166 |#1|)) . 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T) ((-452) -4007 (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-493) |has| |#1| (-1194)) ((-514 (-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((-514 |#1| |#1|) |has| |#1| (-309 |#1|)) ((-556) -4007 (|has| |#1| (-556)) (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-644 #0#) -4007 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-644 |#1|) . T) ((-644 $) . T) ((-637 (-564)) |has| |#1| (-637 (-564))) ((-637 |#1|) . T) ((-714 #0#) -4007 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-714 |#1|) . T) ((-714 $) -4007 (|has| |#1| (-556)) (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-721 |#1| #1#) . T) ((-723) . T) ((-847) |has| |#1| (-847)) ((-897 (-1170)) |has| |#1| (-897 (-1170))) ((-883 (-379)) |has| |#1| (-883 (-379))) ((-883 (-564)) |has| |#1| (-883 (-564))) ((-881 |#1|) . T) ((-906) -12 (|has| |#1| (-307)) (|has| |#1| (-906))) ((-917) -4007 (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-999) -12 (|has| |#1| (-999)) (|has| |#1| (-1194))) ((-1035 (-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) ((-1035 (-564)) |has| |#1| (-1035 (-564))) ((-1035 |#1|) . T) ((-1052 #0#) -4007 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-1052 |#1|) . T) ((-1052 $) . T) ((-1046) . T) ((-1053) . T) ((-1106) . T) ((-1094) . T) ((-1145) |has| |#1| (-349)) ((-1194) |has| |#1| (-1194)) ((-1197) |has| |#1| (-1194)) ((-1209) . 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(|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -4030 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -4030 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -4030 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-614 #0=(-407 (-564))) -12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094))) ((-614 (-564)) -4030 (|has| |#2| (-1046)) (-12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-614 |#2|) -4030 (|has| |#2| (-1094)) (|has| |#2| (-172))) ((-611 (-859)) -4030 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-611 (-859))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-611 (-1259 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1046)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1046))) ((-286 #1=(-564) |#2|) . T) ((-288 #1# |#2|) . T) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-368) |has| |#2| (-368)) ((-377 |#2|) |has| |#2| (-1046)) ((-411 |#2|) |has| |#2| (-1094)) ((-489 |#2|) . T) ((-602 #1# |#2|) . T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-644 |#2|) -4030 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 $) -4030 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-637 (-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1046))) ((-637 |#2|) |has| |#2| (-1046)) ((-714 |#2|) -4030 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-723) -4030 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-723)) (|has| |#2| (-172))) ((-788) |has| |#2| (-845)) ((-789) -4030 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-790) |has| |#2| (-790)) ((-791) -4030 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-792) -4030 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-845) |has| |#2| (-845)) ((-847) -4030 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-897 (-1170)) -12 (|has| |#2| (-897 (-1170))) (|has| |#2| (-1046))) ((-1035 #0#) -12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094))) ((-1035 (-564)) -12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094))) ((-1035 |#2|) |has| |#2| (-1094)) ((-1052 |#2|) -4030 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1052 $) |has| |#2| (-172)) ((-1046) -4030 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-1053) -4030 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-1106) -4030 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-723)) (|has| |#2| (-172))) ((-1094) -4030 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1209) . T) ((-1266 |#2|) |has| |#2| (-363))) -((-1525 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-1699 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-2187 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) -(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -1525 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -1699 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2187 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-768) (-1209) (-1209)) (T -239)) -((-2187 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-768)) (-4 *6 (-1209)) (-4 *7 (-1209)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-1699 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-768)) (-4 *6 (-1209)) (-4 *2 (-1209)) (-5 *1 (-239 *5 *6 *2)))) (-1525 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-768)) (-4 *7 (-1209)) (-4 *5 (-1209)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) -(-10 -7 (-15 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T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -4007 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -4007 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -4007 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-614 #0=(-407 (-564))) -12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094))) ((-614 (-564)) -4007 (|has| |#2| (-1046)) (-12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-614 |#2|) -4007 (|has| |#2| (-1094)) (|has| |#2| (-172))) ((-611 (-859)) -4007 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-611 (-859))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-611 (-1259 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1046)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1046))) ((-286 #1=(-564) |#2|) . T) ((-288 #1# |#2|) . T) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-368) |has| |#2| (-368)) ((-377 |#2|) |has| |#2| (-1046)) ((-411 |#2|) |has| |#2| (-1094)) ((-489 |#2|) . T) ((-602 #1# |#2|) . T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-644 |#2|) -4007 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 $) -4007 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-637 (-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1046))) ((-637 |#2|) |has| |#2| (-1046)) ((-714 |#2|) -4007 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-723) -4007 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-723)) (|has| |#2| (-172))) ((-788) |has| |#2| (-845)) ((-789) -4007 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-790) |has| |#2| (-790)) ((-791) -4007 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-792) -4007 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-845) |has| |#2| (-845)) ((-847) -4007 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-897 (-1170)) -12 (|has| |#2| (-897 (-1170))) (|has| |#2| (-1046))) ((-1035 #0#) -12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094))) ((-1035 (-564)) -12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094))) ((-1035 |#2|) |has| |#2| (-1094)) ((-1052 |#2|) -4007 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1052 $) |has| |#2| (-172)) ((-1046) -4007 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-1053) -4007 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-1106) -4007 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-723)) (|has| |#2| (-172))) ((-1094) -4007 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1209) . T) ((-1266 |#2|) |has| |#2| (-363))) +((-3831 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-4204 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-2318 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) +(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -3831 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -4204 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2318 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-768) (-1209) (-1209)) (T -239)) +((-2318 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-768)) (-4 *6 (-1209)) (-4 *7 (-1209)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-4204 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-768)) (-4 *6 (-1209)) (-4 *2 (-1209)) (-5 *1 (-239 *5 *6 *2)))) (-3831 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-768)) (-4 *7 (-1209)) (-4 *5 (-1209)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-1213) |has| |#1| (-906))) -((-3732 (((-112) $ $) 19 (|has| |#1| (-1094)))) (-2079 ((|#1| $) 54)) (-2519 ((|#1| $) 44)) (-2969 (((-112) $ (-768)) 8)) (-2818 (($) 7 T CONST)) (-1649 (($ $) 60)) (-2797 (($ $) 48)) (-2881 ((|#1| |#1| $) 46)) (-2226 ((|#1| $) 45)) (-3616 (((-641 |#1|) $) 30 (|has| $ (-6 -4411)))) (-2275 (((-112) $ (-768)) 9)) (-1386 (((-641 |#1|) $) 29 (|has| $ (-6 -4411)))) (-2431 (((-112) |#1| $) 27 (-12 (|has| |#1| (-1094)) (|has| $ (-6 -4411))))) (-2606 (($ (-1 |#1| |#1|) $) 34 (|has| $ (-6 -4412)))) (-2187 (($ (-1 |#1| |#1|) $) 35)) (-1500 (((-112) $ (-768)) 10)) (-2395 (((-768) $) 61)) (-2217 (((-1152) $) 22 (|has| |#1| (-1094)))) (-2828 ((|#1| $) 39)) (-2036 ((|#1| |#1| $) 52)) (-2536 ((|#1| |#1| $) 51)) (-2974 (($ |#1| $) 40)) (-3724 (((-768) $) 55)) (-3864 (((-1114) $) 21 (|has| |#1| (-1094)))) (-1945 ((|#1| $) 62)) (-3001 ((|#1| $) 50)) (-1351 ((|#1| $) 49)) (-1292 ((|#1| $) 41)) (-3736 (((-112) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4411)))) (-2416 (($ $ (-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))))) (-1717 (((-112) $ $) 14)) (-2971 ((|#1| |#1| $) 58)) (-4003 (((-112) $) 11)) (-3434 (($) 12)) (-3220 ((|#1| $) 59)) (-1718 (($) 57) (($ (-641 |#1|)) 56)) (-3728 (((-768) $) 43)) (-3873 (((-768) (-1 (-112) |#1|) $) 31 (|has| $ (-6 -4411))) (((-768) |#1| $) 28 (-12 (|has| |#1| (-1094)) (|has| $ (-6 -4411))))) (-3896 (($ $) 13)) (-3742 (((-859) $) 18 (|has| |#1| (-611 (-859))))) (-2716 ((|#1| $) 53)) (-3745 (($ (-641 |#1|)) 42)) (-3957 ((|#1| $) 63)) (-1417 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4411)))) (-1705 (((-112) $ $) 20 (|has| |#1| (-1094)))) (-2641 (((-768) $) 6 (|has| $ (-6 -4411))))) +((-4067 (*1 *2 *3) (-12 (-4 *4 (-1046)) (-4 *3 (-847)) (-4 *5 (-266 *3)) (-4 *6 (-790)) (-5 *2 (-1 *1 (-768))) (-4 *1 (-253 *4 *3 *5 *6)))) (-2831 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1046)) (-4 *4 (-847)) (-4 *5 (-266 *4)) (-4 *6 (-790)) (-5 *2 (-641 *4)))) (-1793 (*1 *2 *1 *3) (-12 (-4 *1 (-253 *4 *3 *5 *6)) (-4 *4 (-1046)) (-4 *3 (-847)) (-4 *5 (-266 *3)) (-4 *6 (-790)) (-5 *2 (-768)))) (-1793 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1046)) (-4 *4 (-847)) (-4 *5 (-266 *4)) (-4 *6 (-790)) (-5 *2 (-768)))) (-1366 (*1 *2 *1 *3) (-12 (-4 *1 (-253 *4 *3 *5 *6)) (-4 *4 (-1046)) (-4 *3 (-847)) (-4 *5 (-266 *3)) (-4 *6 (-790)) (-5 *2 (-768)))) (-3845 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1046)) (-4 *4 (-847)) (-4 *5 (-266 *4)) (-4 *6 (-790)) (-5 *2 (-641 (-768))))) (-2290 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1046)) (-4 *4 (-847)) (-4 *5 (-266 *4)) (-4 *6 (-790)) (-5 *2 (-768)))) (-3845 (*1 *2 *1 *3) (-12 (-4 *1 (-253 *4 *3 *5 *6)) (-4 *4 (-1046)) (-4 *3 (-847)) (-4 *5 (-266 *3)) (-4 *6 (-790)) (-5 *2 (-641 (-768))))) (-2290 (*1 *2 *1 *3) (-12 (-4 *1 (-253 *4 *3 *5 *6)) (-4 *4 (-1046)) (-4 *3 (-847)) (-4 *5 (-266 *3)) (-4 *6 (-790)) (-5 *2 (-768)))) (-1687 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1046)) (-4 *4 (-847)) (-4 *5 (-266 *4)) (-4 *6 (-790)) (-5 *2 (-112)))) (-2716 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *2 *5)) (-4 *3 (-1046)) (-4 *4 (-847)) (-4 *5 (-790)) (-4 *2 (-266 *4)))) (-4354 (*1 *1 *1) (-12 (-4 *1 (-253 *2 *3 *4 *5)) (-4 *2 (-1046)) (-4 *3 (-847)) (-4 *4 (-266 *3)) (-4 *5 (-790)))) (-2303 (*1 *1 *1) (-12 (-4 *1 (-253 *2 *3 *4 *5)) (-4 *2 (-1046)) (-4 *3 (-847)) (-4 *4 (-266 *3)) (-4 *5 (-790)))) (-4067 (*1 *2 *1) (-12 (-4 *3 (-233)) (-4 *3 (-1046)) (-4 *4 (-847)) (-4 *5 (-266 *4)) (-4 *6 (-790)) (-5 *2 (-1 *1 (-768))) (-4 *1 (-253 *3 *4 *5 *6))))) +(-13 (-946 |t#1| |t#4| |t#3|) (-231 |t#1|) (-1035 |t#2|) (-10 -8 (-15 -4067 ((-1 $ (-768)) |t#2|)) (-15 -2831 ((-641 |t#2|) $)) (-15 -1793 ((-768) $ |t#2|)) (-15 -1793 ((-768) $)) (-15 -1366 ((-768) $ |t#2|)) (-15 -3845 ((-641 (-768)) $)) (-15 -2290 ((-768) $)) (-15 -3845 ((-641 (-768)) $ |t#2|)) (-15 -2290 ((-768) $ |t#2|)) (-15 -1687 ((-112) $)) (-15 -2716 (|t#3| $)) (-15 -4354 ($ $)) (-15 -2303 ($ $)) (IF (|has| |t#1| (-233)) (PROGN (-6 (-514 |t#2| |t#1|)) (-6 (-514 |t#2| $)) (-6 (-309 $)) (-15 -4067 ((-1 $ (-768)) $))) |%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 $) -4007 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-407 (-564)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4007 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #0#) -4007 (|has| |#1| (-1035 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 |#1|) . T) ((-614 |#2|) . T) ((-614 |#3|) . T) ((-614 $) -4007 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-611 (-859)) . 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T) ((-302) . T) ((-363) |has| |#1| (-556)) ((-377 |#1|) |has| |#1| (-1046)) ((-400 |#1|) . T) ((-411 |#1|) . T) ((-452) |has| |#1| (-556)) ((-473) |has| |#1| (-473)) ((-514 (-610 $) $) . T) ((-514 $ $) . T) ((-556) |has| |#1| (-556)) ((-644 #0#) |has| |#1| (-556)) ((-644 |#1|) |has| |#1| (-172)) ((-644 $) -4030 (|has| |#1| (-1046)) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-637 (-564)) -12 (|has| |#1| (-637 (-564))) (|has| |#1| (-1046))) ((-637 |#1|) |has| |#1| (-1046)) ((-714 #0#) |has| |#1| (-556)) ((-714 |#1|) |has| |#1| (-172)) ((-714 $) |has| |#1| (-556)) ((-723) -4030 (|has| |#1| (-1106)) (|has| |#1| (-1046)) (|has| |#1| (-556)) (|has| |#1| (-473)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-847) . T) ((-897 (-1170)) |has| |#1| (-1046)) ((-883 (-379)) |has| |#1| (-883 (-379))) ((-883 (-564)) |has| |#1| (-883 (-564))) ((-881 |#1|) . 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T) ((-644 $) . T) ((-637 (-564)) |has| |#1| (-637 (-564))) ((-637 |#1|) . T) ((-714 #1#) |has| |#1| (-38 (-407 (-564)))) ((-714 |#1|) |has| |#1| (-172)) ((-714 $) -4030 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-723) . T) ((-847) |has| |#1| (-847)) ((-897 #2#) . T) ((-897 (-1170)) |has| |#1| (-897 (-1170))) ((-883 (-379)) -12 (|has| (-1076) (-883 (-379))) (|has| |#1| (-883 (-379)))) ((-883 (-564)) -12 (|has| (-1076) (-883 (-564))) (|has| |#1| (-883 (-564)))) ((-946 |#1| #0# #2#) . T) ((-906) |has| |#1| (-906)) ((-917) |has| |#1| (-363)) ((-1035 (-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) ((-1035 (-564)) |has| |#1| (-1035 (-564))) ((-1035 #2#) . T) ((-1035 |#1|) . T) ((-1052 #1#) |has| |#1| (-38 (-407 (-564)))) ((-1052 |#1|) . T) ((-1052 $) -4030 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1046) . T) ((-1053) . T) ((-1106) . T) ((-1094) . T) ((-1145) |has| |#1| (-1145)) ((-1213) |has| |#1| (-906))) -((-4269 (((-641 (-1076)) $) 34)) (-1348 (($ $) 31)) (-4245 (($ |#2| |#3|) NIL) (($ $ (-1076) |#3|) 28) (($ $ (-641 (-1076)) (-641 |#3|)) 27)) (-1309 (($ $) 14)) (-1320 ((|#2| $) 12)) (-2266 ((|#3| $) 10))) -(((-1236 |#1| |#2| |#3|) (-10 -8 (-15 -4269 ((-641 (-1076)) |#1|)) (-15 -4245 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -4245 (|#1| |#1| (-1076) |#3|)) (-15 -1348 (|#1| |#1|)) (-15 -4245 (|#1| |#2| |#3|)) (-15 -2266 (|#3| |#1|)) (-15 -1309 (|#1| |#1|)) (-15 -1320 (|#2| |#1|))) (-1237 |#2| |#3|) (-1046) (-789)) (T -1236)) -NIL -(-10 -8 (-15 -4269 ((-641 (-1076)) |#1|)) (-15 -4245 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -4245 (|#1| |#1| (-1076) |#3|)) (-15 -1348 (|#1| |#1|)) (-15 -4245 (|#1| |#2| |#3|)) (-15 -2266 (|#3| |#1|)) (-15 -1309 (|#1| |#1|)) (-15 -1320 (|#2| |#1|))) -((-3732 (((-112) $ $) 7)) (-4173 (((-112) $) 16)) (-4269 (((-641 (-1076)) $) 77)) (-3851 (((-1170) $) 106)) (-3719 (((-2 (|:| -4176 $) (|:| 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(-768) (-1076)) (-286 |t#1| |t#1|) (-286 $ $) (-233) (-231 |t#1|) (-10 -8 (-15 -3486 ((-1259 |t#1|) $ (-768))) (-15 -1875 ((-1166 |t#1|) $)) (-15 -3381 ($ (-1166 |t#1|))) (-15 -3046 ($ $ (-768))) (-15 -4212 ((-3 $ "failed") $ (-768))) (-15 -3959 ((-2 (|:| -2952 $) (|:| -1744 $)) $ $)) (-15 -3279 ((-2 (|:| -2952 $) (|:| -1744 $)) $ (-768))) (-15 -3394 ($ $ (-768))) (-15 -3982 ($ $ (-768))) (-15 -4244 ($ $ $)) (-15 -1721 ($ $ (-1 |t#1| |t#1|) $)) (IF (|has| |t#1| (-1145)) (-6 (-1145)) |%noBranch|) (IF (|has| |t#1| (-172)) (PROGN (-15 -3602 (|t#1| $)) (-15 -1315 (|t#1| $ $))) |%noBranch|) (IF (|has| |t#1| (-556)) (PROGN (-6 (-286 (-407 $) (-407 $))) (-15 -4380 ((-407 $) (-407 $) (-407 $))) (-15 -1793 ((-768) $ $)) (-15 -2900 ($ $ $)) (-15 -3648 ((-3 $ "failed") $ $)) (-15 -3648 ((-3 (-407 $) "failed") (-407 $) $)) (-15 -3018 ($ $ $)) (-15 -1778 ((-2 (|:| -1838 |t#1|) (|:| -2952 $) (|:| -1744 $)) $ $))) |%noBranch|) (IF (|has| |t#1| (-452)) (-15 -3250 ((-2 (|:| |primePart| $) (|:| |commonPart| $)) $ $)) |%noBranch|) (IF (|has| |t#1| (-363)) (PROGN (-6 (-307)) (-6 -4407) (-15 -4380 (|t#1| (-407 $) |t#1|))) |%noBranch|) (IF (|has| |t#1| (-38 (-407 (-564)))) (-15 -2397 ($ $)) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-768)) . T) ((-25) . T) ((-38 #1=(-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -4007 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-407 (-564)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4007 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #1#) -4007 (|has| |#1| (-1035 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 #2=(-1076)) . T) ((-614 |#1|) . T) ((-614 $) -4007 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-611 (-859)) . T) ((-172) -4007 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-612 (-536)) -12 (|has| (-1076) (-612 (-536))) (|has| |#1| (-612 (-536)))) ((-612 (-889 (-379))) -12 (|has| (-1076) (-612 (-889 (-379)))) (|has| |#1| (-612 (-889 (-379))))) ((-612 (-889 (-564))) -12 (|has| (-1076) (-612 (-889 (-564)))) (|has| |#1| (-612 (-889 (-564))))) ((-231 |#1|) . T) ((-233) . T) ((-286 (-407 $) (-407 $)) |has| |#1| (-556)) ((-286 |#1| |#1|) . T) ((-286 $ $) . T) ((-290) -4007 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-307) |has| |#1| (-363)) ((-309 $) . T) ((-326 |#1| #0#) . T) ((-377 |#1|) . T) ((-411 |#1|) . T) ((-452) -4007 (|has| |#1| (-906)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-514 #2# |#1|) . T) ((-514 #2# $) . T) ((-514 $ $) . T) ((-556) -4007 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-644 #1#) |has| |#1| (-38 (-407 (-564)))) ((-644 |#1|) . T) ((-644 $) . T) ((-637 (-564)) |has| |#1| (-637 (-564))) ((-637 |#1|) . T) ((-714 #1#) |has| |#1| (-38 (-407 (-564)))) ((-714 |#1|) |has| |#1| (-172)) ((-714 $) -4007 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-723) . T) ((-847) |has| |#1| (-847)) ((-897 #2#) . T) ((-897 (-1170)) |has| |#1| (-897 (-1170))) ((-883 (-379)) -12 (|has| (-1076) (-883 (-379))) (|has| |#1| (-883 (-379)))) ((-883 (-564)) -12 (|has| (-1076) (-883 (-564))) (|has| |#1| (-883 (-564)))) ((-946 |#1| #0# #2#) . T) ((-906) |has| |#1| (-906)) ((-917) |has| |#1| (-363)) ((-1035 (-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) ((-1035 (-564)) |has| |#1| (-1035 (-564))) ((-1035 #2#) . T) ((-1035 |#1|) . T) ((-1052 #1#) |has| |#1| (-38 (-407 (-564)))) ((-1052 |#1|) . T) ((-1052 $) -4007 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1046) . T) ((-1053) . T) ((-1106) . T) ((-1094) . T) ((-1145) |has| |#1| (-1145)) ((-1213) |has| |#1| (-906))) +((-4275 (((-641 (-1076)) $) 34)) (-1364 (($ $) 31)) (-4251 (($ |#2| |#3|) NIL) (($ $ (-1076) |#3|) 28) (($ $ (-641 (-1076)) (-641 |#3|)) 27)) (-1318 (($ $) 14)) (-1332 ((|#2| $) 12)) (-1366 ((|#3| $) 10))) +(((-1236 |#1| |#2| |#3|) (-10 -8 (-15 -4275 ((-641 (-1076)) |#1|)) (-15 -4251 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -4251 (|#1| |#1| (-1076) |#3|)) (-15 -1364 (|#1| |#1|)) (-15 -4251 (|#1| |#2| |#3|)) (-15 -1366 (|#3| |#1|)) (-15 -1318 (|#1| |#1|)) (-15 -1332 (|#2| |#1|))) (-1237 |#2| |#3|) (-1046) (-789)) (T -1236)) +NIL +(-10 -8 (-15 -4275 ((-641 (-1076)) |#1|)) (-15 -4251 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -4251 (|#1| |#1| (-1076) |#3|)) (-15 -1364 (|#1| |#1|)) (-15 -4251 (|#1| |#2| |#3|)) (-15 -1366 (|#3| |#1|)) (-15 -1318 (|#1| |#1|)) (-15 -1332 (|#2| |#1|))) +((-3699 (((-112) $ $) 7)) (-2021 (((-112) $) 16)) (-4275 (((-641 (-1076)) $) 77)) (-3826 (((-1170) $) 106)) (-2774 (((-2 (|:| -4131 $) (|:| 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T) ((-23) . T) ((-47 |#1| #0=(-407 (-564))) . T) ((-25) . T) ((-38 #1=(-407 (-564))) -4007 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -4007 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-35) |has| |#1| (-38 (-407 (-564)))) ((-95) |has| |#1| (-38 (-407 (-564)))) ((-102) . T) ((-111 #1# #1#) -4007 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4007 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #1#) -4007 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 |#1|) |has| |#1| (-172)) ((-614 $) -4007 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-611 (-859)) . T) ((-172) -4007 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-233) |has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) ((-243) |has| |#1| (-363)) ((-284) |has| |#1| (-38 (-407 (-564)))) ((-286 $ $) |has| (-407 (-564)) (-1106)) ((-290) -4007 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-307) |has| |#1| (-363)) ((-363) |has| |#1| (-363)) ((-452) |has| |#1| (-363)) ((-493) |has| |#1| (-38 (-407 (-564)))) ((-556) -4007 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-644 #1#) -4007 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-644 |#1|) . T) ((-644 $) . T) ((-714 #1#) -4007 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-714 |#1|) |has| |#1| (-172)) ((-714 $) -4007 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-723) . T) ((-897 (-1170)) -12 (|has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) (|has| |#1| (-897 (-1170)))) ((-970 |#1| #0# (-1076)) . 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(NIL T T) -7 NIL NIL NIL) (-1185 2867729 2874001 2874057 "TBAGG" 2874457 NIL TBAGG (NIL T T) -9 NIL 2874668 NIL) (-1184 2862799 2864287 2866041 "TBAGG-" 2866046 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2862183 2862290 2862435 "TANEXP" 2862688 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2855684 2862040 2862133 "TABLE" 2862138 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2855096 2855195 2855333 "TABLEAU" 2855581 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2849704 2850924 2852172 "TABLBUMP" 2853882 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2848926 2849073 2849254 "SYSTEM" 2849545 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2845385 2846084 2846867 "SYSSOLP" 2848177 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2844419 2844897 2845016 "SYSNNI" 2845202 NIL SYSNNI (NIL NIL) -8 NIL NIL 2845287) (-1176 2843716 2844148 2844227 "SYSINT" 2844287 NIL SYSINT (NIL NIL) -8 NIL NIL 2844332) (-1175 2840050 2840977 2841693 "SYNTAX" 2843022 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2837208 2837810 2838442 "SYMTAB" 2839440 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2832457 2833359 2834342 "SYMS" 2836247 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2829719 2831915 2832145 "SYMPOLY" 2832262 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2829236 2829311 2829434 "SYMFUNC" 2829631 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2825282 2826548 2827361 "SYMBOL" 2828445 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2818821 2820510 2822230 "SWITCH" 2823584 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2812082 2817642 2817945 "SUTS" 2818576 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2804175 2811329 2811602 "SUPXS" 2811867 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2795690 2803793 2803919 "SUP" 2804084 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2794849 2794976 2795193 "SUPFRACF" 2795558 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2794470 2794529 2794642 "SUP2" 2794784 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2792883 2793157 2793520 "SUMRF" 2794169 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2792197 2792263 2792462 "SUMFS" 2792804 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2776191 2791374 2791625 "SULS" 2792004 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2775820 2776013 2776083 "SUCHTAST" 2776143 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2775142 2775345 2775485 "SUCH" 2775728 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2769036 2770048 2771007 "SUBSPACE" 2774230 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2768466 2768556 2768720 "SUBRESP" 2768924 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2761831 2763131 2764442 "STTF" 2767202 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2756004 2757124 2758271 "STTFNC" 2760731 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2747315 2749186 2750980 "STTAYLOR" 2754245 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2740559 2747179 2747262 "STRTBL" 2747267 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2735950 2740514 2740545 "STRING" 2740550 T STRING (NIL) -8 NIL NIL NIL) (-1151 2730838 2735323 2735353 "STRICAT" 2735412 T STRICAT (NIL) -9 NIL 2735474 NIL) (-1150 2723641 2728457 2729068 "STREAM" 2730262 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2723151 2723228 2723372 "STREAM3" 2723558 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2722133 2722316 2722551 "STREAM2" 2722964 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2721821 2721873 2721966 "STREAM1" 2722075 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2720837 2721018 2721249 "STINPROD" 2721637 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2720415 2720599 2720629 "STEP" 2720709 T STEP (NIL) -9 NIL 2720787 NIL) (-1144 2713958 2720314 2720391 "STBL" 2720396 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2709132 2713179 2713222 "STAGG" 2713375 NIL STAGG (NIL T) -9 NIL 2713464 NIL) (-1142 2706834 2707436 2708308 "STAGG-" 2708313 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2705029 2706604 2706696 "STACK" 2706777 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2697752 2703170 2703626 "SREGSET" 2704659 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2690177 2691546 2693059 "SRDCMPK" 2696358 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2683144 2687617 2687647 "SRAGG" 2688950 T SRAGG (NIL) -9 NIL 2689558 NIL) (-1137 2682161 2682416 2682795 "SRAGG-" 2682800 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2676648 2681108 2681529 "SQMATRIX" 2681787 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2670395 2673366 2674093 "SPLTREE" 2675993 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2666385 2667051 2667697 "SPLNODE" 2669821 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2665432 2665665 2665695 "SPFCAT" 2666139 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2664169 2664379 2664643 "SPECOUT" 2665190 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2655821 2657565 2657595 "SPADXPT" 2661987 T SPADXPT (NIL) -9 NIL 2664021 NIL) (-1130 2655582 2655622 2655691 "SPADPRSR" 2655774 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2653764 2655537 2655568 "SPADAST" 2655573 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2645735 2647482 2647525 "SPACEC" 2651898 NIL SPACEC (NIL T) -9 NIL 2653714 NIL) (-1127 2643892 2645667 2645716 "SPACE3" 2645721 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2642644 2642815 2643106 "SORTPAK" 2643697 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2640694 2640997 2641416 "SOLVETRA" 2642308 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2639705 2639927 2640201 "SOLVESER" 2640467 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2634916 2635806 2636808 "SOLVERAD" 2638757 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2630731 2631340 2632069 "SOLVEFOR" 2634283 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2625028 2630080 2630177 "SNTSCAT" 2630182 NIL SNTSCAT (NIL T T T T) -9 NIL 2630252 NIL) (-1120 2619161 2623351 2623742 "SMTS" 2624718 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2613601 2619049 2619126 "SMP" 2619131 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2611760 2612061 2612459 "SMITH" 2613298 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2604647 2608811 2608914 "SMATCAT" 2610265 NIL SMATCAT (NIL NIL T T T) -9 NIL 2610815 NIL) (-1116 2601587 2602410 2603588 "SMATCAT-" 2603593 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2599300 2600823 2600866 "SKAGG" 2601127 NIL SKAGG (NIL T) -9 NIL 2601262 NIL) (-1114 2595635 2598716 2598911 "SINT" 2599098 T SINT (NIL) -8 NIL NIL 2599271) (-1113 2595407 2595445 2595511 "SIMPAN" 2595591 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2594713 2594942 2595082 "SIG" 2595289 T SIG (NIL) -8 NIL NIL NIL) (-1111 2593551 2593772 2594047 "SIGNRF" 2594472 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2592356 2592507 2592798 "SIGNEF" 2593380 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2591689 2591939 2592063 "SIGAST" 2592254 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2589379 2589833 2590339 "SHP" 2591230 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2583279 2589280 2589356 "SHDP" 2589361 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2582878 2583044 2583074 "SGROUP" 2583167 T SGROUP (NIL) -9 NIL 2583229 NIL) (-1105 2582736 2582762 2582835 "SGROUP-" 2582840 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2579571 2580269 2580992 "SGCF" 2582035 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2573966 2579018 2579115 "SFRTCAT" 2579120 NIL SFRTCAT (NIL T T T T) -9 NIL 2579159 NIL) (-1102 2567387 2568405 2569541 "SFRGCD" 2572949 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2560514 2561586 2562772 "SFQCMPK" 2566320 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2560136 2560225 2560335 "SFORT" 2560455 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2559281 2559976 2560097 "SEXOF" 2560102 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2558415 2559162 2559230 "SEX" 2559235 T SEX (NIL) -8 NIL NIL NIL) (-1097 2553954 2554643 2554738 "SEXCAT" 2557675 NIL SEXCAT (NIL T T T T T) -9 NIL 2558253 NIL) (-1096 2551134 2553888 2553936 "SET" 2553941 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2549385 2549847 2550152 "SETMN" 2550875 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2548991 2549117 2549147 "SETCAT" 2549264 T SETCAT (NIL) -9 NIL 2549349 NIL) (-1093 2548771 2548823 2548922 "SETCAT-" 2548927 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2545158 2547232 2547275 "SETAGG" 2548145 NIL SETAGG (NIL T) -9 NIL 2548485 NIL) (-1091 2544616 2544732 2544969 "SETAGG-" 2544974 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2544086 2544312 2544413 "SEQAST" 2544537 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2543285 2543579 2543640 "SEGXCAT" 2543926 NIL SEGXCAT (NIL T T) -9 NIL 2544046 NIL) (-1088 2542339 2542951 2543133 "SEG" 2543138 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2541318 2541532 2541575 "SEGCAT" 2542097 NIL SEGCAT (NIL T) -9 NIL 2542318 NIL) (-1086 2540367 2540697 2540897 "SEGBIND" 2541153 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2539988 2540047 2540160 "SEGBIND2" 2540302 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2539588 2539789 2539866 "SEGAST" 2539933 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2538807 2538933 2539137 "SEG2" 2539432 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2538244 2538742 2538789 "SDVAR" 2538794 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2530526 2538014 2538144 "SDPOL" 2538149 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2529119 2529385 2529704 "SCPKG" 2530241 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2528279 2528452 2528645 "SCOPE" 2528948 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2527499 2527633 2527812 "SCACHE" 2528134 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2527171 2527331 2527361 "SASTCAT" 2527366 T SASTCAT (NIL) -9 NIL 2527379 NIL) (-1076 2526685 2527006 2527082 "SAOS" 2527117 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2526250 2526285 2526458 "SAERFFC" 2526644 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2520216 2526147 2526227 "SAE" 2526232 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2519809 2519844 2520003 "SAEFACT" 2520175 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2518130 2518444 2518845 "RURPK" 2519475 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2516766 2517045 2517357 "RULESET" 2517964 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2513953 2514456 2514921 "RULE" 2516447 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2513592 2513747 2513830 "RULECOLD" 2513905 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2513090 2513309 2513403 "RSTRCAST" 2513520 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1067 2507938 2508733 2509653 "RSETGCD" 2512289 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1066 2497195 2502247 2502344 "RSETCAT" 2506463 NIL RSETCAT (NIL T T T T) -9 NIL 2507560 NIL) (-1065 2495122 2495661 2496485 "RSETCAT-" 2496490 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1064 2487507 2488884 2490404 "RSDCMPK" 2493721 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1063 2485512 2485953 2486027 "RRCC" 2487113 NIL RRCC (NIL T T) -9 NIL 2487457 NIL) (-1062 2484863 2485037 2485316 "RRCC-" 2485321 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1061 2484333 2484559 2484660 "RPTAST" 2484784 T RPTAST (NIL) -8 NIL NIL NIL) (-1060 2458331 2467926 2467993 "RPOLCAT" 2478657 NIL RPOLCAT (NIL T T T) -9 NIL 2481816 NIL) (-1059 2449829 2452169 2455291 "RPOLCAT-" 2455296 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1058 2440876 2448040 2448522 "ROUTINE" 2449369 T ROUTINE (NIL) -8 NIL NIL NIL) (-1057 2437701 2440502 2440642 "ROMAN" 2440758 T ROMAN (NIL) -8 NIL NIL NIL) (-1056 2435972 2436561 2436821 "ROIRC" 2437506 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1055 2432357 2434608 2434638 "RNS" 2434942 T RNS (NIL) -9 NIL 2435215 NIL) (-1054 2430866 2431249 2431783 "RNS-" 2431858 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1053 2430315 2430697 2430727 "RNG" 2430732 T RNG (NIL) -9 NIL 2430753 NIL) (-1052 2429707 2430069 2430112 "RMODULE" 2430174 NIL RMODULE (NIL T) -9 NIL 2430216 NIL) (-1051 2428543 2428637 2428973 "RMCAT2" 2429608 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1050 2425420 2427889 2428186 "RMATRIX" 2428305 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1049 2418362 2420596 2420711 "RMATCAT" 2424070 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2425052 NIL) (-1048 2417737 2417884 2418191 "RMATCAT-" 2418196 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1047 2417304 2417379 2417507 "RINTERP" 2417656 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1046 2416423 2416951 2416981 "RING" 2417037 T RING (NIL) -9 NIL 2417129 NIL) (-1045 2416215 2416259 2416356 "RING-" 2416361 NIL RING- (NIL T) -8 NIL NIL NIL) (-1044 2415056 2415293 2415551 "RIDIST" 2415979 T RIDIST (NIL) -7 NIL NIL NIL) (-1043 2406372 2414524 2414730 "RGCHAIN" 2414904 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1042 2405748 2406128 2406169 "RGBCSPC" 2406227 NIL RGBCSPC (NIL T) -9 NIL 2406279 NIL) (-1041 2404932 2405287 2405328 "RGBCMDL" 2405560 NIL RGBCMDL (NIL T) -9 NIL 2405674 NIL) (-1040 2401926 2402540 2403210 "RF" 2404296 NIL RF (NIL T) -7 NIL NIL NIL) (-1039 2401572 2401635 2401738 "RFFACTOR" 2401857 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1038 2401297 2401332 2401429 "RFFACT" 2401531 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1037 2399414 2399778 2400160 "RFDIST" 2400937 T RFDIST (NIL) -7 NIL NIL NIL) (-1036 2398867 2398959 2399122 "RETSOL" 2399316 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1035 2398503 2398583 2398626 "RETRACT" 2398759 NIL RETRACT (NIL T) -9 NIL 2398846 NIL) (-1034 2398352 2398377 2398464 "RETRACT-" 2398469 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1033 2397981 2398174 2398244 "RETAST" 2398304 T RETAST (NIL) -8 NIL NIL NIL) (-1032 2390835 2397634 2397761 "RESULT" 2397876 T RESULT (NIL) -8 NIL NIL NIL) (-1031 2389453 2390104 2390303 "RESRING" 2390738 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1030 2389089 2389138 2389236 "RESLATC" 2389390 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1029 2388794 2388829 2388936 "REPSQ" 2389048 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1028 2386216 2386796 2387398 "REP" 2388214 T REP (NIL) -7 NIL NIL NIL) (-1027 2385913 2385948 2386059 "REPDB" 2386175 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1026 2379813 2381202 2382425 "REP2" 2384725 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1025 2376190 2376871 2377679 "REP1" 2379040 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1024 2368913 2374331 2374787 "REGSET" 2375820 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1023 2367726 2368061 2368311 "REF" 2368698 NIL REF (NIL T) -8 NIL NIL NIL) (-1022 2367103 2367206 2367373 "REDORDER" 2367610 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1021 2363098 2366316 2366543 "RECLOS" 2366931 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1020 2362150 2362331 2362546 "REALSOLV" 2362905 T REALSOLV (NIL) -7 NIL NIL NIL) (-1019 2361996 2362037 2362067 "REAL" 2362072 T REAL (NIL) -9 NIL 2362107 NIL) (-1018 2358479 2359281 2360165 "REAL0Q" 2361161 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1017 2354080 2355068 2356129 "REAL0" 2357460 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1016 2353578 2353797 2353891 "RDUCEAST" 2354008 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1015 2352983 2353055 2353262 "RDIV" 2353500 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1014 2352051 2352225 2352438 "RDIST" 2352805 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1013 2350648 2350935 2351307 "RDETRS" 2351759 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1012 2348460 2348914 2349452 "RDETR" 2350190 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1011 2347071 2347349 2347753 "RDEEFS" 2348176 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1010 2345566 2345872 2346304 "RDEEF" 2346759 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1009 2339819 2342702 2342732 "RCFIELD" 2344027 T RCFIELD (NIL) -9 NIL 2344757 NIL) (-1008 2337883 2338387 2339083 "RCFIELD-" 2339158 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1007 2334199 2335984 2336027 "RCAGG" 2337111 NIL RCAGG (NIL T) -9 NIL 2337576 NIL) (-1006 2333827 2333921 2334084 "RCAGG-" 2334089 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1005 2333162 2333274 2333439 "RATRET" 2333711 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1004 2332715 2332782 2332903 "RATFACT" 2333090 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1003 2332023 2332143 2332295 "RANDSRC" 2332585 T RANDSRC (NIL) -7 NIL NIL NIL) (-1002 2331757 2331801 2331874 "RADUTIL" 2331972 T RADUTIL (NIL) -7 NIL NIL NIL) (-1001 2324900 2330590 2330900 "RADIX" 2331481 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1000 2316546 2324742 2324872 "RADFF" 2324877 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-999 2316198 2316273 2316301 "RADCAT" 2316458 T RADCAT (NIL) -9 NIL NIL NIL) (-998 2315983 2316031 2316128 "RADCAT-" 2316133 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-997 2314134 2315758 2315847 "QUEUE" 2315927 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-996 2310702 2314071 2314116 "QUAT" 2314121 NIL QUAT (NIL T) -8 NIL NIL NIL) (-995 2310340 2310383 2310510 "QUATCT2" 2310653 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-994 2304079 2307389 2307429 "QUATCAT" 2308209 NIL QUATCAT (NIL T) -9 NIL 2308975 NIL) (-993 2300223 2301260 2302647 "QUATCAT-" 2302741 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-992 2297743 2299307 2299348 "QUAGG" 2299723 NIL QUAGG (NIL T) -9 NIL 2299898 NIL) (-991 2297375 2297568 2297636 "QQUTAST" 2297695 T QQUTAST (NIL) -8 NIL NIL NIL) (-990 2296300 2296773 2296945 "QFORM" 2297247 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-989 2287504 2292717 2292757 "QFCAT" 2293415 NIL QFCAT (NIL T) -9 NIL 2294416 NIL) (-988 2283076 2284277 2285868 "QFCAT-" 2285962 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-987 2282714 2282757 2282884 "QFCAT2" 2283027 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-986 2282174 2282284 2282414 "QEQUAT" 2282604 T QEQUAT (NIL) -8 NIL NIL NIL) (-985 2275321 2276393 2277577 "QCMPACK" 2281107 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-984 2272897 2273318 2273746 "QALGSET" 2274976 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-983 2272142 2272316 2272548 "QALGSET2" 2272717 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-982 2270832 2271056 2271373 "PWFFINTB" 2271915 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-981 2269014 2269182 2269536 "PUSHVAR" 2270646 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-980 2264932 2265986 2266027 "PTRANFN" 2267911 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-979 2263334 2263625 2263947 "PTPACK" 2264643 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-978 2262966 2263023 2263132 "PTFUNC2" 2263271 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-977 2257493 2261838 2261879 "PTCAT" 2262175 NIL PTCAT (NIL T) -9 NIL 2262328 NIL) (-976 2257151 2257186 2257310 "PSQFR" 2257452 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-975 2255746 2256044 2256378 "PSEUDLIN" 2256849 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-974 2242509 2244880 2247204 "PSETPK" 2253506 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-973 2235553 2238267 2238363 "PSETCAT" 2241384 NIL PSETCAT (NIL T T T T) -9 NIL 2242198 NIL) (-972 2233389 2234023 2234844 "PSETCAT-" 2234849 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-971 2232738 2232903 2232931 "PSCURVE" 2233199 T PSCURVE (NIL) -9 NIL 2233366 NIL) (-970 2229086 2230576 2230641 "PSCAT" 2231485 NIL PSCAT (NIL T T T) -9 NIL 2231725 NIL) (-969 2228149 2228365 2228765 "PSCAT-" 2228770 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-968 2226881 2227514 2227719 "PRTITION" 2227964 T PRTITION (NIL) -8 NIL NIL NIL) (-967 2226383 2226602 2226694 "PRTDAST" 2226809 T PRTDAST (NIL) -8 NIL NIL NIL) (-966 2215473 2217687 2219875 "PRS" 2224245 NIL PRS (NIL T T) -7 NIL NIL NIL) (-965 2213331 2214823 2214863 "PRQAGG" 2215046 NIL PRQAGG (NIL T) -9 NIL 2215148 NIL) (-964 2212717 2212946 2212974 "PROPLOG" 2213159 T PROPLOG (NIL) -9 NIL 2213281 NIL) (-963 2209887 2210531 2210995 "PROPFRML" 2212285 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-962 2209347 2209457 2209587 "PROPERTY" 2209777 T PROPERTY (NIL) -8 NIL NIL NIL) (-961 2203432 2207513 2208333 "PRODUCT" 2208573 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-960 2200737 2202890 2203124 "PR" 2203243 NIL PR (NIL T T) -8 NIL NIL NIL) (-959 2200533 2200565 2200624 "PRINT" 2200698 T PRINT (NIL) -7 NIL NIL NIL) (-958 2199873 2199990 2200142 "PRIMES" 2200413 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-957 2197938 2198339 2198805 "PRIMELT" 2199452 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-956 2197667 2197716 2197744 "PRIMCAT" 2197868 T PRIMCAT (NIL) -9 NIL NIL NIL) (-955 2193828 2197605 2197650 "PRIMARR" 2197655 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-954 2192835 2193013 2193241 "PRIMARR2" 2193646 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-953 2192478 2192534 2192645 "PREASSOC" 2192773 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-952 2191953 2192086 2192114 "PPCURVE" 2192319 T PPCURVE (NIL) -9 NIL 2192455 NIL) (-951 2191575 2191748 2191831 "PORTNUM" 2191890 T PORTNUM (NIL) -8 NIL NIL NIL) (-950 2188934 2189333 2189925 "POLYROOT" 2191156 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-949 2182871 2188538 2188698 "POLY" 2188807 NIL POLY (NIL T) -8 NIL NIL NIL) (-948 2182254 2182312 2182546 "POLYLIFT" 2182807 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-947 2178529 2178978 2179607 "POLYCATQ" 2181799 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-946 2165338 2170704 2170769 "POLYCAT" 2174283 NIL POLYCAT (NIL T T T) -9 NIL 2176211 NIL) (-945 2158787 2160649 2163033 "POLYCAT-" 2163038 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-944 2158374 2158442 2158562 "POLY2UP" 2158713 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-943 2158006 2158063 2158172 "POLY2" 2158311 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-942 2156691 2156930 2157206 "POLUTIL" 2157780 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-941 2155046 2155323 2155654 "POLTOPOL" 2156413 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-940 2150563 2154982 2155028 "POINT" 2155033 NIL POINT (NIL T) -8 NIL NIL NIL) (-939 2148750 2149107 2149482 "PNTHEORY" 2150208 T PNTHEORY (NIL) -7 NIL NIL NIL) (-938 2147169 2147466 2147878 "PMTOOLS" 2148448 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-937 2146762 2146840 2146957 "PMSYM" 2147085 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-936 2146272 2146341 2146515 "PMQFCAT" 2146687 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-935 2145627 2145737 2145893 "PMPRED" 2146149 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-934 2145023 2145109 2145270 "PMPREDFS" 2145528 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-933 2143666 2143874 2144259 "PMPLCAT" 2144785 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-932 2143198 2143277 2143429 "PMLSAGG" 2143581 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-931 2142673 2142749 2142930 "PMKERNEL" 2143116 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-930 2142290 2142365 2142478 "PMINS" 2142592 NIL PMINS (NIL T) -7 NIL NIL NIL) (-929 2141718 2141787 2142003 "PMFS" 2142215 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-928 2140946 2141064 2141269 "PMDOWN" 2141595 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-927 2140109 2140268 2140450 "PMASS" 2140784 T PMASS (NIL) -7 NIL NIL NIL) (-926 2139383 2139494 2139657 "PMASSFS" 2139995 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-925 2139038 2139106 2139200 "PLOTTOOL" 2139309 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-924 2133645 2134849 2135997 "PLOT" 2137910 T PLOT (NIL) -8 NIL NIL NIL) (-923 2129449 2130493 2131414 "PLOT3D" 2132744 T PLOT3D (NIL) -8 NIL NIL NIL) (-922 2128361 2128538 2128773 "PLOT1" 2129253 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-921 2103750 2108427 2113278 "PLEQN" 2123627 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-920 2103068 2103190 2103370 "PINTERP" 2103615 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-919 2102761 2102808 2102911 "PINTERPA" 2103015 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-918 2102009 2102530 2102617 "PI" 2102657 T PI (NIL) -8 NIL NIL 2102724) (-917 2100398 2101347 2101375 "PID" 2101557 T PID (NIL) -9 NIL 2101691 NIL) (-916 2100123 2100160 2100248 "PICOERCE" 2100355 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-915 2099443 2099582 2099758 "PGROEB" 2099979 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-914 2095030 2095844 2096749 "PGE" 2098558 T PGE (NIL) -7 NIL NIL NIL) (-913 2093153 2093400 2093766 "PGCD" 2094747 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-912 2092491 2092594 2092755 "PFRPAC" 2093037 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-911 2089159 2091039 2091392 "PFR" 2092170 NIL PFR (NIL T) -8 NIL NIL NIL) (-910 2087548 2087792 2088117 "PFOTOOLS" 2088906 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-909 2086081 2086320 2086671 "PFOQ" 2087305 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-908 2084554 2084766 2085129 "PFO" 2085865 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-907 2081134 2084443 2084512 "PF" 2084517 NIL PF (NIL NIL) -8 NIL NIL NIL) (-906 2078560 2079805 2079833 "PFECAT" 2080418 T PFECAT (NIL) -9 NIL 2080802 NIL) (-905 2078005 2078159 2078373 "PFECAT-" 2078378 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-904 2076608 2076860 2077161 "PFBRU" 2077754 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-903 2074473 2074826 2075258 "PFBR" 2076259 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-902 2070382 2071849 2072525 "PERM" 2073830 NIL PERM (NIL T) -8 NIL NIL NIL) (-901 2065643 2066589 2067459 "PERMGRP" 2069545 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-900 2063775 2064706 2064747 "PERMCAT" 2065193 NIL PERMCAT (NIL T) -9 NIL 2065498 NIL) (-899 2063428 2063469 2063593 "PERMAN" 2063728 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-898 2060964 2063093 2063215 "PENDTREE" 2063339 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-897 2059049 2059791 2059832 "PDRING" 2060489 NIL PDRING (NIL T) -9 NIL 2060775 NIL) (-896 2058152 2058370 2058732 "PDRING-" 2058737 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-895 2055394 2056145 2056813 "PDEPROB" 2057504 T PDEPROB (NIL) -8 NIL NIL NIL) (-894 2052939 2053443 2053998 "PDEPACK" 2054859 T PDEPACK (NIL) -7 NIL NIL NIL) (-893 2051851 2052041 2052292 "PDECOMP" 2052738 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-892 2049456 2050273 2050301 "PDECAT" 2051088 T PDECAT (NIL) -9 NIL 2051801 NIL) (-891 2049207 2049240 2049330 "PCOMP" 2049417 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-890 2047412 2048008 2048305 "PBWLB" 2048936 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-889 2039912 2041485 2042823 "PATTERN" 2046095 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-888 2039544 2039601 2039710 "PATTERN2" 2039849 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-887 2037301 2037689 2038146 "PATTERN1" 2039133 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-886 2034696 2035250 2035731 "PATRES" 2036866 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-885 2034260 2034327 2034459 "PATRES2" 2034623 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-884 2032143 2032548 2032955 "PATMATCH" 2033927 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-883 2031679 2031862 2031903 "PATMAB" 2032010 NIL PATMAB (NIL T) -9 NIL 2032093 NIL) (-882 2030224 2030533 2030791 "PATLRES" 2031484 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-881 2029770 2029893 2029934 "PATAB" 2029939 NIL PATAB (NIL T) -9 NIL 2030111 NIL) (-880 2027251 2027783 2028356 "PARTPERM" 2029217 T PARTPERM (NIL) -7 NIL NIL NIL) (-879 2026872 2026935 2027037 "PARSURF" 2027182 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-878 2026504 2026561 2026670 "PARSU2" 2026809 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-877 2026268 2026308 2026375 "PARSER" 2026457 T PARSER (NIL) -7 NIL NIL NIL) (-876 2025889 2025952 2026054 "PARSCURV" 2026199 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-875 2025521 2025578 2025687 "PARSC2" 2025826 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-874 2025160 2025218 2025315 "PARPCURV" 2025457 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-873 2024792 2024849 2024958 "PARPC2" 2025097 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-872 2024312 2024398 2024517 "PAN2EXPR" 2024693 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-871 2023116 2023433 2023661 "PALETTE" 2024104 T PALETTE (NIL) -8 NIL NIL NIL) (-870 2021584 2022121 2022481 "PAIR" 2022802 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-869 2015481 2020843 2021037 "PADICRC" 2021439 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-868 2008737 2014827 2015011 "PADICRAT" 2015329 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-867 2007079 2008674 2008719 "PADIC" 2008724 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-866 2004281 2005819 2005859 "PADICCT" 2006440 NIL PADICCT (NIL NIL) -9 NIL 2006722 NIL) (-865 2003238 2003438 2003706 "PADEPAC" 2004068 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-864 2002450 2002583 2002789 "PADE" 2003100 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-863 2000864 2001658 2001938 "OWP" 2002254 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-862 2000384 2000570 2000667 "OVERSET" 2000787 T OVERSET (NIL) -8 NIL NIL NIL) (-861 1999457 1999989 2000161 "OVAR" 2000252 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-860 1998721 1998842 1999003 "OUT" 1999316 T OUT (NIL) -7 NIL NIL NIL) (-859 1987619 1989830 1992030 "OUTFORM" 1996541 T OUTFORM (NIL) -8 NIL NIL NIL) (-858 1986955 1987216 1987343 "OUTBFILE" 1987512 T OUTBFILE (NIL) -8 NIL NIL NIL) (-857 1986262 1986427 1986455 "OUTBCON" 1986773 T OUTBCON (NIL) -9 NIL 1986939 NIL) (-856 1985863 1985975 1986132 "OUTBCON-" 1986137 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-855 1985270 1985592 1985681 "OSI" 1985794 T OSI (NIL) -8 NIL NIL NIL) (-854 1984826 1985138 1985166 "OSGROUP" 1985171 T OSGROUP (NIL) -9 NIL 1985193 NIL) (-853 1983571 1983798 1984083 "ORTHPOL" 1984573 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-852 1981149 1983406 1983527 "OREUP" 1983532 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-851 1978579 1980840 1980967 "ORESUP" 1981091 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-850 1976107 1976607 1977168 "OREPCTO" 1978068 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-849 1969923 1972098 1972139 "OREPCAT" 1974487 NIL OREPCAT (NIL T) -9 NIL 1975591 NIL) (-848 1967070 1967852 1968910 "OREPCAT-" 1968915 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-847 1966247 1966519 1966547 "ORDSET" 1966856 T ORDSET (NIL) -9 NIL 1967020 NIL) (-846 1965766 1965888 1966081 "ORDSET-" 1966086 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-845 1964392 1965157 1965185 "ORDRING" 1965387 T ORDRING (NIL) -9 NIL 1965512 NIL) (-844 1964037 1964131 1964275 "ORDRING-" 1964280 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-843 1963443 1963880 1963908 "ORDMON" 1963913 T ORDMON (NIL) -9 NIL 1963934 NIL) (-842 1962605 1962752 1962947 "ORDFUNS" 1963292 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-841 1961969 1962362 1962390 "ORDFIN" 1962455 T ORDFIN (NIL) -9 NIL 1962529 NIL) (-840 1958555 1960555 1960964 "ORDCOMP" 1961593 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-839 1957821 1957948 1958134 "ORDCOMP2" 1958415 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-838 1954429 1955312 1956126 "OPTPROB" 1957027 T OPTPROB (NIL) -8 NIL NIL NIL) (-837 1951231 1951870 1952574 "OPTPACK" 1953745 T OPTPACK (NIL) -7 NIL NIL NIL) (-836 1948944 1949684 1949712 "OPTCAT" 1950531 T OPTCAT (NIL) -9 NIL 1951181 NIL) (-835 1948387 1948621 1948726 "OPSIG" 1948859 T OPSIG (NIL) -8 NIL NIL NIL) (-834 1948155 1948194 1948260 "OPQUERY" 1948341 T OPQUERY (NIL) -7 NIL NIL NIL) (-833 1945313 1946466 1946970 "OP" 1947684 NIL OP (NIL T) -8 NIL NIL NIL) (-832 1944848 1945019 1945060 "OPERCAT" 1945195 NIL OPERCAT (NIL T) -9 NIL 1945263 NIL) (-831 1944694 1944721 1944807 "OPERCAT-" 1944812 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-830 1941533 1943491 1943860 "ONECOMP" 1944358 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-829 1940838 1940953 1941127 "ONECOMP2" 1941405 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-828 1940257 1940363 1940493 "OMSERVER" 1940728 T OMSERVER (NIL) -7 NIL NIL NIL) (-827 1937145 1939697 1939737 "OMSAGG" 1939798 NIL OMSAGG (NIL T) -9 NIL 1939862 NIL) (-826 1935768 1936031 1936313 "OMPKG" 1936883 T OMPKG (NIL) -7 NIL NIL NIL) (-825 1935198 1935301 1935329 "OM" 1935628 T OM (NIL) -9 NIL NIL NIL) (-824 1933772 1934747 1934916 "OMLO" 1935079 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-823 1932697 1932844 1933071 "OMEXPR" 1933598 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-822 1932015 1932243 1932379 "OMERR" 1932581 T OMERR (NIL) -8 NIL NIL NIL) (-821 1931193 1931436 1931596 "OMERRK" 1931875 T OMERRK (NIL) -8 NIL NIL NIL) (-820 1930671 1930870 1930978 "OMENC" 1931105 T OMENC (NIL) -8 NIL NIL NIL) (-819 1924566 1925751 1926922 "OMDEV" 1929520 T OMDEV (NIL) -8 NIL NIL NIL) (-818 1923635 1923806 1924000 "OMCONN" 1924392 T OMCONN (NIL) -8 NIL NIL NIL) (-817 1922248 1923198 1923226 "OINTDOM" 1923231 T OINTDOM (NIL) -9 NIL 1923252 NIL) (-816 1918054 1919238 1919954 "OFMONOID" 1921564 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-815 1917492 1917991 1918036 "ODVAR" 1918041 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-814 1914942 1917237 1917392 "ODR" 1917397 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-813 1907278 1914718 1914844 "ODPOL" 1914849 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-812 1901148 1907150 1907255 "ODP" 1907260 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-811 1899914 1900129 1900404 "ODETOOLS" 1900922 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-810 1896881 1897539 1898255 "ODESYS" 1899247 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-809 1891763 1892671 1893696 "ODERTRIC" 1895956 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-808 1891189 1891271 1891465 "ODERED" 1891675 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-807 1888077 1888625 1889302 "ODERAT" 1890612 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-806 1885034 1885501 1886098 "ODEPRRIC" 1887606 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-805 1883004 1883573 1884059 "ODEPROB" 1884568 T ODEPROB (NIL) -8 NIL NIL NIL) (-804 1879524 1880009 1880656 "ODEPRIM" 1882483 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-803 1878773 1878875 1879135 "ODEPAL" 1879416 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-802 1874935 1875726 1876590 "ODEPACK" 1877929 T ODEPACK (NIL) -7 NIL NIL NIL) (-801 1873968 1874075 1874304 "ODEINT" 1874824 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-800 1868069 1869494 1870941 "ODEIFTBL" 1872541 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-799 1863404 1864190 1865149 "ODEEF" 1867228 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-798 1862739 1862828 1863058 "ODECONST" 1863309 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-797 1860890 1861525 1861553 "ODECAT" 1862158 T ODECAT (NIL) -9 NIL 1862689 NIL) (-796 1857789 1860602 1860721 "OCT" 1860803 NIL OCT (NIL T) -8 NIL NIL NIL) (-795 1857427 1857470 1857597 "OCTCT2" 1857740 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-794 1852193 1854601 1854641 "OC" 1855738 NIL OC (NIL T) -9 NIL 1856596 NIL) (-793 1849420 1850168 1851158 "OC-" 1851252 NIL OC- (NIL T T) -8 NIL NIL NIL) (-792 1848798 1849240 1849268 "OCAMON" 1849273 T OCAMON (NIL) -9 NIL 1849294 NIL) (-791 1848355 1848670 1848698 "OASGP" 1848703 T OASGP (NIL) -9 NIL 1848723 NIL) (-790 1847642 1848105 1848133 "OAMONS" 1848173 T OAMONS (NIL) -9 NIL 1848216 NIL) (-789 1847082 1847489 1847517 "OAMON" 1847522 T OAMON (NIL) -9 NIL 1847542 NIL) (-788 1846386 1846878 1846906 "OAGROUP" 1846911 T OAGROUP (NIL) -9 NIL 1846931 NIL) (-787 1846076 1846126 1846214 "NUMTUBE" 1846330 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-786 1839649 1841167 1842703 "NUMQUAD" 1844560 T NUMQUAD (NIL) -7 NIL NIL NIL) (-785 1835405 1836393 1837418 "NUMODE" 1838644 T NUMODE (NIL) -7 NIL NIL NIL) (-784 1832786 1833640 1833668 "NUMINT" 1834591 T NUMINT (NIL) -9 NIL 1835355 NIL) (-783 1831734 1831931 1832149 "NUMFMT" 1832588 T NUMFMT (NIL) -7 NIL NIL NIL) (-782 1818093 1821038 1823570 "NUMERIC" 1829241 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-781 1812490 1817542 1817637 "NTSCAT" 1817642 NIL NTSCAT (NIL T T T T) -9 NIL 1817681 NIL) (-780 1811684 1811849 1812042 "NTPOLFN" 1812329 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-779 1799516 1808509 1809321 "NSUP" 1810905 NIL NSUP (NIL T) -8 NIL NIL NIL) (-778 1799148 1799205 1799314 "NSUP2" 1799453 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-777 1789131 1798922 1799055 "NSMP" 1799060 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-776 1787563 1787864 1788221 "NREP" 1788819 NIL NREP (NIL T) -7 NIL NIL NIL) (-775 1786154 1786406 1786764 "NPCOEF" 1787306 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-774 1785220 1785335 1785551 "NORMRETR" 1786035 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-773 1783261 1783551 1783960 "NORMPK" 1784928 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-772 1782946 1782974 1783098 "NORMMA" 1783227 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-771 1782773 1782903 1782932 "NONE" 1782937 T NONE (NIL) -8 NIL NIL NIL) (-770 1782562 1782591 1782660 "NONE1" 1782737 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-769 1782045 1782107 1782293 "NODE1" 1782494 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-768 1780315 1781139 1781394 "NNI" 1781741 T NNI (NIL) -8 NIL NIL 1781976) (-767 1778735 1779048 1779412 "NLINSOL" 1779983 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-766 1775003 1775971 1776870 "NIPROB" 1777856 T NIPROB (NIL) -8 NIL NIL NIL) (-765 1773760 1773994 1774296 "NFINTBAS" 1774765 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-764 1772934 1773410 1773451 "NETCLT" 1773623 NIL NETCLT (NIL T) -9 NIL 1773705 NIL) (-763 1771642 1771873 1772154 "NCODIV" 1772702 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-762 1771404 1771441 1771516 "NCNTFRAC" 1771599 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-761 1769584 1769948 1770368 "NCEP" 1771029 NIL NCEP (NIL T) -7 NIL NIL NIL) (-760 1768481 1769228 1769256 "NASRING" 1769366 T NASRING (NIL) -9 NIL 1769446 NIL) (-759 1768276 1768320 1768414 "NASRING-" 1768419 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-758 1767429 1767928 1767956 "NARNG" 1768073 T NARNG (NIL) -9 NIL 1768164 NIL) (-757 1767121 1767188 1767322 "NARNG-" 1767327 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-756 1766000 1766207 1766442 "NAGSP" 1766906 T NAGSP (NIL) -7 NIL NIL NIL) (-755 1757272 1758956 1760629 "NAGS" 1764347 T NAGS (NIL) -7 NIL NIL NIL) (-754 1755820 1756128 1756459 "NAGF07" 1756961 T NAGF07 (NIL) -7 NIL NIL NIL) (-753 1750358 1751649 1752956 "NAGF04" 1754533 T NAGF04 (NIL) -7 NIL NIL NIL) (-752 1743326 1744940 1746573 "NAGF02" 1748745 T NAGF02 (NIL) -7 NIL NIL NIL) (-751 1738550 1739650 1740767 "NAGF01" 1742229 T NAGF01 (NIL) -7 NIL NIL NIL) (-750 1732178 1733744 1735329 "NAGE04" 1736985 T NAGE04 (NIL) -7 NIL NIL NIL) (-749 1723347 1725468 1727598 "NAGE02" 1730068 T NAGE02 (NIL) -7 NIL NIL NIL) (-748 1719300 1720247 1721211 "NAGE01" 1722403 T NAGE01 (NIL) -7 NIL NIL NIL) (-747 1717095 1717629 1718187 "NAGD03" 1718762 T NAGD03 (NIL) -7 NIL NIL NIL) (-746 1708845 1710773 1712727 "NAGD02" 1715161 T NAGD02 (NIL) -7 NIL NIL NIL) (-745 1702656 1704081 1705521 "NAGD01" 1707425 T NAGD01 (NIL) -7 NIL NIL NIL) (-744 1698865 1699687 1700524 "NAGC06" 1701839 T NAGC06 (NIL) -7 NIL NIL NIL) (-743 1697330 1697662 1698018 "NAGC05" 1698529 T NAGC05 (NIL) -7 NIL NIL NIL) (-742 1696706 1696825 1696969 "NAGC02" 1697206 T NAGC02 (NIL) -7 NIL NIL NIL) (-741 1695766 1696323 1696363 "NAALG" 1696442 NIL NAALG (NIL T) -9 NIL 1696503 NIL) (-740 1695601 1695630 1695720 "NAALG-" 1695725 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-739 1689551 1690659 1691846 "MULTSQFR" 1694497 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-738 1688870 1688945 1689129 "MULTFACT" 1689463 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-737 1681955 1685833 1685886 "MTSCAT" 1686956 NIL MTSCAT (NIL T T) -9 NIL 1687470 NIL) (-736 1681667 1681721 1681813 "MTHING" 1681895 NIL MTHING (NIL T) -7 NIL NIL NIL) (-735 1681459 1681492 1681552 "MSYSCMD" 1681627 T MSYSCMD (NIL) -7 NIL NIL NIL) (-734 1677568 1680214 1680534 "MSET" 1681172 NIL MSET (NIL T) -8 NIL NIL NIL) (-733 1674663 1677129 1677170 "MSETAGG" 1677175 NIL MSETAGG (NIL T) -9 NIL 1677209 NIL) (-732 1670531 1672042 1672787 "MRING" 1673963 NIL MRING (NIL T T) -8 NIL NIL NIL) (-731 1670097 1670164 1670295 "MRF2" 1670458 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-730 1669715 1669750 1669894 "MRATFAC" 1670056 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-729 1667327 1667622 1668053 "MPRFF" 1669420 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-728 1661379 1667181 1667278 "MPOLY" 1667283 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-727 1660869 1660904 1661112 "MPCPF" 1661338 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-726 1660383 1660426 1660610 "MPC3" 1660820 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-725 1659578 1659659 1659880 "MPC2" 1660298 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1657879 1658216 1658606 "MONOTOOL" 1659238 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-723 1657130 1657421 1657449 "MONOID" 1657668 T MONOID (NIL) -9 NIL 1657815 NIL) (-722 1656676 1656795 1656976 "MONOID-" 1656981 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-721 1647527 1653443 1653502 "MONOGEN" 1654176 NIL MONOGEN (NIL T T) -9 NIL 1654632 NIL) (-720 1644745 1645480 1646480 "MONOGEN-" 1646599 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-719 1643604 1644024 1644052 "MONADWU" 1644444 T MONADWU (NIL) -9 NIL 1644682 NIL) (-718 1642976 1643135 1643383 "MONADWU-" 1643388 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-717 1642361 1642579 1642607 "MONAD" 1642814 T MONAD (NIL) -9 NIL 1642926 NIL) (-716 1642046 1642124 1642256 "MONAD-" 1642261 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-715 1640362 1640959 1641238 "MOEBIUS" 1641799 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-714 1639754 1640132 1640172 "MODULE" 1640177 NIL MODULE (NIL T) -9 NIL 1640203 NIL) (-713 1639322 1639418 1639608 "MODULE-" 1639613 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-712 1637029 1637686 1638013 "MODRING" 1639146 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-711 1634000 1635134 1635655 "MODOP" 1636558 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-710 1632615 1633067 1633344 "MODMONOM" 1633863 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-709 1622412 1630906 1631320 "MODMON" 1632252 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-708 1619595 1621256 1621532 "MODFIELD" 1622287 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-707 1618599 1618876 1619066 "MMLFORM" 1619425 T MMLFORM (NIL) -8 NIL NIL NIL) (-706 1618125 1618168 1618347 "MMAP" 1618550 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-705 1616334 1617075 1617116 "MLO" 1617539 NIL MLO (NIL T) -9 NIL 1617781 NIL) (-704 1613700 1614216 1614818 "MLIFT" 1615815 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-703 1613091 1613175 1613329 "MKUCFUNC" 1613611 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-702 1612690 1612760 1612883 "MKRECORD" 1613014 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-701 1611737 1611899 1612127 "MKFUNC" 1612501 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-700 1611125 1611229 1611385 "MKFLCFN" 1611620 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-699 1610668 1611035 1611094 "MKCHSET" 1611099 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-698 1609945 1610047 1610232 "MKBCFUNC" 1610561 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1606679 1609499 1609635 "MINT" 1609829 T MINT (NIL) -8 NIL NIL NIL) (-696 1605491 1605734 1606011 "MHROWRED" 1606434 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1600898 1604026 1604431 "MFLOAT" 1605106 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1600255 1600331 1600502 "MFINFACT" 1600810 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1596570 1597418 1598302 "MESH" 1599391 T MESH (NIL) -7 NIL NIL NIL) (-692 1594960 1595272 1595625 "MDDFACT" 1596257 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1591802 1594119 1594160 "MDAGG" 1594415 NIL MDAGG (NIL T) -9 NIL 1594558 NIL) (-690 1581572 1591095 1591302 "MCMPLX" 1591615 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1580713 1580859 1581059 "MCDEN" 1581421 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1578603 1578873 1579253 "MCALCFN" 1580443 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1577528 1577768 1578001 "MAYBE" 1578409 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1575140 1575663 1576225 "MATSTOR" 1576999 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1571145 1574512 1574760 "MATRIX" 1574925 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1566909 1567618 1568354 "MATLIN" 1570502 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1557063 1560201 1560278 "MATCAT" 1565158 NIL MATCAT (NIL T T T) -9 NIL 1566575 NIL) (-682 1553419 1554440 1555796 "MATCAT-" 1555801 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1552013 1552166 1552499 "MATCAT2" 1553254 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1550125 1550449 1550833 "MAPPKG3" 1551688 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1549106 1549279 1549501 "MAPPKG2" 1549949 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1547605 1547889 1548216 "MAPPKG1" 1548812 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1546711 1547011 1547188 "MAPPAST" 1547448 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1546322 1546380 1546503 "MAPHACK3" 1546647 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1545914 1545975 1546089 "MAPHACK2" 1546254 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1545351 1545455 1545597 "MAPHACK1" 1545805 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1543457 1544051 1544355 "MAGMA" 1545079 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1542963 1543181 1543272 "MACROAST" 1543386 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1539429 1541202 1541663 "M3D" 1542535 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1533583 1537798 1537839 "LZSTAGG" 1538621 NIL LZSTAGG (NIL T) -9 NIL 1538916 NIL) (-669 1529540 1530714 1532171 "LZSTAGG-" 1532176 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1526654 1527431 1527918 "LWORD" 1529085 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1526257 1526458 1526533 "LSTAST" 1526599 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1519450 1526028 1526162 "LSQM" 1526167 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1518674 1518813 1519041 "LSPP" 1519305 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1516486 1516787 1517243 "LSMP" 1518363 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1513265 1513939 1514669 "LSMP1" 1515788 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1507190 1512432 1512473 "LSAGG" 1512535 NIL LSAGG (NIL T) -9 NIL 1512613 NIL) (-661 1503885 1504809 1506022 "LSAGG-" 1506027 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1501511 1503029 1503278 "LPOLY" 1503680 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1501093 1501178 1501301 "LPEFRAC" 1501420 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1499440 1500187 1500440 "LO" 1500925 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1499092 1499204 1499232 "LOGIC" 1499343 T LOGIC (NIL) -9 NIL 1499424 NIL) (-656 1498954 1498977 1499048 "LOGIC-" 1499053 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1498147 1498287 1498480 "LODOOPS" 1498810 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1495597 1498063 1498129 "LODO" 1498134 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1494135 1494370 1494723 "LODOF" 1495344 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1490483 1492888 1492929 "LODOCAT" 1493367 NIL LODOCAT (NIL T) -9 NIL 1493578 NIL) (-651 1490216 1490274 1490401 "LODOCAT-" 1490406 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1487563 1490057 1490175 "LODO2" 1490180 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1485025 1487500 1487545 "LODO1" 1487550 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1483885 1484050 1484362 "LODEEF" 1484848 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1479171 1482015 1482056 "LNAGG" 1483003 NIL LNAGG (NIL T) -9 NIL 1483447 NIL) (-646 1478318 1478532 1478874 "LNAGG-" 1478879 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1474481 1475243 1475882 "LMOPS" 1477733 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1473876 1474238 1474279 "LMODULE" 1474340 NIL LMODULE (NIL T) -9 NIL 1474382 NIL) (-643 1471122 1473521 1473644 "LMDICT" 1473786 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1470848 1471030 1471090 "LITERAL" 1471095 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1464079 1469794 1470092 "LIST" 1470583 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1463604 1463678 1463817 "LIST3" 1463999 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1462611 1462789 1463017 "LIST2" 1463422 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1460745 1461057 1461456 "LIST2MAP" 1462258 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1459467 1460111 1460152 "LINEXP" 1460407 NIL LINEXP (NIL T) -9 NIL 1460556 NIL) (-636 1458114 1458374 1458671 "LINDEP" 1459219 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1454881 1455600 1456377 "LIMITRF" 1457369 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1453156 1453452 1453868 "LIMITPS" 1454576 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1447611 1452667 1452895 "LIE" 1452977 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1446660 1447103 1447143 "LIECAT" 1447283 NIL LIECAT (NIL T) -9 NIL 1447434 NIL) (-631 1446501 1446528 1446616 "LIECAT-" 1446621 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1439113 1445950 1446115 "LIB" 1446356 T LIB (NIL) -8 NIL NIL NIL) (-629 1434748 1435631 1436566 "LGROBP" 1438230 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1432614 1432888 1433250 "LF" 1434469 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1431454 1432146 1432174 "LFCAT" 1432381 T LFCAT (NIL) -9 NIL 1432520 NIL) (-626 1428356 1428986 1429674 "LEXTRIPK" 1430818 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1425127 1425926 1426429 "LEXP" 1427936 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1424630 1424848 1424940 "LETAST" 1425055 T LETAST (NIL) -8 NIL NIL NIL) (-623 1423028 1423341 1423742 "LEADCDET" 1424312 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1422218 1422292 1422521 "LAZM3PK" 1422949 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1417162 1420295 1420833 "LAUPOL" 1421730 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1416727 1416771 1416939 "LAPLACE" 1417112 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1414693 1415828 1416079 "LA" 1416560 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1413766 1414324 1414365 "LALG" 1414427 NIL LALG (NIL T) -9 NIL 1414486 NIL) (-617 1413480 1413539 1413675 "LALG-" 1413680 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1413315 1413339 1413380 "KVTFROM" 1413442 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1412115 1412532 1412761 "KTVLOGIC" 1413106 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1411950 1411974 1412015 "KRCFROM" 1412077 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1410854 1411041 1411340 "KOVACIC" 1411750 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1410689 1410713 1410754 "KONVERT" 1410816 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1410524 1410548 1410589 "KOERCE" 1410651 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1408258 1409018 1409411 "KERNEL" 1410163 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1407760 1407841 1407971 "KERNEL2" 1408172 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1401611 1406299 1406353 "KDAGG" 1406730 NIL KDAGG (NIL T T) -9 NIL 1406936 NIL) (-607 1401140 1401264 1401469 "KDAGG-" 1401474 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1394315 1400801 1400956 "KAFILE" 1401018 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1388770 1393826 1394054 "JORDAN" 1394136 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1388176 1388419 1388540 "JOINAST" 1388669 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1388022 1388081 1388136 "JAVACODE" 1388141 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1384321 1386227 1386281 "IXAGG" 1387210 NIL IXAGG (NIL T T) -9 NIL 1387669 NIL) (-601 1383240 1383546 1383965 "IXAGG-" 1383970 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1378820 1383162 1383221 "IVECTOR" 1383226 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1377586 1377823 1378089 "ITUPLE" 1378587 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1376022 1376199 1376505 "ITRIGMNP" 1377408 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1374767 1374971 1375254 "ITFUN3" 1375798 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1374399 1374456 1374565 "ITFUN2" 1374704 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1372228 1373261 1373560 "ITAYLOR" 1374133 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1361200 1366365 1367528 "ISUPS" 1371098 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1360304 1360444 1360680 "ISUMP" 1361047 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1355568 1360105 1360184 "ISTRING" 1360257 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1355071 1355289 1355381 "ISAST" 1355496 T ISAST (NIL) -8 NIL NIL NIL) (-590 1354281 1354362 1354578 "IRURPK" 1354985 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1353217 1353418 1353658 "IRSN" 1354061 T IRSN (NIL) -7 NIL NIL NIL) (-588 1351246 1351601 1352037 "IRRF2F" 1352855 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1350993 1351031 1351107 "IRREDFFX" 1351202 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1349608 1349867 1350166 "IROOT" 1350726 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1346239 1347292 1347984 "IR" 1348948 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1343852 1344347 1344913 "IR2" 1345717 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1342924 1343037 1343258 "IR2F" 1343735 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1342715 1342749 1342809 "IPRNTPK" 1342884 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1339322 1342604 1342673 "IPF" 1342678 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1337676 1339247 1339304 "IPADIC" 1339309 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1337015 1337236 1337366 "IP4ADDR" 1337566 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1336515 1336719 1336829 "IOMODE" 1336925 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1335588 1336112 1336239 "IOBFILE" 1336408 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1335076 1335492 1335520 "IOBCON" 1335525 T IOBCON (NIL) -9 NIL 1335546 NIL) (-575 1334573 1334631 1334821 "INVLAPLA" 1335012 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1324221 1326575 1328961 "INTTR" 1332237 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1320565 1321307 1322171 "INTTOOLS" 1323406 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1320151 1320242 1320359 "INTSLPE" 1320468 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1318132 1320074 1320133 "INTRVL" 1320138 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1315734 1316246 1316821 "INTRF" 1317617 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1315145 1315242 1315384 "INTRET" 1315632 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1313142 1313531 1314001 "INTRAT" 1314753 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1310370 1310953 1311579 "INTPM" 1312627 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1307072 1307672 1308417 "INTPAF" 1309756 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1302251 1303213 1304264 "INTPACK" 1306041 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1299155 1301980 1302107 "INT" 1302144 T INT (NIL) -8 NIL NIL NIL) (-563 1298407 1298559 1298767 "INTHERTR" 1298997 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1297846 1297926 1298114 "INTHERAL" 1298321 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1295692 1296135 1296592 "INTHEORY" 1297409 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1287000 1288621 1290400 "INTG0" 1294044 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1267573 1272363 1277173 "INTFTBL" 1282210 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1266822 1266960 1267133 "INTFACT" 1267432 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1264207 1264653 1265217 "INTEF" 1266376 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1262666 1263379 1263407 "INTDOM" 1263708 T INTDOM (NIL) -9 NIL 1263915 NIL) (-555 1262035 1262209 1262451 "INTDOM-" 1262456 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1258522 1260419 1260473 "INTCAT" 1261272 NIL INTCAT (NIL T) -9 NIL 1261592 NIL) (-553 1257994 1258097 1258225 "INTBIT" 1258414 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1256665 1256819 1257133 "INTALG" 1257839 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1256122 1256212 1256382 "INTAF" 1256569 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1249576 1255932 1256072 "INTABL" 1256077 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1248907 1249346 1249411 "INT8" 1249445 T INT8 (NIL) -8 NIL NIL 1249490) (-548 1248237 1248676 1248741 "INT64" 1248775 T INT64 (NIL) -8 NIL NIL 1248820) (-547 1247567 1248006 1248071 "INT32" 1248105 T INT32 (NIL) -8 NIL NIL 1248150) (-546 1246897 1247336 1247401 "INT16" 1247435 T INT16 (NIL) -8 NIL NIL 1247480) (-545 1241904 1244586 1244614 "INS" 1245548 T INS (NIL) -9 NIL 1246213 NIL) (-544 1239144 1239915 1240889 "INS-" 1240962 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1237919 1238146 1238444 "INPSIGN" 1238897 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1237037 1237154 1237351 "INPRODPF" 1237799 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1235931 1236048 1236285 "INPRODFF" 1236917 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1234931 1235083 1235343 "INNMFACT" 1235767 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1234128 1234225 1234413 "INMODGCD" 1234830 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1232636 1232881 1233205 "INFSP" 1233873 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1231820 1231937 1232120 "INFPROD0" 1232516 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1228702 1229885 1230400 "INFORM" 1231313 T INFORM (NIL) -8 NIL NIL NIL) (-535 1228312 1228372 1228470 "INFORM1" 1228637 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1227835 1227924 1228038 "INFINITY" 1228218 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1227011 1227555 1227656 "INETCLTS" 1227754 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1225627 1225877 1226198 "INEP" 1226759 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1224903 1225524 1225589 "INDE" 1225594 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1224467 1224535 1224652 "INCRMAPS" 1224830 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1223285 1223736 1223942 "INBFILE" 1224281 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1218585 1219521 1220465 "INBFF" 1222373 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1217493 1217762 1217790 "INBCON" 1218303 T INBCON (NIL) -9 NIL 1218569 NIL) (-526 1216745 1216968 1217244 "INBCON-" 1217249 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1216247 1216466 1216558 "INAST" 1216673 T INAST (NIL) -8 NIL NIL NIL) (-524 1215701 1215926 1216032 "IMPTAST" 1216161 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1212195 1215545 1215649 "IMATRIX" 1215654 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1210907 1211030 1211345 "IMATQF" 1212051 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1209127 1209354 1209691 "IMATLIN" 1210663 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1203753 1209051 1209109 "ILIST" 1209114 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1201706 1203613 1203726 "IIARRAY2" 1203731 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1197131 1201617 1201681 "IFF" 1201686 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1196505 1196748 1196864 "IFAST" 1197035 T IFAST (NIL) -8 NIL NIL NIL) (-516 1191548 1195797 1195985 "IFARRAY" 1196362 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1190755 1191452 1191525 "IFAMON" 1191530 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1190339 1190404 1190458 "IEVALAB" 1190665 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1190014 1190082 1190242 "IEVALAB-" 1190247 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1189672 1189928 1189991 "IDPO" 1189996 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1188949 1189561 1189636 "IDPOAMS" 1189641 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1188283 1188838 1188913 "IDPOAM" 1188918 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1187368 1187618 1187671 "IDPC" 1188084 NIL IDPC (NIL T T) -9 NIL 1188233 NIL) (-508 1186864 1187260 1187333 "IDPAM" 1187338 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1186267 1186756 1186829 "IDPAG" 1186834 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1186035 1186182 1186232 "IDENT" 1186237 T IDENT (NIL) -8 NIL NIL NIL) (-505 1182290 1183138 1184033 "IDECOMP" 1185192 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1175154 1176213 1177260 "IDEAL" 1181326 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1174318 1174430 1174629 "ICDEN" 1175038 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1173416 1173798 1173945 "ICARD" 1174191 T ICARD (NIL) -8 NIL NIL NIL) (-501 1171476 1171789 1172194 "IBPTOOLS" 1173093 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1167110 1171096 1171209 "IBITS" 1171395 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1163833 1164409 1165104 "IBATOOL" 1166527 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1161612 1162074 1162607 "IBACHIN" 1163368 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1159489 1161458 1161561 "IARRAY2" 1161566 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1155642 1159415 1159472 "IARRAY1" 1159477 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1149626 1154054 1154535 "IAN" 1155181 T IAN (NIL) -8 NIL NIL NIL) (-494 1149137 1149194 1149367 "IALGFACT" 1149563 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1148665 1148778 1148806 "HYPCAT" 1149013 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1148203 1148320 1148506 "HYPCAT-" 1148511 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1147825 1147998 1148081 "HOSTNAME" 1148140 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1147670 1147707 1147748 "HOMOTOP" 1147753 NIL HOMOTOP (NIL T) -9 NIL 1147786 NIL) (-489 1144349 1145680 1145721 "HOAGG" 1146702 NIL HOAGG (NIL T) -9 NIL 1147381 NIL) (-488 1142943 1143342 1143868 "HOAGG-" 1143873 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1136974 1142538 1142687 "HEXADEC" 1142814 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1135722 1135944 1136207 "HEUGCD" 1136751 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1134825 1135559 1135689 "HELLFDIV" 1135694 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1133052 1134602 1134690 "HEAP" 1134769 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1132342 1132604 1132738 "HEADAST" 1132938 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1126256 1132257 1132319 "HDP" 1132324 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1119999 1125891 1126043 "HDMP" 1126157 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1119323 1119463 1119627 "HB" 1119855 T HB (NIL) -7 NIL NIL NIL) (-479 1112820 1119169 1119273 "HASHTBL" 1119278 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1112323 1112541 1112633 "HASAST" 1112748 T HASAST (NIL) -8 NIL NIL NIL) (-477 1110128 1111945 1112127 "HACKPI" 1112161 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1105823 1109981 1110094 "GTSET" 1110099 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1099349 1105701 1105799 "GSTBL" 1105804 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1091654 1098380 1098645 "GSERIES" 1099140 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1090821 1091212 1091240 "GROUP" 1091443 T GROUP (NIL) -9 NIL 1091577 NIL) (-472 1090187 1090346 1090597 "GROUP-" 1090602 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1088554 1088875 1089262 "GROEBSOL" 1089864 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1087494 1087756 1087807 "GRMOD" 1088336 NIL GRMOD (NIL T T) -9 NIL 1088504 NIL) (-469 1087262 1087298 1087426 "GRMOD-" 1087431 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1082579 1083616 1084616 "GRIMAGE" 1086282 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1081045 1081306 1081630 "GRDEF" 1082275 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1080489 1080605 1080746 "GRAY" 1080924 T GRAY (NIL) -7 NIL NIL NIL) (-465 1079702 1080082 1080133 "GRALG" 1080286 NIL GRALG (NIL T T) -9 NIL 1080379 NIL) (-464 1079363 1079436 1079599 "GRALG-" 1079604 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1076167 1078948 1079126 "GPOLSET" 1079270 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1075521 1075578 1075836 "GOSPER" 1076104 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1071280 1071959 1072485 "GMODPOL" 1075220 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1070285 1070469 1070707 "GHENSEL" 1071092 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1064336 1065179 1066206 "GENUPS" 1069369 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1064033 1064084 1064173 "GENUFACT" 1064279 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1063445 1063522 1063687 "GENPGCD" 1063951 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1062919 1062954 1063167 "GENMFACT" 1063404 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1061485 1061742 1062049 "GENEEZ" 1062662 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1055386 1061096 1061258 "GDMP" 1061408 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1044755 1049157 1050263 "GCNAALG" 1054369 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1043174 1044010 1044038 "GCDDOM" 1044293 T GCDDOM (NIL) -9 NIL 1044450 NIL) (-451 1042644 1042771 1042986 "GCDDOM-" 1042991 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1041316 1041501 1041805 "GB" 1042423 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1029932 1032262 1034654 "GBINTERN" 1039007 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1027769 1028061 1028482 "GBF" 1029607 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1026550 1026715 1026982 "GBEUCLID" 1027585 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1025899 1026024 1026173 "GAUSSFAC" 1026421 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1024266 1024568 1024882 "GALUTIL" 1025618 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1022574 1022848 1023172 "GALPOLYU" 1023993 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1019939 1020229 1020636 "GALFACTU" 1022271 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1011745 1013244 1014852 "GALFACT" 1018371 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1009133 1009791 1009819 "FVFUN" 1010975 T FVFUN (NIL) -9 NIL 1011695 NIL) (-440 1008399 1008581 1008609 "FVC" 1008900 T FVC (NIL) -9 NIL 1009083 NIL) (-439 1008069 1008224 1008292 "FUNDESC" 1008351 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1007711 1007866 1007947 "FUNCTION" 1008021 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1005482 1006033 1006499 "FT" 1007265 T FT (NIL) -8 NIL NIL NIL) (-436 1004300 1004783 1004986 "FTEM" 1005299 T FTEM (NIL) -8 NIL NIL NIL) (-435 1002556 1002845 1003249 "FSUPFACT" 1003991 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1000953 1001242 1001574 "FST" 1002244 T FST (NIL) -8 NIL NIL NIL) (-433 1000124 1000230 1000425 "FSRED" 1000835 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 998802 999058 999412 "FSPRMELT" 999839 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 995887 996325 996824 "FSPECF" 998365 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 977941 986390 986430 "FS" 990278 NIL FS (NIL T) -9 NIL 992567 NIL) (-429 966588 969581 973637 "FS-" 973934 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 966102 966156 966333 "FSINT" 966529 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 964421 965095 965398 "FSERIES" 965881 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 963435 963551 963782 "FSCINT" 964301 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 959669 962379 962420 "FSAGG" 962790 NIL FSAGG (NIL T) -9 NIL 963049 NIL) (-424 957431 958032 958828 "FSAGG-" 958923 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 956473 956616 956843 "FSAGG2" 957284 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 954127 954407 954961 "FS2UPS" 956191 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 953709 953752 953907 "FS2" 954078 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 952566 952737 953046 "FS2EXPXP" 953534 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 951992 952107 952259 "FRUTIL" 952446 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 943432 947487 948845 "FR" 950666 NIL FR (NIL T) -8 NIL NIL NIL) (-417 938507 941150 941190 "FRNAALG" 942586 NIL FRNAALG (NIL T) -9 NIL 943193 NIL) (-416 934180 935256 936531 "FRNAALG-" 937281 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 933818 933861 933988 "FRNAAF2" 934131 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 932225 932672 932967 "FRMOD" 933630 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 930003 930608 930925 "FRIDEAL" 932016 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 929198 929285 929574 "FRIDEAL2" 929910 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 928331 928745 928786 "FRETRCT" 928791 NIL FRETRCT (NIL T) -9 NIL 928967 NIL) (-410 927443 927674 928025 "FRETRCT-" 928030 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 924647 925831 925890 "FRAMALG" 926772 NIL FRAMALG (NIL T T) -9 NIL 927064 NIL) (-408 922781 923236 923866 "FRAMALG-" 924089 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 916729 922256 922532 "FRAC" 922537 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 916365 916422 916529 "FRAC2" 916666 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 916001 916058 916165 "FR2" 916302 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 910666 913526 913554 "FPS" 914673 T FPS (NIL) -9 NIL 915230 NIL) (-403 910115 910224 910388 "FPS-" 910534 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 907561 909204 909232 "FPC" 909457 T FPC (NIL) -9 NIL 909599 NIL) (-401 907354 907394 907491 "FPC-" 907496 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 906232 906842 906883 "FPATMAB" 906888 NIL FPATMAB (NIL T) -9 NIL 907040 NIL) (-399 903932 904408 904834 "FPARFRAC" 905869 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 899325 899824 900506 "FORTRAN" 903364 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 897041 897541 898080 "FORT" 898806 T FORT (NIL) -7 NIL NIL NIL) (-396 894717 895279 895307 "FORTFN" 896367 T FORTFN (NIL) -9 NIL 896991 NIL) (-395 894481 894531 894559 "FORTCAT" 894618 T FORTCAT (NIL) -9 NIL 894680 NIL) (-394 892614 893097 893487 "FORMULA" 894111 T FORMULA (NIL) -8 NIL NIL NIL) (-393 892402 892432 892501 "FORMULA1" 892578 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 891925 891977 892150 "FORDER" 892344 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 891021 891185 891378 "FOP" 891752 T FOP (NIL) -7 NIL NIL NIL) (-390 889629 890301 890475 "FNLA" 890903 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 888384 888773 888801 "FNCAT" 889261 T FNCAT (NIL) -9 NIL 889521 NIL) (-388 887950 888343 888371 "FNAME" 888376 T FNAME (NIL) -8 NIL NIL NIL) (-387 886605 887542 887570 "FMTC" 887575 T FMTC (NIL) -9 NIL 887611 NIL) (-386 882965 884128 884757 "FMONOID" 886009 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 882184 882707 882856 "FM" 882861 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 879608 880254 880282 "FMFUN" 881426 T FMFUN (NIL) -9 NIL 882134 NIL) (-383 878877 879058 879086 "FMC" 879376 T FMC (NIL) -9 NIL 879558 NIL) (-382 876071 876905 876959 "FMCAT" 878154 NIL FMCAT (NIL T T) -9 NIL 878649 NIL) (-381 874964 875837 875937 "FM1" 876016 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 872738 873154 873648 "FLOATRP" 874515 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 866339 870467 871088 "FLOAT" 872137 T FLOAT (NIL) -8 NIL NIL NIL) (-378 863777 864277 864855 "FLOATCP" 865806 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 862578 863390 863431 "FLINEXP" 863436 NIL FLINEXP (NIL T) -9 NIL 863529 NIL) (-376 861732 861967 862295 "FLINEXP-" 862300 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 860808 860952 861176 "FLASORT" 861584 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 858025 858867 858919 "FLALG" 860146 NIL FLALG (NIL T T) -9 NIL 860613 NIL) (-373 851809 855511 855552 "FLAGG" 856814 NIL FLAGG (NIL T) -9 NIL 857466 NIL) (-372 850535 850874 851364 "FLAGG-" 851369 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 849577 849720 849947 "FLAGG2" 850388 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 846544 847526 847585 "FINRALG" 848713 NIL FINRALG (NIL T T) -9 NIL 849221 NIL) (-369 845704 845933 846272 "FINRALG-" 846277 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 845110 845323 845351 "FINITE" 845547 T FINITE (NIL) -9 NIL 845654 NIL) (-367 837568 839729 839769 "FINAALG" 843436 NIL FINAALG (NIL T) -9 NIL 844889 NIL) (-366 832900 833950 835094 "FINAALG-" 836473 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 832295 832655 832758 "FILE" 832830 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 830979 831291 831345 "FILECAT" 832029 NIL FILECAT (NIL T T) -9 NIL 832245 NIL) (-363 828839 830341 830369 "FIELD" 830409 T FIELD (NIL) -9 NIL 830489 NIL) (-362 827459 827844 828355 "FIELD-" 828360 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 825336 826094 826441 "FGROUP" 827145 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 824426 824590 824810 "FGLMICPK" 825168 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 820285 824351 824408 "FFX" 824413 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 819886 819947 820082 "FFSLPE" 820218 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 815875 816658 817454 "FFPOLY" 819122 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 815379 815415 815624 "FFPOLY2" 815833 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 811249 815298 815361 "FFP" 815366 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 806674 811160 811224 "FF" 811229 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 801827 806017 806207 "FFNBX" 806528 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 796783 800962 801220 "FFNBP" 801681 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 791443 796067 796278 "FFNB" 796616 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 790275 790473 790788 "FFINTBAS" 791240 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 786495 788682 788710 "FFIELDC" 789330 T FFIELDC (NIL) -9 NIL 789706 NIL) (-348 785157 785528 786025 "FFIELDC-" 786030 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 784726 784772 784896 "FFHOM" 785099 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 782421 782908 783425 "FFF" 784241 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778066 782163 782264 "FFCGX" 782364 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 773714 777798 777905 "FFCGP" 778009 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 768924 773441 773549 "FFCG" 773650 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 750749 759795 759881 "FFCAT" 765046 NIL FFCAT (NIL T T T) -9 NIL 766497 NIL) (-341 745947 746994 748308 "FFCAT-" 749538 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 745358 745401 745636 "FFCAT2" 745898 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 734555 738330 739550 "FEXPR" 744210 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 733555 733990 734031 "FEVALAB" 734115 NIL FEVALAB (NIL T) -9 NIL 734376 NIL) (-337 732714 732924 733262 "FEVALAB-" 733267 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 731307 732097 732300 "FDIV" 732613 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 728373 729088 729203 "FDIVCAT" 730771 NIL FDIVCAT (NIL T T T T) -9 NIL 731208 NIL) (-334 728135 728162 728332 "FDIVCAT-" 728337 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 727355 727442 727719 "FDIV2" 728042 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726041 726300 726589 "FCPAK1" 727086 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725167 725541 725682 "FCOMP" 725932 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 708896 712317 715855 "FC" 721649 T FC (NIL) -8 NIL NIL NIL) (-329 701467 705460 705500 "FAXF" 707302 NIL FAXF (NIL T) -9 NIL 707994 NIL) (-328 698743 699401 700226 "FAXF-" 700691 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 693843 698119 698295 "FARRAY" 698600 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689088 691128 691181 "FAMR" 692204 NIL FAMR (NIL T T) -9 NIL 692664 NIL) (-325 687978 688280 688715 "FAMR-" 688720 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687174 687900 687953 "FAMONOID" 687958 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 684986 685670 685723 "FAMONC" 686664 NIL FAMONC (NIL T T) -9 NIL 687050 NIL) (-322 683678 684740 684877 "FAGROUP" 684882 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 681473 681792 682195 "FACUTIL" 683359 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 680572 680757 680979 "FACTFUNC" 681283 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 672969 679823 680035 "EXPUPXS" 680428 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 670452 670992 671578 "EXPRTUBE" 672403 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 666646 667238 667975 "EXPRODE" 669791 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 652012 665301 665729 "EXPR" 666250 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 646419 647006 647819 "EXPR2UPS" 651310 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646055 646112 646219 "EXPR2" 646356 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 637452 645187 645484 "EXPEXPAN" 645892 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 637279 637409 637438 "EXIT" 637443 T EXIT (NIL) -8 NIL NIL NIL) (-311 636786 637003 637094 "EXITAST" 637208 T EXITAST (NIL) -8 NIL NIL NIL) (-310 636413 636475 636588 "EVALCYC" 636718 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 635954 636072 636113 "EVALAB" 636283 NIL EVALAB (NIL T) -9 NIL 636387 NIL) (-308 635435 635557 635778 "EVALAB-" 635783 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 632895 634171 634199 "EUCDOM" 634754 T EUCDOM (NIL) -9 NIL 635104 NIL) (-306 631300 631742 632332 "EUCDOM-" 632337 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 618838 621598 624348 "ESTOOLS" 628570 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 618470 618527 618636 "ESTOOLS2" 618775 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618221 618263 618343 "ESTOOLS1" 618422 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612126 613854 613882 "ES" 616650 T ES (NIL) -9 NIL 618059 NIL) (-301 607073 608360 610177 "ES-" 610341 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 603447 604208 604988 "ESCONT" 606313 T ESCONT (NIL) -7 NIL NIL NIL) (-299 603192 603224 603306 "ESCONT1" 603409 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 602867 602917 603017 "ES2" 603136 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 602497 602555 602664 "ES1" 602803 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 601713 601842 602018 "ERROR" 602341 T ERROR (NIL) -7 NIL NIL NIL) (-295 595216 601572 601663 "EQTBL" 601668 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 587767 590530 591979 "EQ" 593800 NIL -3317 (NIL T) -8 NIL NIL NIL) (-293 587399 587456 587565 "EQ2" 587704 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 582688 583737 584830 "EP" 586338 NIL EP (NIL T) -7 NIL NIL NIL) (-291 581266 581563 581875 "ENV" 582396 T ENV (NIL) -8 NIL NIL NIL) (-290 580437 580965 580993 "ENTIRER" 580998 T ENTIRER (NIL) -9 NIL 581044 NIL) (-289 576931 578392 578762 "EMR" 580236 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576075 576260 576314 "ELTAGG" 576694 NIL ELTAGG (NIL T T) -9 NIL 576905 NIL) (-287 575794 575856 575997 "ELTAGG-" 576002 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 575583 575612 575666 "ELTAB" 575750 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 574709 574855 575054 "ELFUTS" 575434 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 574451 574507 574535 "ELEMFUN" 574640 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 574321 574342 574410 "ELEMFUN-" 574415 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569212 572421 572462 "ELAGG" 573402 NIL ELAGG (NIL T) -9 NIL 573865 NIL) (-281 567497 567931 568594 "ELAGG-" 568599 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566154 566434 566729 "ELABEXPR" 567222 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559018 560821 561648 "EFUPXS" 565430 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 552468 554269 555079 "EFULS" 558294 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 549890 550248 550727 "EFSTRUC" 552100 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 538961 540527 542087 "EF" 548405 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 538062 538446 538595 "EAB" 538832 T EAB (NIL) -8 NIL NIL NIL) (-274 537271 538021 538049 "E04UCFA" 538054 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 536480 537230 537258 "E04NAFA" 537263 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 535689 536439 536467 "E04MBFA" 536472 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 534898 535648 535676 "E04JAFA" 535681 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 534109 534857 534885 "E04GCFA" 534890 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 533320 534068 534096 "E04FDFA" 534101 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 532529 533279 533307 "E04DGFA" 533312 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 526702 528054 529418 "E04AGNT" 531185 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 525408 525888 525928 "DVARCAT" 526403 NIL DVARCAT (NIL T) -9 NIL 526602 NIL) (-265 524612 524824 525138 "DVARCAT-" 525143 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 517504 524411 524540 "DSMP" 524545 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 512313 513449 514517 "DROPT" 516456 T DROPT (NIL) -8 NIL NIL NIL) (-262 511978 512037 512135 "DROPT1" 512248 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 507093 508219 509356 "DROPT0" 510861 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 505438 505763 506149 "DRAWPT" 506727 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 500025 500948 502027 "DRAW" 504412 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 499658 499711 499829 "DRAWHACK" 499966 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 498389 498658 498949 "DRAWCX" 499387 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 497904 497973 498124 "DRAWCURV" 498315 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 488372 490334 492449 "DRAWCFUN" 495809 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 485185 487067 487108 "DQAGG" 487737 NIL DQAGG (NIL T) -9 NIL 488010 NIL) (-253 473456 480163 480246 "DPOLCAT" 482098 NIL DPOLCAT (NIL T T T T) -9 NIL 482643 NIL) (-252 468292 469641 471599 "DPOLCAT-" 471604 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 461441 468153 468251 "DPMO" 468256 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 454493 461221 461388 "DPMM" 461393 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 454125 454412 454460 "DOMCTOR" 454465 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 453420 453647 453784 "DOMAIN" 454008 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 447163 453055 453207 "DMP" 453321 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 446763 446819 446963 "DLP" 447101 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 440633 446090 446280 "DLIST" 446605 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 437477 439486 439527 "DLAGG" 440077 NIL DLAGG (NIL T) -9 NIL 440307 NIL) (-243 436282 436920 436948 "DIVRING" 437040 T DIVRING (NIL) -9 NIL 437123 NIL) (-242 435519 435709 436009 "DIVRING-" 436014 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 433621 433978 434384 "DISPLAY" 435133 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 427557 433535 433598 "DIRPROD" 433603 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 426405 426608 426873 "DIRPROD2" 427350 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 415662 421620 421673 "DIRPCAT" 422083 NIL DIRPCAT (NIL NIL T) -9 NIL 422923 NIL) (-237 412988 413630 414511 "DIRPCAT-" 414848 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 412275 412435 412621 "DIOSP" 412822 T DIOSP (NIL) -7 NIL NIL NIL) (-235 408977 411187 411228 "DIOPS" 411662 NIL DIOPS (NIL T) -9 NIL 411891 NIL) (-234 408526 408640 408831 "DIOPS-" 408836 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 407410 408012 408040 "DIFRING" 408227 T DIFRING (NIL) -9 NIL 408337 NIL) (-232 407056 407133 407285 "DIFRING-" 407290 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 404853 406099 406140 "DIFEXT" 406503 NIL DIFEXT (NIL T) -9 NIL 406797 NIL) (-230 403138 403566 404232 "DIFEXT-" 404237 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 400460 402670 402711 "DIAGG" 402716 NIL DIAGG (NIL T) -9 NIL 402736 NIL) (-228 399844 400001 400253 "DIAGG-" 400258 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 395309 398803 399080 "DHMATRIX" 399613 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 390921 391830 392840 "DFSFUN" 394319 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 386026 389852 390164 "DFLOAT" 390629 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 384254 384535 384931 "DFINTTLS" 385734 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 381310 382275 382675 "DERHAM" 383920 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 379159 381085 381174 "DEQUEUE" 381254 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 378374 378507 378703 "DEGRED" 379021 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 374769 375514 376367 "DEFINTRF" 377602 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 372296 372765 373364 "DEFINTEF" 374288 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 371673 371916 372031 "DEFAST" 372201 T DEFAST (NIL) -8 NIL NIL NIL) (-217 365704 371268 371417 "DECIMAL" 371544 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 363214 363674 364180 "DDFACT" 365248 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 362810 362853 363004 "DBLRESP" 363165 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 360709 361043 361403 "DBASE" 362577 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 359978 360189 360335 "DATAARY" 360608 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 359111 359937 359965 "D03FAFA" 359970 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 358245 359070 359098 "D03EEFA" 359103 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 356195 356661 357150 "D03AGNT" 357776 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 355511 356154 356182 "D02EJFA" 356187 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 354827 355470 355498 "D02CJFA" 355503 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 354143 354786 354814 "D02BHFA" 354819 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 353459 354102 354130 "D02BBFA" 354135 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 346656 348245 349851 "D02AGNT" 351873 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 344424 344947 345493 "D01WGTS" 346130 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 343518 344383 344411 "D01TRNS" 344416 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 342613 343477 343505 "D01GBFA" 343510 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 341708 342572 342600 "D01FCFA" 342605 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 340803 341667 341695 "D01ASFA" 341700 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 339898 340762 340790 "D01AQFA" 340795 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 338993 339857 339885 "D01APFA" 339890 T D01APFA (NIL) -8 NIL NIL NIL) (-197 338088 338952 338980 "D01ANFA" 338985 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 337183 338047 338075 "D01AMFA" 338080 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 336278 337142 337170 "D01ALFA" 337175 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 335373 336237 336265 "D01AKFA" 336270 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 334468 335332 335360 "D01AJFA" 335365 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 327763 329316 330877 "D01AGNT" 332927 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327100 327228 327380 "CYCLOTOM" 327631 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 323835 324548 325275 "CYCLES" 326393 T CYCLES (NIL) -7 NIL NIL NIL) (-189 323147 323281 323452 "CVMP" 323696 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 320918 321176 321552 "CTRIGMNP" 322875 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 320409 320709 320783 "CTOR" 320864 T CTOR (NIL) -8 NIL NIL NIL) (-186 319945 320140 320241 "CTORKIND" 320328 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 319293 319552 319580 "CTORCAT" 319762 T CTORCAT (NIL) -9 NIL 319875 NIL) (-184 318891 319002 319161 "CTORCAT-" 319166 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 318407 318594 318692 "CTORCALL" 318813 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 317781 317880 318033 "CSTTOOLS" 318304 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 313580 314237 314995 "CRFP" 317093 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 313082 313301 313393 "CRCEAST" 313508 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 312129 312314 312542 "CRAPACK" 312886 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 311513 311614 311818 "CPMATCH" 312005 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 311238 311266 311372 "CPIMA" 311479 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 307602 308274 308992 "COORDSYS" 310573 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307010 307132 307275 "CONTOUR" 307479 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 302928 305013 305505 "CONTFRAC" 306550 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 302808 302829 302857 "CONDUIT" 302894 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 301973 302501 302529 "COMRING" 302534 T COMRING (NIL) -9 NIL 302586 NIL) (-171 301054 301331 301515 "COMPPROP" 301809 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 300715 300750 300878 "COMPLPAT" 301013 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 290764 300524 300633 "COMPLEX" 300638 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 290400 290457 290564 "COMPLEX2" 290701 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 290118 290153 290251 "COMPFACT" 290359 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 274272 284500 284540 "COMPCAT" 285544 NIL COMPCAT (NIL T) -9 NIL 286940 NIL) (-165 263783 266711 270338 "COMPCAT-" 270694 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 263512 263540 263643 "COMMUPC" 263749 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 263307 263340 263399 "COMMONOP" 263473 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 262890 263058 263145 "COMM" 263240 T COMM (NIL) -8 NIL NIL NIL) (-161 262493 262694 262769 "COMMAAST" 262835 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 261742 261936 261964 "COMBOPC" 262302 T COMBOPC (NIL) -9 NIL 262477 NIL) (-159 260638 260848 261090 "COMBINAT" 261532 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 256835 257409 258049 "COMBF" 260060 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 255620 255951 256186 "COLOR" 256620 T COLOR (NIL) -8 NIL NIL NIL) (-156 255123 255341 255433 "COLONAST" 255548 T COLONAST (NIL) -8 NIL NIL NIL) (-155 254763 254810 254935 "CMPLXRT" 255070 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 254238 254463 254562 "CLLCTAST" 254684 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 249738 250768 251848 "CLIP" 253178 T CLIP (NIL) -7 NIL NIL NIL) (-152 248111 248844 249083 "CLIF" 249565 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 244333 246257 246298 "CLAGG" 247227 NIL CLAGG (NIL T) -9 NIL 247763 NIL) (-150 242755 243212 243795 "CLAGG-" 243800 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 242299 242384 242524 "CINTSLPE" 242664 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 239800 240271 240819 "CHVAR" 241827 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 239035 239563 239591 "CHARZ" 239596 T CHARZ (NIL) -9 NIL 239611 NIL) (-146 238789 238829 238907 "CHARPOL" 238989 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 237908 238469 238497 "CHARNZ" 238544 T CHARNZ (NIL) -9 NIL 238600 NIL) (-144 235897 236598 236933 "CHAR" 237593 T CHAR (NIL) -8 NIL NIL NIL) (-143 235623 235684 235712 "CFCAT" 235823 T CFCAT (NIL) -9 NIL NIL NIL) (-142 234868 234979 235161 "CDEN" 235507 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 230860 234021 234301 "CCLASS" 234608 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230167 230310 230473 "CATEGORY" 230717 T -10 (NIL) -8 NIL NIL NIL) (-139 229799 230086 230134 "CATCTOR" 230139 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 229273 229499 229598 "CATAST" 229720 T CATAST (NIL) -8 NIL NIL NIL) (-137 228776 228994 229086 "CASEAST" 229201 T CASEAST (NIL) -8 NIL NIL NIL) (-136 223812 224805 225558 "CARTEN" 228079 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 222920 223068 223289 "CARTEN2" 223659 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 221262 222070 222327 "CARD" 222683 T CARD (NIL) -8 NIL NIL NIL) (-133 220865 221066 221141 "CAPSLAST" 221207 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220237 220565 220593 "CACHSET" 220725 T CACHSET (NIL) -9 NIL 220802 NIL) (-131 219733 220029 220057 "CABMON" 220107 T CABMON (NIL) -9 NIL 220163 NIL) (-130 219233 219437 219547 "BYTEORD" 219643 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 218236 218767 218909 "BYTE" 219072 T BYTE (NIL) -8 NIL NIL 219194) (-128 213636 217741 217913 "BYTEBUF" 218084 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211193 213328 213435 "BTREE" 213562 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 208690 210841 210963 "BTOURN" 211103 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 206107 208160 208201 "BTCAT" 208269 NIL BTCAT (NIL T) -9 NIL 208346 NIL) (-124 205774 205854 206003 "BTCAT-" 206008 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201066 204917 204945 "BTAGG" 205167 T BTAGG (NIL) -9 NIL 205328 NIL) (-122 200556 200681 200887 "BTAGG-" 200892 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197599 199834 200049 "BSTREE" 200373 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 196737 196863 197047 "BRILL" 197455 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193436 195463 195504 "BRAGG" 196153 NIL BRAGG (NIL T) -9 NIL 196411 NIL) (-118 191965 192371 192926 "BRAGG-" 192931 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185221 191311 191495 "BPADICRT" 191813 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183563 185158 185203 "BPADIC" 185208 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183261 183291 183405 "BOUNDZRO" 183527 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178776 179867 180734 "BOP" 182414 T BOP (NIL) -8 NIL NIL NIL) (-113 176397 176841 177361 "BOP1" 178289 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175099 175821 176014 "BOOLEAN" 176224 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174461 174839 174893 "BMODULE" 174898 NIL BMODULE (NIL T T) -9 NIL 174963 NIL) (-110 170289 174259 174332 "BITS" 174408 T BITS (NIL) -8 NIL NIL NIL) (-109 169701 169823 169965 "BINDING" 170167 T BINDING (NIL) -8 NIL NIL NIL) (-108 163735 169298 169446 "BINARY" 169573 T BINARY (NIL) -8 NIL NIL NIL) (-107 161562 162990 163031 "BGAGG" 163291 NIL BGAGG (NIL T) -9 NIL 163428 NIL) (-106 161393 161425 161516 "BGAGG-" 161521 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160491 160777 160982 "BFUNCT" 161208 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159181 159359 159647 "BEZOUT" 160315 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155698 158033 158363 "BBTREE" 158884 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155432 155485 155513 "BASTYPE" 155632 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155285 155313 155386 "BASTYPE-" 155391 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154719 154795 154947 "BALFACT" 155196 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153602 154134 154320 "AUTOMOR" 154564 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153328 153333 153359 "ATTREG" 153364 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151607 152025 152377 "ATTRBUT" 152994 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151242 151435 151501 "ATTRAST" 151559 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150778 150891 150917 "ATRIG" 151118 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150587 150628 150715 "ATRIG-" 150720 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150258 150418 150444 "ASTCAT" 150449 T ASTCAT (NIL) -9 NIL 150479 NIL) (-92 149985 150044 150163 "ASTCAT-" 150168 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148182 149761 149849 "ASTACK" 149928 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146687 146984 147349 "ASSOCEQ" 147864 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145719 146346 146470 "ASP9" 146594 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145482 145667 145706 "ASP8" 145711 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144350 145087 145229 "ASP80" 145371 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143248 143985 144117 "ASP7" 144249 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142202 142925 143043 "ASP78" 143161 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141171 141882 141999 "ASP77" 142116 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140083 140809 140940 "ASP74" 141071 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 138983 139718 139850 "ASP73" 139982 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138087 138809 138909 "ASP6" 138914 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137031 137764 137882 "ASP55" 138000 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 135980 136705 136824 "ASP50" 136943 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135068 135681 135791 "ASP4" 135901 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134156 134769 134879 "ASP49" 134989 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 132940 133695 133863 "ASP42" 134045 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131716 132473 132643 "ASP41" 132827 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130666 131393 131511 "ASP35" 131629 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130431 130614 130653 "ASP34" 130658 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130168 130235 130311 "ASP33" 130386 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129061 129803 129935 "ASP31" 130067 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 128826 129009 129048 "ASP30" 129053 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128561 128630 128706 "ASP29" 128781 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128326 128509 128548 "ASP28" 128553 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128091 128274 128313 "ASP27" 128318 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127175 127789 127900 "ASP24" 128011 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126251 126977 127089 "ASP20" 127094 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125339 125952 126062 "ASP1" 126172 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124281 125013 125132 "ASP19" 125251 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124018 124085 124161 "ASP12" 124236 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 122870 123617 123761 "ASP10" 123905 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 120769 122714 122805 "ARRAY2" 122810 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116583 120417 120531 "ARRAY1" 120686 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115615 115788 116009 "ARRAY12" 116406 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 109974 111845 111920 "ARR2CAT" 114550 NIL ARR2CAT (NIL T T T) -9 NIL 115308 NIL) (-56 107408 108152 109106 "ARR2CAT-" 109111 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107000 107235 107314 "ARITY" 107347 T ARITY (NIL) -8 NIL NIL NIL) (-54 105748 105900 106206 "APPRULE" 106836 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105399 105447 105566 "APPLYORE" 105694 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104373 104664 104859 "ANY" 105222 T ANY (NIL) -8 NIL NIL NIL) (-51 103651 103774 103931 "ANY1" 104247 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101208 102088 102415 "ANTISYM" 103375 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100723 100912 101009 "ANON" 101129 T ANON (NIL) -8 NIL NIL NIL) (-48 94847 99262 99716 "AN" 100287 T AN (NIL) -8 NIL NIL NIL) (-47 91095 92457 92508 "AMR" 93256 NIL AMR (NIL T T) -9 NIL 93856 NIL) (-46 90207 90428 90791 "AMR-" 90796 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74757 90124 90185 "ALIST" 90190 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71586 74351 74520 "ALGSC" 74675 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68141 68696 69303 "ALGPKG" 71026 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67418 67519 67703 "ALGMFACT" 68027 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63155 63842 64497 "ALGMANIP" 66941 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54552 62781 62931 "ALGFF" 63088 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53748 53879 54058 "ALGFACT" 54410 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52805 53379 53417 "ALGEBRA" 53422 NIL ALGEBRA (NIL T) -9 NIL 53463 NIL) (-37 52523 52582 52714 "ALGEBRA-" 52719 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34782 50525 50577 "ALAGG" 50713 NIL ALAGG (NIL T T) -9 NIL 50874 NIL) (-35 34318 34431 34457 "AHYP" 34658 T AHYP (NIL) -9 NIL NIL NIL) (-34 33249 33497 33523 "AGG" 34022 T AGG (NIL) -9 NIL 34301 NIL) (-33 32683 32845 33059 "AGG-" 33064 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30359 30782 31200 "AF" 32325 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29866 30084 30174 "ADDAST" 30287 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29134 29393 29549 "ACPLOT" 29728 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18418 26347 26398 "ACFS" 27109 NIL ACFS (NIL T) -9 NIL 27348 NIL) (-28 16432 16922 17697 "ACFS-" 17702 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14599 14625 "ACF" 15504 T ACF (NIL) -9 NIL 15916 NIL) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351 NIL) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804 NIL) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812 NIL) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3199804 3199809 3199814 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3199789 3199794 3199799 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3199774 3199779 3199784 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3199759 3199764 3199769 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1287 3198928 3199634 3199711 "ZMOD" 3199716 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1286 3198038 3198202 3198411 "ZLINDEP" 3198760 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1285 3187338 3189106 3191078 "ZDSOLVE" 3196168 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1284 3186584 3186725 3186914 "YSTREAM" 3187184 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1283 3184385 3185885 3186089 "XRPOLY" 3186427 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1282 3180965 3182256 3182831 "XPR" 3183857 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1281 3178713 3180296 3180500 "XPOLY" 3180796 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1280 3176496 3177838 3177893 "XPOLYC" 3178181 NIL XPOLYC (NIL T T) -9 NIL 3178294 NIL) (-1279 3172899 3175013 3175401 "XPBWPOLY" 3176154 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1278 3168802 3171062 3171104 "XF" 3171725 NIL XF (NIL T) -9 NIL 3172125 NIL) (-1277 3168423 3168511 3168680 "XF-" 3168685 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1276 3163749 3165012 3165067 "XFALG" 3167239 NIL XFALG (NIL T T) -9 NIL 3168028 NIL) (-1275 3162882 3162986 3163191 "XEXPPKG" 3163641 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1274 3161018 3162732 3162828 "XDPOLY" 3162833 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1273 3159955 3160529 3160572 "XALG" 3160577 NIL XALG (NIL T) -9 NIL 3160688 NIL) (-1272 3153424 3157932 3158426 "WUTSET" 3159547 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1271 3151707 3152476 3152799 "WP" 3153235 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1270 3151336 3151529 3151599 "WHILEAST" 3151659 T WHILEAST (NIL) -8 NIL NIL NIL) (-1269 3150835 3151053 3151147 "WHEREAST" 3151264 T WHEREAST (NIL) -8 NIL NIL NIL) (-1268 3149721 3149919 3150214 "WFFINTBS" 3150632 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1267 3147625 3148052 3148514 "WEIER" 3149293 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1266 3146772 3147196 3147238 "VSPACE" 3147374 NIL VSPACE (NIL T) -9 NIL 3147448 NIL) (-1265 3146610 3146637 3146728 "VSPACE-" 3146733 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1264 3146418 3146461 3146529 "VOID" 3146564 T VOID (NIL) -8 NIL NIL NIL) (-1263 3144554 3144913 3145319 "VIEW" 3146034 T VIEW (NIL) -7 NIL NIL NIL) (-1262 3140978 3141617 3142354 "VIEWDEF" 3143839 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1261 3130309 3132526 3134699 "VIEW3D" 3138827 T VIEW3D (NIL) -8 NIL NIL NIL) (-1260 3122587 3124220 3125799 "VIEW2D" 3128752 T VIEW2D (NIL) -8 NIL NIL NIL) (-1259 3117989 3122357 3122449 "VECTOR" 3122530 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1258 3116566 3116825 3117143 "VECTOR2" 3117719 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1257 3110093 3114350 3114393 "VECTCAT" 3115386 NIL VECTCAT (NIL T) -9 NIL 3115972 NIL) (-1256 3109107 3109361 3109751 "VECTCAT-" 3109756 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1255 3108588 3108758 3108878 "VARIABLE" 3109022 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1254 3108521 3108526 3108556 "UTYPE" 3108561 T UTYPE (NIL) -9 NIL NIL NIL) (-1253 3107351 3107505 3107767 "UTSODETL" 3108347 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1252 3104791 3105251 3105775 "UTSODE" 3106892 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1251 3096655 3102417 3102906 "UTS" 3104360 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1250 3087890 3093222 3093265 "UTSCAT" 3094377 NIL UTSCAT (NIL T) -9 NIL 3095134 NIL) (-1249 3085238 3085960 3086949 "UTSCAT-" 3086954 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1248 3084865 3084908 3085041 "UTS2" 3085189 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1247 3079138 3081703 3081746 "URAGG" 3083816 NIL URAGG (NIL T) -9 NIL 3084539 NIL) (-1246 3076077 3076940 3078063 "URAGG-" 3078068 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1245 3071793 3074691 3075163 "UPXSSING" 3075741 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1244 3063886 3071040 3071313 "UPXS" 3071578 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1243 3056986 3063790 3063862 "UPXSCONS" 3063867 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1242 3047223 3053981 3054043 "UPXSCCA" 3054617 NIL UPXSCCA (NIL T T) -9 NIL 3054850 NIL) (-1241 3046861 3046946 3047120 "UPXSCCA-" 3047125 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1240 3036951 3043482 3043525 "UPXSCAT" 3044173 NIL UPXSCAT (NIL T) -9 NIL 3044781 NIL) (-1239 3036381 3036460 3036639 "UPXS2" 3036866 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1238 3035035 3035288 3035639 "UPSQFREE" 3036124 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1237 3028815 3031837 3031892 "UPSCAT" 3033053 NIL UPSCAT (NIL T T) -9 NIL 3033827 NIL) (-1236 3028019 3028226 3028553 "UPSCAT-" 3028558 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1235 3013861 3021867 3021910 "UPOLYC" 3024011 NIL UPOLYC (NIL T) -9 NIL 3025232 NIL) (-1234 3005189 3007615 3010762 "UPOLYC-" 3010767 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1233 3004816 3004859 3004992 "UPOLYC2" 3005140 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1232 2996382 3004499 3004628 "UP" 3004735 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1231 2995721 2995828 2995992 "UPMP" 2996271 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1230 2995274 2995355 2995494 "UPDIVP" 2995634 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1229 2993842 2994091 2994407 "UPDECOMP" 2995023 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1228 2993077 2993189 2993374 "UPCDEN" 2993726 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1227 2992596 2992665 2992814 "UP2" 2993002 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1226 2991111 2991800 2992077 "UNISEG" 2992354 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1225 2990326 2990453 2990658 "UNISEG2" 2990954 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1224 2989386 2989566 2989792 "UNIFACT" 2990142 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1223 2973345 2988563 2988814 "ULS" 2989193 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1222 2961371 2973249 2973321 "ULSCONS" 2973326 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1221 2943979 2955929 2955991 "ULSCCAT" 2956629 NIL ULSCCAT (NIL T T) -9 NIL 2956917 NIL) (-1220 2943029 2943274 2943662 "ULSCCAT-" 2943667 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1219 2932896 2939341 2939384 "ULSCAT" 2940247 NIL ULSCAT (NIL T) -9 NIL 2940977 NIL) (-1218 2932326 2932405 2932584 "ULS2" 2932811 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1217 2931443 2931926 2932033 "UINT8" 2932144 T UINT8 (NIL) -8 NIL NIL 2932229) (-1216 2930559 2931042 2931149 "UINT64" 2931260 T UINT64 (NIL) -8 NIL NIL 2931345) (-1215 2929675 2930158 2930265 "UINT32" 2930376 T UINT32 (NIL) -8 NIL NIL 2930461) (-1214 2928791 2929274 2929381 "UINT16" 2929492 T UINT16 (NIL) -8 NIL NIL 2929577) (-1213 2927186 2928117 2928147 "UFD" 2928359 T UFD (NIL) -9 NIL 2928473 NIL) (-1212 2926980 2927026 2927121 "UFD-" 2927126 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1211 2926062 2926245 2926461 "UDVO" 2926786 T UDVO (NIL) -7 NIL NIL NIL) (-1210 2923878 2924287 2924758 "UDPO" 2925626 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1209 2923811 2923816 2923846 "TYPE" 2923851 T TYPE (NIL) -9 NIL NIL NIL) (-1208 2923598 2923766 2923797 "TYPEAST" 2923802 T TYPEAST (NIL) -8 NIL NIL NIL) (-1207 2922569 2922771 2923011 "TWOFACT" 2923392 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1206 2921640 2921978 2922213 "TUPLE" 2922369 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1205 2919331 2919850 2920389 "TUBETOOL" 2921123 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1204 2918180 2918385 2918626 "TUBE" 2919124 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1203 2912936 2917152 2917435 "TS" 2917932 NIL TS (NIL T) -8 NIL NIL NIL) (-1202 2901603 2905695 2905792 "TSETCAT" 2911061 NIL TSETCAT (NIL T T T T) -9 NIL 2912592 NIL) (-1201 2896335 2897935 2899826 "TSETCAT-" 2899831 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1200 2890597 2891444 2892386 "TRMANIP" 2895471 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1199 2890038 2890101 2890264 "TRIMAT" 2890529 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1198 2887834 2888071 2888435 "TRIGMNIP" 2889787 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1197 2887354 2887467 2887497 "TRIGCAT" 2887710 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1196 2887023 2887102 2887243 "TRIGCAT-" 2887248 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1195 2883916 2885881 2886162 "TREE" 2886777 NIL TREE (NIL T) -8 NIL NIL NIL) (-1194 2883190 2883718 2883748 "TRANFUN" 2883783 T TRANFUN (NIL) -9 NIL 2883849 NIL) (-1193 2882469 2882660 2882940 "TRANFUN-" 2882945 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1192 2882273 2882305 2882366 "TOPSP" 2882430 T TOPSP (NIL) -7 NIL NIL NIL) (-1191 2881621 2881736 2881890 "TOOLSIGN" 2882154 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1190 2880282 2880798 2881037 "TEXTFILE" 2881404 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1189 2878221 2878735 2879164 "TEX" 2879875 T TEX (NIL) -8 NIL NIL NIL) (-1188 2878002 2878033 2878105 "TEX1" 2878184 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2877650 2877713 2877803 "TEMUTL" 2877934 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2875804 2876084 2876409 "TBCMPPK" 2877373 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2867692 2873964 2874020 "TBAGG" 2874420 NIL TBAGG (NIL T T) -9 NIL 2874631 NIL) (-1184 2862762 2864250 2866004 "TBAGG-" 2866009 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2862146 2862253 2862398 "TANEXP" 2862651 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2855647 2862003 2862096 "TABLE" 2862101 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2855059 2855158 2855296 "TABLEAU" 2855544 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2849667 2850887 2852135 "TABLBUMP" 2853845 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2848889 2849036 2849217 "SYSTEM" 2849508 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2845348 2846047 2846830 "SYSSOLP" 2848140 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2844382 2844860 2844979 "SYSNNI" 2845165 NIL SYSNNI (NIL NIL) -8 NIL NIL 2845250) (-1176 2843679 2844111 2844190 "SYSINT" 2844250 NIL SYSINT (NIL NIL) -8 NIL NIL 2844295) (-1175 2840038 2840957 2841667 "SYNTAX" 2842991 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2837196 2837798 2838430 "SYMTAB" 2839428 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2832445 2833347 2834330 "SYMS" 2836235 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2829707 2831903 2832133 "SYMPOLY" 2832250 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2829224 2829299 2829422 "SYMFUNC" 2829619 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2825270 2826536 2827349 "SYMBOL" 2828433 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2818809 2820498 2822218 "SWITCH" 2823572 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2812070 2817630 2817933 "SUTS" 2818564 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2804163 2811317 2811590 "SUPXS" 2811855 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2795678 2803781 2803907 "SUP" 2804072 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2794837 2794964 2795181 "SUPFRACF" 2795546 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2794458 2794517 2794630 "SUP2" 2794772 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2792871 2793145 2793508 "SUMRF" 2794157 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2792185 2792251 2792450 "SUMFS" 2792792 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2776179 2791362 2791613 "SULS" 2791992 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2775808 2776001 2776071 "SUCHTAST" 2776131 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2775130 2775333 2775473 "SUCH" 2775716 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2769024 2770036 2770995 "SUBSPACE" 2774218 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2768454 2768544 2768708 "SUBRESP" 2768912 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2761819 2763119 2764430 "STTF" 2767190 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2755992 2757112 2758259 "STTFNC" 2760719 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2747303 2749174 2750968 "STTAYLOR" 2754233 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2740547 2747167 2747250 "STRTBL" 2747255 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2735938 2740502 2740533 "STRING" 2740538 T STRING (NIL) -8 NIL NIL NIL) (-1151 2730826 2735311 2735341 "STRICAT" 2735400 T STRICAT (NIL) -9 NIL 2735462 NIL) (-1150 2723629 2728445 2729056 "STREAM" 2730250 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2723139 2723216 2723360 "STREAM3" 2723546 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2722121 2722304 2722539 "STREAM2" 2722952 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2721809 2721861 2721954 "STREAM1" 2722063 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2720825 2721006 2721237 "STINPROD" 2721625 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2720403 2720587 2720617 "STEP" 2720697 T STEP (NIL) -9 NIL 2720775 NIL) (-1144 2713946 2720302 2720379 "STBL" 2720384 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2709120 2713167 2713210 "STAGG" 2713363 NIL STAGG (NIL T) -9 NIL 2713452 NIL) (-1142 2706822 2707424 2708296 "STAGG-" 2708301 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2705017 2706592 2706684 "STACK" 2706765 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2697740 2703158 2703614 "SREGSET" 2704647 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2690165 2691534 2693047 "SRDCMPK" 2696346 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2683132 2687605 2687635 "SRAGG" 2688938 T SRAGG (NIL) -9 NIL 2689546 NIL) (-1137 2682149 2682404 2682783 "SRAGG-" 2682788 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2676636 2681096 2681517 "SQMATRIX" 2681775 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2670383 2673354 2674081 "SPLTREE" 2675981 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2666373 2667039 2667685 "SPLNODE" 2669809 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2665420 2665653 2665683 "SPFCAT" 2666127 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2664157 2664367 2664631 "SPECOUT" 2665178 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2655809 2657553 2657583 "SPADXPT" 2661975 T SPADXPT (NIL) -9 NIL 2664009 NIL) (-1130 2655570 2655610 2655679 "SPADPRSR" 2655762 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2653752 2655525 2655556 "SPADAST" 2655561 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2645723 2647470 2647513 "SPACEC" 2651886 NIL SPACEC (NIL T) -9 NIL 2653702 NIL) (-1127 2643880 2645655 2645704 "SPACE3" 2645709 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2642632 2642803 2643094 "SORTPAK" 2643685 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2640682 2640985 2641404 "SOLVETRA" 2642296 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2639693 2639915 2640189 "SOLVESER" 2640455 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2634904 2635794 2636796 "SOLVERAD" 2638745 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2630719 2631328 2632057 "SOLVEFOR" 2634271 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2625016 2630068 2630165 "SNTSCAT" 2630170 NIL SNTSCAT (NIL T T T T) -9 NIL 2630240 NIL) (-1120 2619149 2623339 2623730 "SMTS" 2624706 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2613589 2619037 2619114 "SMP" 2619119 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2611748 2612049 2612447 "SMITH" 2613286 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2604635 2608799 2608902 "SMATCAT" 2610253 NIL SMATCAT (NIL NIL T T T) -9 NIL 2610803 NIL) (-1116 2601575 2602398 2603576 "SMATCAT-" 2603581 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2599288 2600811 2600854 "SKAGG" 2601115 NIL SKAGG (NIL T) -9 NIL 2601250 NIL) (-1114 2595623 2598704 2598899 "SINT" 2599086 T SINT (NIL) -8 NIL NIL 2599259) (-1113 2595395 2595433 2595499 "SIMPAN" 2595579 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2594701 2594930 2595070 "SIG" 2595277 T SIG (NIL) -8 NIL NIL NIL) (-1111 2593539 2593760 2594035 "SIGNRF" 2594460 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2592344 2592495 2592786 "SIGNEF" 2593368 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2591677 2591927 2592051 "SIGAST" 2592242 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2589367 2589821 2590327 "SHP" 2591218 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2583267 2589268 2589344 "SHDP" 2589349 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2582866 2583032 2583062 "SGROUP" 2583155 T SGROUP (NIL) -9 NIL 2583217 NIL) (-1105 2582724 2582750 2582823 "SGROUP-" 2582828 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2579559 2580257 2580980 "SGCF" 2582023 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2573954 2579006 2579103 "SFRTCAT" 2579108 NIL SFRTCAT (NIL T T T T) -9 NIL 2579147 NIL) (-1102 2567375 2568393 2569529 "SFRGCD" 2572937 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2560502 2561574 2562760 "SFQCMPK" 2566308 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2560124 2560213 2560323 "SFORT" 2560443 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2559269 2559964 2560085 "SEXOF" 2560090 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2558403 2559150 2559218 "SEX" 2559223 T SEX (NIL) -8 NIL NIL NIL) (-1097 2553942 2554631 2554726 "SEXCAT" 2557663 NIL SEXCAT (NIL T T T T T) -9 NIL 2558241 NIL) (-1096 2551122 2553876 2553924 "SET" 2553929 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2549373 2549835 2550140 "SETMN" 2550863 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2548979 2549105 2549135 "SETCAT" 2549252 T SETCAT (NIL) -9 NIL 2549337 NIL) (-1093 2548759 2548811 2548910 "SETCAT-" 2548915 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2545146 2547220 2547263 "SETAGG" 2548133 NIL SETAGG (NIL T) -9 NIL 2548473 NIL) (-1091 2544604 2544720 2544957 "SETAGG-" 2544962 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2544074 2544300 2544401 "SEQAST" 2544525 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2543273 2543567 2543628 "SEGXCAT" 2543914 NIL SEGXCAT (NIL T T) -9 NIL 2544034 NIL) (-1088 2542327 2542939 2543121 "SEG" 2543126 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2541306 2541520 2541563 "SEGCAT" 2542085 NIL SEGCAT (NIL T) -9 NIL 2542306 NIL) (-1086 2540355 2540685 2540885 "SEGBIND" 2541141 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2539976 2540035 2540148 "SEGBIND2" 2540290 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2539576 2539777 2539854 "SEGAST" 2539921 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2538795 2538921 2539125 "SEG2" 2539420 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2538232 2538730 2538777 "SDVAR" 2538782 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2530514 2538002 2538132 "SDPOL" 2538137 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2529107 2529373 2529692 "SCPKG" 2530229 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2528267 2528440 2528633 "SCOPE" 2528936 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2527487 2527621 2527800 "SCACHE" 2528122 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2527159 2527319 2527349 "SASTCAT" 2527354 T SASTCAT (NIL) -9 NIL 2527367 NIL) (-1076 2526673 2526994 2527070 "SAOS" 2527105 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2526238 2526273 2526446 "SAERFFC" 2526632 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2520204 2526135 2526215 "SAE" 2526220 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2519797 2519832 2519991 "SAEFACT" 2520163 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2518118 2518432 2518833 "RURPK" 2519463 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2516754 2517033 2517345 "RULESET" 2517952 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2513941 2514444 2514909 "RULE" 2516435 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2513580 2513735 2513818 "RULECOLD" 2513893 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2513078 2513297 2513391 "RSTRCAST" 2513508 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1067 2507926 2508721 2509641 "RSETGCD" 2512277 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1066 2497183 2502235 2502332 "RSETCAT" 2506451 NIL RSETCAT (NIL T T T T) -9 NIL 2507548 NIL) (-1065 2495110 2495649 2496473 "RSETCAT-" 2496478 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1064 2487495 2488872 2490392 "RSDCMPK" 2493709 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1063 2485500 2485941 2486015 "RRCC" 2487101 NIL RRCC (NIL T T) -9 NIL 2487445 NIL) (-1062 2484851 2485025 2485304 "RRCC-" 2485309 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1061 2484321 2484547 2484648 "RPTAST" 2484772 T RPTAST (NIL) -8 NIL NIL NIL) (-1060 2458319 2467914 2467981 "RPOLCAT" 2478645 NIL RPOLCAT (NIL T T T) -9 NIL 2481804 NIL) (-1059 2449817 2452157 2455279 "RPOLCAT-" 2455284 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1058 2440864 2448028 2448510 "ROUTINE" 2449357 T ROUTINE (NIL) -8 NIL NIL NIL) (-1057 2437689 2440490 2440630 "ROMAN" 2440746 T ROMAN (NIL) -8 NIL NIL NIL) (-1056 2435960 2436549 2436809 "ROIRC" 2437494 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1055 2432345 2434596 2434626 "RNS" 2434930 T RNS (NIL) -9 NIL 2435203 NIL) (-1054 2430854 2431237 2431771 "RNS-" 2431846 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1053 2430303 2430685 2430715 "RNG" 2430720 T RNG (NIL) -9 NIL 2430741 NIL) (-1052 2429695 2430057 2430100 "RMODULE" 2430162 NIL RMODULE (NIL T) -9 NIL 2430204 NIL) (-1051 2428531 2428625 2428961 "RMCAT2" 2429596 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1050 2425408 2427877 2428174 "RMATRIX" 2428293 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1049 2418350 2420584 2420699 "RMATCAT" 2424058 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2425040 NIL) (-1048 2417725 2417872 2418179 "RMATCAT-" 2418184 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1047 2417292 2417367 2417495 "RINTERP" 2417644 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1046 2416411 2416939 2416969 "RING" 2417025 T RING (NIL) -9 NIL 2417117 NIL) (-1045 2416203 2416247 2416344 "RING-" 2416349 NIL RING- (NIL T) -8 NIL NIL NIL) (-1044 2415044 2415281 2415539 "RIDIST" 2415967 T RIDIST (NIL) -7 NIL NIL NIL) (-1043 2406360 2414512 2414718 "RGCHAIN" 2414892 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1042 2405736 2406116 2406157 "RGBCSPC" 2406215 NIL RGBCSPC (NIL T) -9 NIL 2406267 NIL) (-1041 2404920 2405275 2405316 "RGBCMDL" 2405548 NIL RGBCMDL (NIL T) -9 NIL 2405662 NIL) (-1040 2401914 2402528 2403198 "RF" 2404284 NIL RF (NIL T) -7 NIL NIL NIL) (-1039 2401560 2401623 2401726 "RFFACTOR" 2401845 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1038 2401285 2401320 2401417 "RFFACT" 2401519 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1037 2399402 2399766 2400148 "RFDIST" 2400925 T RFDIST (NIL) -7 NIL NIL NIL) (-1036 2398855 2398947 2399110 "RETSOL" 2399304 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1035 2398491 2398571 2398614 "RETRACT" 2398747 NIL RETRACT (NIL T) -9 NIL 2398834 NIL) (-1034 2398340 2398365 2398452 "RETRACT-" 2398457 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1033 2397969 2398162 2398232 "RETAST" 2398292 T RETAST (NIL) -8 NIL NIL NIL) (-1032 2390823 2397622 2397749 "RESULT" 2397864 T RESULT (NIL) -8 NIL NIL NIL) (-1031 2389441 2390092 2390291 "RESRING" 2390726 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1030 2389077 2389126 2389224 "RESLATC" 2389378 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1029 2388782 2388817 2388924 "REPSQ" 2389036 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1028 2386204 2386784 2387386 "REP" 2388202 T REP (NIL) -7 NIL NIL NIL) (-1027 2385901 2385936 2386047 "REPDB" 2386163 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1026 2379801 2381190 2382413 "REP2" 2384713 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1025 2376178 2376859 2377667 "REP1" 2379028 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1024 2368901 2374319 2374775 "REGSET" 2375808 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1023 2367714 2368049 2368299 "REF" 2368686 NIL REF (NIL T) -8 NIL NIL NIL) (-1022 2367091 2367194 2367361 "REDORDER" 2367598 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1021 2363086 2366304 2366531 "RECLOS" 2366919 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1020 2362138 2362319 2362534 "REALSOLV" 2362893 T REALSOLV (NIL) -7 NIL NIL NIL) (-1019 2361984 2362025 2362055 "REAL" 2362060 T REAL (NIL) -9 NIL 2362095 NIL) (-1018 2358467 2359269 2360153 "REAL0Q" 2361149 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1017 2354068 2355056 2356117 "REAL0" 2357448 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1016 2353566 2353785 2353879 "RDUCEAST" 2353996 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1015 2352971 2353043 2353250 "RDIV" 2353488 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1014 2352039 2352213 2352426 "RDIST" 2352793 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1013 2350636 2350923 2351295 "RDETRS" 2351747 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1012 2348448 2348902 2349440 "RDETR" 2350178 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1011 2347059 2347337 2347741 "RDEEFS" 2348164 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1010 2345554 2345860 2346292 "RDEEF" 2346747 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1009 2339807 2342690 2342720 "RCFIELD" 2344015 T RCFIELD (NIL) -9 NIL 2344745 NIL) (-1008 2337871 2338375 2339071 "RCFIELD-" 2339146 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1007 2334187 2335972 2336015 "RCAGG" 2337099 NIL RCAGG (NIL T) -9 NIL 2337564 NIL) (-1006 2333815 2333909 2334072 "RCAGG-" 2334077 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1005 2333150 2333262 2333427 "RATRET" 2333699 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1004 2332703 2332770 2332891 "RATFACT" 2333078 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1003 2332011 2332131 2332283 "RANDSRC" 2332573 T RANDSRC (NIL) -7 NIL NIL NIL) (-1002 2331745 2331789 2331862 "RADUTIL" 2331960 T RADUTIL (NIL) -7 NIL NIL NIL) (-1001 2324888 2330578 2330888 "RADIX" 2331469 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1000 2316534 2324730 2324860 "RADFF" 2324865 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-999 2316186 2316261 2316289 "RADCAT" 2316446 T RADCAT (NIL) -9 NIL NIL NIL) (-998 2315971 2316019 2316116 "RADCAT-" 2316121 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-997 2314122 2315746 2315835 "QUEUE" 2315915 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-996 2310690 2314059 2314104 "QUAT" 2314109 NIL QUAT (NIL T) -8 NIL NIL NIL) (-995 2310328 2310371 2310498 "QUATCT2" 2310641 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-994 2304067 2307377 2307417 "QUATCAT" 2308197 NIL QUATCAT (NIL T) -9 NIL 2308963 NIL) (-993 2300211 2301248 2302635 "QUATCAT-" 2302729 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-992 2297731 2299295 2299336 "QUAGG" 2299711 NIL QUAGG (NIL T) -9 NIL 2299886 NIL) (-991 2297363 2297556 2297624 "QQUTAST" 2297683 T QQUTAST (NIL) -8 NIL NIL NIL) (-990 2296288 2296761 2296933 "QFORM" 2297235 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-989 2287492 2292705 2292745 "QFCAT" 2293403 NIL QFCAT (NIL T) -9 NIL 2294404 NIL) (-988 2283064 2284265 2285856 "QFCAT-" 2285950 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-987 2282702 2282745 2282872 "QFCAT2" 2283015 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-986 2282162 2282272 2282402 "QEQUAT" 2282592 T QEQUAT (NIL) -8 NIL NIL NIL) (-985 2275309 2276381 2277565 "QCMPACK" 2281095 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-984 2272885 2273306 2273734 "QALGSET" 2274964 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-983 2272130 2272304 2272536 "QALGSET2" 2272705 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-982 2270820 2271044 2271361 "PWFFINTB" 2271903 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-981 2269002 2269170 2269524 "PUSHVAR" 2270634 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-980 2264920 2265974 2266015 "PTRANFN" 2267899 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-979 2263322 2263613 2263935 "PTPACK" 2264631 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-978 2262954 2263011 2263120 "PTFUNC2" 2263259 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-977 2257481 2261826 2261867 "PTCAT" 2262163 NIL PTCAT (NIL T) -9 NIL 2262316 NIL) (-976 2257139 2257174 2257298 "PSQFR" 2257440 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-975 2255734 2256032 2256366 "PSEUDLIN" 2256837 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-974 2242497 2244868 2247192 "PSETPK" 2253494 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-973 2235541 2238255 2238351 "PSETCAT" 2241372 NIL PSETCAT (NIL T T T T) -9 NIL 2242186 NIL) (-972 2233377 2234011 2234832 "PSETCAT-" 2234837 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-971 2232726 2232891 2232919 "PSCURVE" 2233187 T PSCURVE (NIL) -9 NIL 2233354 NIL) (-970 2229074 2230564 2230629 "PSCAT" 2231473 NIL PSCAT (NIL T T T) -9 NIL 2231713 NIL) (-969 2228137 2228353 2228753 "PSCAT-" 2228758 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-968 2226869 2227502 2227707 "PRTITION" 2227952 T PRTITION (NIL) -8 NIL NIL NIL) (-967 2226371 2226590 2226682 "PRTDAST" 2226797 T PRTDAST (NIL) -8 NIL NIL NIL) (-966 2215461 2217675 2219863 "PRS" 2224233 NIL PRS (NIL T T) -7 NIL NIL NIL) (-965 2213319 2214811 2214851 "PRQAGG" 2215034 NIL PRQAGG (NIL T) -9 NIL 2215136 NIL) (-964 2212705 2212934 2212962 "PROPLOG" 2213147 T PROPLOG (NIL) -9 NIL 2213269 NIL) (-963 2209875 2210519 2210983 "PROPFRML" 2212273 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-962 2209335 2209445 2209575 "PROPERTY" 2209765 T PROPERTY (NIL) -8 NIL NIL NIL) (-961 2203420 2207501 2208321 "PRODUCT" 2208561 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-960 2200725 2202878 2203112 "PR" 2203231 NIL PR (NIL T T) -8 NIL NIL NIL) (-959 2200521 2200553 2200612 "PRINT" 2200686 T PRINT (NIL) -7 NIL NIL NIL) (-958 2199861 2199978 2200130 "PRIMES" 2200401 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-957 2197926 2198327 2198793 "PRIMELT" 2199440 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-956 2197655 2197704 2197732 "PRIMCAT" 2197856 T PRIMCAT (NIL) -9 NIL NIL NIL) (-955 2193816 2197593 2197638 "PRIMARR" 2197643 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-954 2192823 2193001 2193229 "PRIMARR2" 2193634 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-953 2192466 2192522 2192633 "PREASSOC" 2192761 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-952 2191941 2192074 2192102 "PPCURVE" 2192307 T PPCURVE (NIL) -9 NIL 2192443 NIL) (-951 2191563 2191736 2191819 "PORTNUM" 2191878 T PORTNUM (NIL) -8 NIL NIL NIL) (-950 2188922 2189321 2189913 "POLYROOT" 2191144 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-949 2182859 2188526 2188686 "POLY" 2188795 NIL POLY (NIL T) -8 NIL NIL NIL) (-948 2182242 2182300 2182534 "POLYLIFT" 2182795 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-947 2178517 2178966 2179595 "POLYCATQ" 2181787 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-946 2165326 2170692 2170757 "POLYCAT" 2174271 NIL POLYCAT (NIL T T T) -9 NIL 2176199 NIL) (-945 2158775 2160637 2163021 "POLYCAT-" 2163026 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-944 2158362 2158430 2158550 "POLY2UP" 2158701 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-943 2157994 2158051 2158160 "POLY2" 2158299 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-942 2156679 2156918 2157194 "POLUTIL" 2157768 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-941 2155034 2155311 2155642 "POLTOPOL" 2156401 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-940 2150551 2154970 2155016 "POINT" 2155021 NIL POINT (NIL T) -8 NIL NIL NIL) (-939 2148738 2149095 2149470 "PNTHEORY" 2150196 T PNTHEORY (NIL) -7 NIL NIL NIL) (-938 2147157 2147454 2147866 "PMTOOLS" 2148436 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-937 2146750 2146828 2146945 "PMSYM" 2147073 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-936 2146260 2146329 2146503 "PMQFCAT" 2146675 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-935 2145615 2145725 2145881 "PMPRED" 2146137 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-934 2145011 2145097 2145258 "PMPREDFS" 2145516 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-933 2143654 2143862 2144247 "PMPLCAT" 2144773 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-932 2143186 2143265 2143417 "PMLSAGG" 2143569 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-931 2142661 2142737 2142918 "PMKERNEL" 2143104 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-930 2142278 2142353 2142466 "PMINS" 2142580 NIL PMINS (NIL T) -7 NIL NIL NIL) (-929 2141706 2141775 2141991 "PMFS" 2142203 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-928 2140934 2141052 2141257 "PMDOWN" 2141583 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-927 2140097 2140256 2140438 "PMASS" 2140772 T PMASS (NIL) -7 NIL NIL NIL) (-926 2139371 2139482 2139645 "PMASSFS" 2139983 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-925 2139026 2139094 2139188 "PLOTTOOL" 2139297 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-924 2133633 2134837 2135985 "PLOT" 2137898 T PLOT (NIL) -8 NIL NIL NIL) (-923 2129437 2130481 2131402 "PLOT3D" 2132732 T PLOT3D (NIL) -8 NIL NIL NIL) (-922 2128349 2128526 2128761 "PLOT1" 2129241 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-921 2103738 2108415 2113266 "PLEQN" 2123615 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-920 2103056 2103178 2103358 "PINTERP" 2103603 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-919 2102749 2102796 2102899 "PINTERPA" 2103003 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-918 2101997 2102518 2102605 "PI" 2102645 T PI (NIL) -8 NIL NIL 2102712) (-917 2100386 2101335 2101363 "PID" 2101545 T PID (NIL) -9 NIL 2101679 NIL) (-916 2100111 2100148 2100236 "PICOERCE" 2100343 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-915 2099431 2099570 2099746 "PGROEB" 2099967 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-914 2095018 2095832 2096737 "PGE" 2098546 T PGE (NIL) -7 NIL NIL NIL) (-913 2093141 2093388 2093754 "PGCD" 2094735 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-912 2092479 2092582 2092743 "PFRPAC" 2093025 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-911 2089147 2091027 2091380 "PFR" 2092158 NIL PFR (NIL T) -8 NIL NIL NIL) (-910 2087536 2087780 2088105 "PFOTOOLS" 2088894 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-909 2086069 2086308 2086659 "PFOQ" 2087293 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-908 2084542 2084754 2085117 "PFO" 2085853 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-907 2081122 2084431 2084500 "PF" 2084505 NIL PF (NIL NIL) -8 NIL NIL NIL) (-906 2078548 2079793 2079821 "PFECAT" 2080406 T PFECAT (NIL) -9 NIL 2080790 NIL) (-905 2077993 2078147 2078361 "PFECAT-" 2078366 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-904 2076596 2076848 2077149 "PFBRU" 2077742 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-903 2074461 2074814 2075246 "PFBR" 2076247 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-902 2070370 2071837 2072513 "PERM" 2073818 NIL PERM (NIL T) -8 NIL NIL NIL) (-901 2065631 2066577 2067447 "PERMGRP" 2069533 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-900 2063763 2064694 2064735 "PERMCAT" 2065181 NIL PERMCAT (NIL T) -9 NIL 2065486 NIL) (-899 2063416 2063457 2063581 "PERMAN" 2063716 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-898 2060952 2063081 2063203 "PENDTREE" 2063327 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-897 2059037 2059779 2059820 "PDRING" 2060477 NIL PDRING (NIL T) -9 NIL 2060763 NIL) (-896 2058140 2058358 2058720 "PDRING-" 2058725 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-895 2055382 2056133 2056801 "PDEPROB" 2057492 T PDEPROB (NIL) -8 NIL NIL NIL) (-894 2052927 2053431 2053986 "PDEPACK" 2054847 T PDEPACK (NIL) -7 NIL NIL NIL) (-893 2051839 2052029 2052280 "PDECOMP" 2052726 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-892 2049444 2050261 2050289 "PDECAT" 2051076 T PDECAT (NIL) -9 NIL 2051789 NIL) (-891 2049195 2049228 2049318 "PCOMP" 2049405 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-890 2047400 2047996 2048293 "PBWLB" 2048924 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-889 2039900 2041473 2042811 "PATTERN" 2046083 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-888 2039532 2039589 2039698 "PATTERN2" 2039837 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-887 2037289 2037677 2038134 "PATTERN1" 2039121 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-886 2034684 2035238 2035719 "PATRES" 2036854 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-885 2034248 2034315 2034447 "PATRES2" 2034611 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-884 2032131 2032536 2032943 "PATMATCH" 2033915 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-883 2031667 2031850 2031891 "PATMAB" 2031998 NIL PATMAB (NIL T) -9 NIL 2032081 NIL) (-882 2030212 2030521 2030779 "PATLRES" 2031472 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-881 2029758 2029881 2029922 "PATAB" 2029927 NIL PATAB (NIL T) -9 NIL 2030099 NIL) (-880 2027239 2027771 2028344 "PARTPERM" 2029205 T PARTPERM (NIL) -7 NIL NIL NIL) (-879 2026860 2026923 2027025 "PARSURF" 2027170 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-878 2026492 2026549 2026658 "PARSU2" 2026797 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-877 2026256 2026296 2026363 "PARSER" 2026445 T PARSER (NIL) -7 NIL NIL NIL) (-876 2025877 2025940 2026042 "PARSCURV" 2026187 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-875 2025509 2025566 2025675 "PARSC2" 2025814 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-874 2025148 2025206 2025303 "PARPCURV" 2025445 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-873 2024780 2024837 2024946 "PARPC2" 2025085 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-872 2024300 2024386 2024505 "PAN2EXPR" 2024681 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-871 2023104 2023421 2023649 "PALETTE" 2024092 T PALETTE (NIL) -8 NIL NIL NIL) (-870 2021572 2022109 2022469 "PAIR" 2022790 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-869 2015469 2020831 2021025 "PADICRC" 2021427 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-868 2008725 2014815 2014999 "PADICRAT" 2015317 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-867 2007067 2008662 2008707 "PADIC" 2008712 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-866 2004269 2005807 2005847 "PADICCT" 2006428 NIL PADICCT (NIL NIL) -9 NIL 2006710 NIL) (-865 2003226 2003426 2003694 "PADEPAC" 2004056 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-864 2002438 2002571 2002777 "PADE" 2003088 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-863 2000852 2001646 2001926 "OWP" 2002242 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-862 2000372 2000558 2000655 "OVERSET" 2000775 T OVERSET (NIL) -8 NIL NIL NIL) (-861 1999445 1999977 2000149 "OVAR" 2000240 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-860 1998709 1998830 1998991 "OUT" 1999304 T OUT (NIL) -7 NIL NIL NIL) (-859 1987607 1989818 1992018 "OUTFORM" 1996529 T OUTFORM (NIL) -8 NIL NIL NIL) (-858 1986943 1987204 1987331 "OUTBFILE" 1987500 T OUTBFILE (NIL) -8 NIL NIL NIL) (-857 1986250 1986415 1986443 "OUTBCON" 1986761 T OUTBCON (NIL) -9 NIL 1986927 NIL) (-856 1985851 1985963 1986120 "OUTBCON-" 1986125 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-855 1985258 1985580 1985669 "OSI" 1985782 T OSI (NIL) -8 NIL NIL NIL) (-854 1984814 1985126 1985154 "OSGROUP" 1985159 T OSGROUP (NIL) -9 NIL 1985181 NIL) (-853 1983559 1983786 1984071 "ORTHPOL" 1984561 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-852 1981137 1983394 1983515 "OREUP" 1983520 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-851 1978567 1980828 1980955 "ORESUP" 1981079 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-850 1976095 1976595 1977156 "OREPCTO" 1978056 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-849 1969911 1972086 1972127 "OREPCAT" 1974475 NIL OREPCAT (NIL T) -9 NIL 1975579 NIL) (-848 1967058 1967840 1968898 "OREPCAT-" 1968903 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-847 1966235 1966507 1966535 "ORDSET" 1966844 T ORDSET (NIL) -9 NIL 1967008 NIL) (-846 1965754 1965876 1966069 "ORDSET-" 1966074 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-845 1964380 1965145 1965173 "ORDRING" 1965375 T ORDRING (NIL) -9 NIL 1965500 NIL) (-844 1964025 1964119 1964263 "ORDRING-" 1964268 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-843 1963431 1963868 1963896 "ORDMON" 1963901 T ORDMON (NIL) -9 NIL 1963922 NIL) (-842 1962593 1962740 1962935 "ORDFUNS" 1963280 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-841 1961957 1962350 1962378 "ORDFIN" 1962443 T ORDFIN (NIL) -9 NIL 1962517 NIL) (-840 1958543 1960543 1960952 "ORDCOMP" 1961581 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-839 1957809 1957936 1958122 "ORDCOMP2" 1958403 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-838 1954417 1955300 1956114 "OPTPROB" 1957015 T OPTPROB (NIL) -8 NIL NIL NIL) (-837 1951219 1951858 1952562 "OPTPACK" 1953733 T OPTPACK (NIL) -7 NIL NIL NIL) (-836 1948932 1949672 1949700 "OPTCAT" 1950519 T OPTCAT (NIL) -9 NIL 1951169 NIL) (-835 1948375 1948609 1948714 "OPSIG" 1948847 T OPSIG (NIL) -8 NIL NIL NIL) (-834 1948143 1948182 1948248 "OPQUERY" 1948329 T OPQUERY (NIL) -7 NIL NIL NIL) (-833 1945301 1946454 1946958 "OP" 1947672 NIL OP (NIL T) -8 NIL NIL NIL) (-832 1944836 1945007 1945048 "OPERCAT" 1945183 NIL OPERCAT (NIL T) -9 NIL 1945251 NIL) (-831 1944682 1944709 1944795 "OPERCAT-" 1944800 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-830 1941521 1943479 1943848 "ONECOMP" 1944346 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-829 1940826 1940941 1941115 "ONECOMP2" 1941393 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-828 1940245 1940351 1940481 "OMSERVER" 1940716 T OMSERVER (NIL) -7 NIL NIL NIL) (-827 1937133 1939685 1939725 "OMSAGG" 1939786 NIL OMSAGG (NIL T) -9 NIL 1939850 NIL) (-826 1935756 1936019 1936301 "OMPKG" 1936871 T OMPKG (NIL) -7 NIL NIL NIL) (-825 1935186 1935289 1935317 "OM" 1935616 T OM (NIL) -9 NIL NIL NIL) (-824 1933760 1934735 1934904 "OMLO" 1935067 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-823 1932685 1932832 1933059 "OMEXPR" 1933586 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-822 1932003 1932231 1932367 "OMERR" 1932569 T OMERR (NIL) -8 NIL NIL NIL) (-821 1931181 1931424 1931584 "OMERRK" 1931863 T OMERRK (NIL) -8 NIL NIL NIL) (-820 1930659 1930858 1930966 "OMENC" 1931093 T OMENC (NIL) -8 NIL NIL NIL) (-819 1924554 1925739 1926910 "OMDEV" 1929508 T OMDEV (NIL) -8 NIL NIL NIL) (-818 1923623 1923794 1923988 "OMCONN" 1924380 T OMCONN (NIL) -8 NIL NIL NIL) (-817 1922236 1923186 1923214 "OINTDOM" 1923219 T OINTDOM (NIL) -9 NIL 1923240 NIL) (-816 1918042 1919226 1919942 "OFMONOID" 1921552 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-815 1917480 1917979 1918024 "ODVAR" 1918029 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-814 1914930 1917225 1917380 "ODR" 1917385 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-813 1907266 1914706 1914832 "ODPOL" 1914837 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-812 1901136 1907138 1907243 "ODP" 1907248 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-811 1899902 1900117 1900392 "ODETOOLS" 1900910 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-810 1896869 1897527 1898243 "ODESYS" 1899235 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-809 1891751 1892659 1893684 "ODERTRIC" 1895944 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-808 1891177 1891259 1891453 "ODERED" 1891663 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-807 1888065 1888613 1889290 "ODERAT" 1890600 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-806 1885022 1885489 1886086 "ODEPRRIC" 1887594 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-805 1882992 1883561 1884047 "ODEPROB" 1884556 T ODEPROB (NIL) -8 NIL NIL NIL) (-804 1879512 1879997 1880644 "ODEPRIM" 1882471 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-803 1878761 1878863 1879123 "ODEPAL" 1879404 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-802 1874923 1875714 1876578 "ODEPACK" 1877917 T ODEPACK (NIL) -7 NIL NIL NIL) (-801 1873956 1874063 1874292 "ODEINT" 1874812 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-800 1868057 1869482 1870929 "ODEIFTBL" 1872529 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-799 1863392 1864178 1865137 "ODEEF" 1867216 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-798 1862727 1862816 1863046 "ODECONST" 1863297 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-797 1860878 1861513 1861541 "ODECAT" 1862146 T ODECAT (NIL) -9 NIL 1862677 NIL) (-796 1857777 1860590 1860709 "OCT" 1860791 NIL OCT (NIL T) -8 NIL NIL NIL) (-795 1857415 1857458 1857585 "OCTCT2" 1857728 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-794 1852181 1854589 1854629 "OC" 1855726 NIL OC (NIL T) -9 NIL 1856584 NIL) (-793 1849408 1850156 1851146 "OC-" 1851240 NIL OC- (NIL T T) -8 NIL NIL NIL) (-792 1848786 1849228 1849256 "OCAMON" 1849261 T OCAMON (NIL) -9 NIL 1849282 NIL) (-791 1848343 1848658 1848686 "OASGP" 1848691 T OASGP (NIL) -9 NIL 1848711 NIL) (-790 1847630 1848093 1848121 "OAMONS" 1848161 T OAMONS (NIL) -9 NIL 1848204 NIL) (-789 1847070 1847477 1847505 "OAMON" 1847510 T OAMON (NIL) -9 NIL 1847530 NIL) (-788 1846374 1846866 1846894 "OAGROUP" 1846899 T OAGROUP (NIL) -9 NIL 1846919 NIL) (-787 1846064 1846114 1846202 "NUMTUBE" 1846318 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-786 1839637 1841155 1842691 "NUMQUAD" 1844548 T NUMQUAD (NIL) -7 NIL NIL NIL) (-785 1835393 1836381 1837406 "NUMODE" 1838632 T NUMODE (NIL) -7 NIL NIL NIL) (-784 1832774 1833628 1833656 "NUMINT" 1834579 T NUMINT (NIL) -9 NIL 1835343 NIL) (-783 1831722 1831919 1832137 "NUMFMT" 1832576 T NUMFMT (NIL) -7 NIL NIL NIL) (-782 1818081 1821026 1823558 "NUMERIC" 1829229 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-781 1812478 1817530 1817625 "NTSCAT" 1817630 NIL NTSCAT (NIL T T T T) -9 NIL 1817669 NIL) (-780 1811672 1811837 1812030 "NTPOLFN" 1812317 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-779 1799504 1808497 1809309 "NSUP" 1810893 NIL NSUP (NIL T) -8 NIL NIL NIL) (-778 1799136 1799193 1799302 "NSUP2" 1799441 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-777 1789119 1798910 1799043 "NSMP" 1799048 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-776 1787551 1787852 1788209 "NREP" 1788807 NIL NREP (NIL T) -7 NIL NIL NIL) (-775 1786142 1786394 1786752 "NPCOEF" 1787294 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-774 1785208 1785323 1785539 "NORMRETR" 1786023 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-773 1783249 1783539 1783948 "NORMPK" 1784916 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-772 1782934 1782962 1783086 "NORMMA" 1783215 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-771 1782761 1782891 1782920 "NONE" 1782925 T NONE (NIL) -8 NIL NIL NIL) (-770 1782550 1782579 1782648 "NONE1" 1782725 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-769 1782033 1782095 1782281 "NODE1" 1782482 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-768 1780303 1781127 1781382 "NNI" 1781729 T NNI (NIL) -8 NIL NIL 1781964) (-767 1778723 1779036 1779400 "NLINSOL" 1779971 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-766 1774991 1775959 1776858 "NIPROB" 1777844 T NIPROB (NIL) -8 NIL NIL NIL) (-765 1773748 1773982 1774284 "NFINTBAS" 1774753 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-764 1772922 1773398 1773439 "NETCLT" 1773611 NIL NETCLT (NIL T) -9 NIL 1773693 NIL) (-763 1771630 1771861 1772142 "NCODIV" 1772690 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-762 1771392 1771429 1771504 "NCNTFRAC" 1771587 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-761 1769572 1769936 1770356 "NCEP" 1771017 NIL NCEP (NIL T) -7 NIL NIL NIL) (-760 1768469 1769216 1769244 "NASRING" 1769354 T NASRING (NIL) -9 NIL 1769434 NIL) (-759 1768264 1768308 1768402 "NASRING-" 1768407 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-758 1767417 1767916 1767944 "NARNG" 1768061 T NARNG (NIL) -9 NIL 1768152 NIL) (-757 1767109 1767176 1767310 "NARNG-" 1767315 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-756 1765988 1766195 1766430 "NAGSP" 1766894 T NAGSP (NIL) -7 NIL NIL NIL) (-755 1757260 1758944 1760617 "NAGS" 1764335 T NAGS (NIL) -7 NIL NIL NIL) (-754 1755808 1756116 1756447 "NAGF07" 1756949 T NAGF07 (NIL) -7 NIL NIL NIL) (-753 1750346 1751637 1752944 "NAGF04" 1754521 T NAGF04 (NIL) -7 NIL NIL NIL) (-752 1743314 1744928 1746561 "NAGF02" 1748733 T NAGF02 (NIL) -7 NIL NIL NIL) (-751 1738538 1739638 1740755 "NAGF01" 1742217 T NAGF01 (NIL) -7 NIL NIL NIL) (-750 1732166 1733732 1735317 "NAGE04" 1736973 T NAGE04 (NIL) -7 NIL NIL NIL) (-749 1723335 1725456 1727586 "NAGE02" 1730056 T NAGE02 (NIL) -7 NIL NIL NIL) (-748 1719288 1720235 1721199 "NAGE01" 1722391 T NAGE01 (NIL) -7 NIL NIL NIL) (-747 1717083 1717617 1718175 "NAGD03" 1718750 T NAGD03 (NIL) -7 NIL NIL NIL) (-746 1708833 1710761 1712715 "NAGD02" 1715149 T NAGD02 (NIL) -7 NIL NIL NIL) (-745 1702644 1704069 1705509 "NAGD01" 1707413 T NAGD01 (NIL) -7 NIL NIL NIL) (-744 1698853 1699675 1700512 "NAGC06" 1701827 T NAGC06 (NIL) -7 NIL NIL NIL) (-743 1697318 1697650 1698006 "NAGC05" 1698517 T NAGC05 (NIL) -7 NIL NIL NIL) (-742 1696694 1696813 1696957 "NAGC02" 1697194 T NAGC02 (NIL) -7 NIL NIL NIL) (-741 1695754 1696311 1696351 "NAALG" 1696430 NIL NAALG (NIL T) -9 NIL 1696491 NIL) (-740 1695589 1695618 1695708 "NAALG-" 1695713 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-739 1689539 1690647 1691834 "MULTSQFR" 1694485 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-738 1688858 1688933 1689117 "MULTFACT" 1689451 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-737 1681943 1685821 1685874 "MTSCAT" 1686944 NIL MTSCAT (NIL T T) -9 NIL 1687458 NIL) (-736 1681655 1681709 1681801 "MTHING" 1681883 NIL MTHING (NIL T) -7 NIL NIL NIL) (-735 1681447 1681480 1681540 "MSYSCMD" 1681615 T MSYSCMD (NIL) -7 NIL NIL NIL) (-734 1677556 1680202 1680522 "MSET" 1681160 NIL MSET (NIL T) -8 NIL NIL NIL) (-733 1674651 1677117 1677158 "MSETAGG" 1677163 NIL MSETAGG (NIL T) -9 NIL 1677197 NIL) (-732 1670519 1672030 1672775 "MRING" 1673951 NIL MRING (NIL T T) -8 NIL NIL NIL) (-731 1670085 1670152 1670283 "MRF2" 1670446 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-730 1669703 1669738 1669882 "MRATFAC" 1670044 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-729 1667315 1667610 1668041 "MPRFF" 1669408 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-728 1661367 1667169 1667266 "MPOLY" 1667271 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-727 1660857 1660892 1661100 "MPCPF" 1661326 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-726 1660371 1660414 1660598 "MPC3" 1660808 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-725 1659566 1659647 1659868 "MPC2" 1660286 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1657867 1658204 1658594 "MONOTOOL" 1659226 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-723 1657118 1657409 1657437 "MONOID" 1657656 T MONOID (NIL) -9 NIL 1657803 NIL) (-722 1656664 1656783 1656964 "MONOID-" 1656969 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-721 1647515 1653431 1653490 "MONOGEN" 1654164 NIL MONOGEN (NIL T T) -9 NIL 1654620 NIL) (-720 1644733 1645468 1646468 "MONOGEN-" 1646587 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-719 1643592 1644012 1644040 "MONADWU" 1644432 T MONADWU (NIL) -9 NIL 1644670 NIL) (-718 1642964 1643123 1643371 "MONADWU-" 1643376 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-717 1642349 1642567 1642595 "MONAD" 1642802 T MONAD (NIL) -9 NIL 1642914 NIL) (-716 1642034 1642112 1642244 "MONAD-" 1642249 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-715 1640350 1640947 1641226 "MOEBIUS" 1641787 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-714 1639742 1640120 1640160 "MODULE" 1640165 NIL MODULE (NIL T) -9 NIL 1640191 NIL) (-713 1639310 1639406 1639596 "MODULE-" 1639601 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-712 1637017 1637674 1638001 "MODRING" 1639134 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-711 1633988 1635122 1635643 "MODOP" 1636546 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-710 1632603 1633055 1633332 "MODMONOM" 1633851 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-709 1622400 1630894 1631308 "MODMON" 1632240 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-708 1619583 1621244 1621520 "MODFIELD" 1622275 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-707 1618587 1618864 1619054 "MMLFORM" 1619413 T MMLFORM (NIL) -8 NIL NIL NIL) (-706 1618113 1618156 1618335 "MMAP" 1618538 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-705 1616322 1617063 1617104 "MLO" 1617527 NIL MLO (NIL T) -9 NIL 1617769 NIL) (-704 1613688 1614204 1614806 "MLIFT" 1615803 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-703 1613079 1613163 1613317 "MKUCFUNC" 1613599 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-702 1612678 1612748 1612871 "MKRECORD" 1613002 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-701 1611725 1611887 1612115 "MKFUNC" 1612489 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-700 1611113 1611217 1611373 "MKFLCFN" 1611608 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-699 1610656 1611023 1611082 "MKCHSET" 1611087 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-698 1609933 1610035 1610220 "MKBCFUNC" 1610549 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1606667 1609487 1609623 "MINT" 1609817 T MINT (NIL) -8 NIL NIL NIL) (-696 1605479 1605722 1605999 "MHROWRED" 1606422 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1600886 1604014 1604419 "MFLOAT" 1605094 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1600243 1600319 1600490 "MFINFACT" 1600798 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1596558 1597406 1598290 "MESH" 1599379 T MESH (NIL) -7 NIL NIL NIL) (-692 1594948 1595260 1595613 "MDDFACT" 1596245 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1591790 1594107 1594148 "MDAGG" 1594403 NIL MDAGG (NIL T) -9 NIL 1594546 NIL) (-690 1581560 1591083 1591290 "MCMPLX" 1591603 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1580701 1580847 1581047 "MCDEN" 1581409 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1578591 1578861 1579241 "MCALCFN" 1580431 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1577516 1577756 1577989 "MAYBE" 1578397 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1575128 1575651 1576213 "MATSTOR" 1576987 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1571133 1574500 1574748 "MATRIX" 1574913 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1566897 1567606 1568342 "MATLIN" 1570490 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1557051 1560189 1560266 "MATCAT" 1565146 NIL MATCAT (NIL T T T) -9 NIL 1566563 NIL) (-682 1553407 1554428 1555784 "MATCAT-" 1555789 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1552001 1552154 1552487 "MATCAT2" 1553242 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1550113 1550437 1550821 "MAPPKG3" 1551676 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1549094 1549267 1549489 "MAPPKG2" 1549937 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1547593 1547877 1548204 "MAPPKG1" 1548800 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1546699 1546999 1547176 "MAPPAST" 1547436 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1546310 1546368 1546491 "MAPHACK3" 1546635 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1545902 1545963 1546077 "MAPHACK2" 1546242 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1545339 1545443 1545585 "MAPHACK1" 1545793 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1543445 1544039 1544343 "MAGMA" 1545067 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1542951 1543169 1543260 "MACROAST" 1543374 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1539417 1541190 1541651 "M3D" 1542523 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1533571 1537786 1537827 "LZSTAGG" 1538609 NIL LZSTAGG (NIL T) -9 NIL 1538904 NIL) (-669 1529528 1530702 1532159 "LZSTAGG-" 1532164 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1526642 1527419 1527906 "LWORD" 1529073 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1526245 1526446 1526521 "LSTAST" 1526587 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1519438 1526016 1526150 "LSQM" 1526155 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1518662 1518801 1519029 "LSPP" 1519293 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1516474 1516775 1517231 "LSMP" 1518351 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1513253 1513927 1514657 "LSMP1" 1515776 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1507178 1512420 1512461 "LSAGG" 1512523 NIL LSAGG (NIL T) -9 NIL 1512601 NIL) (-661 1503873 1504797 1506010 "LSAGG-" 1506015 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1501499 1503017 1503266 "LPOLY" 1503668 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1501081 1501166 1501289 "LPEFRAC" 1501408 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1499428 1500175 1500428 "LO" 1500913 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1499080 1499192 1499220 "LOGIC" 1499331 T LOGIC (NIL) -9 NIL 1499412 NIL) (-656 1498942 1498965 1499036 "LOGIC-" 1499041 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1498135 1498275 1498468 "LODOOPS" 1498798 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1495585 1498051 1498117 "LODO" 1498122 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1494123 1494358 1494711 "LODOF" 1495332 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1490471 1492876 1492917 "LODOCAT" 1493355 NIL LODOCAT (NIL T) -9 NIL 1493566 NIL) (-651 1490204 1490262 1490389 "LODOCAT-" 1490394 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1487551 1490045 1490163 "LODO2" 1490168 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1485013 1487488 1487533 "LODO1" 1487538 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1483873 1484038 1484350 "LODEEF" 1484836 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1479159 1482003 1482044 "LNAGG" 1482991 NIL LNAGG (NIL T) -9 NIL 1483435 NIL) (-646 1478306 1478520 1478862 "LNAGG-" 1478867 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1474469 1475231 1475870 "LMOPS" 1477721 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1473864 1474226 1474267 "LMODULE" 1474328 NIL LMODULE (NIL T) -9 NIL 1474370 NIL) (-643 1471110 1473509 1473632 "LMDICT" 1473774 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1470836 1471018 1471078 "LITERAL" 1471083 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1464067 1469782 1470080 "LIST" 1470571 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1463592 1463666 1463805 "LIST3" 1463987 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1462599 1462777 1463005 "LIST2" 1463410 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1460733 1461045 1461444 "LIST2MAP" 1462246 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1459455 1460099 1460140 "LINEXP" 1460395 NIL LINEXP (NIL T) -9 NIL 1460544 NIL) (-636 1458102 1458362 1458659 "LINDEP" 1459207 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1454869 1455588 1456365 "LIMITRF" 1457357 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1453144 1453440 1453856 "LIMITPS" 1454564 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1447599 1452655 1452883 "LIE" 1452965 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1446648 1447091 1447131 "LIECAT" 1447271 NIL LIECAT (NIL T) -9 NIL 1447422 NIL) (-631 1446489 1446516 1446604 "LIECAT-" 1446609 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1439101 1445938 1446103 "LIB" 1446344 T LIB (NIL) -8 NIL NIL NIL) (-629 1434736 1435619 1436554 "LGROBP" 1438218 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1432602 1432876 1433238 "LF" 1434457 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1431442 1432134 1432162 "LFCAT" 1432369 T LFCAT (NIL) -9 NIL 1432508 NIL) (-626 1428344 1428974 1429662 "LEXTRIPK" 1430806 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1425115 1425914 1426417 "LEXP" 1427924 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1424618 1424836 1424928 "LETAST" 1425043 T LETAST (NIL) -8 NIL NIL NIL) (-623 1423016 1423329 1423730 "LEADCDET" 1424300 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1422206 1422280 1422509 "LAZM3PK" 1422937 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1417150 1420283 1420821 "LAUPOL" 1421718 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1416715 1416759 1416927 "LAPLACE" 1417100 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1414681 1415816 1416067 "LA" 1416548 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1413754 1414312 1414353 "LALG" 1414415 NIL LALG (NIL T) -9 NIL 1414474 NIL) (-617 1413468 1413527 1413663 "LALG-" 1413668 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1413303 1413327 1413368 "KVTFROM" 1413430 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1412103 1412520 1412749 "KTVLOGIC" 1413094 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1411938 1411962 1412003 "KRCFROM" 1412065 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1410842 1411029 1411328 "KOVACIC" 1411738 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1410677 1410701 1410742 "KONVERT" 1410804 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1410512 1410536 1410577 "KOERCE" 1410639 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1408246 1409006 1409399 "KERNEL" 1410151 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1407748 1407829 1407959 "KERNEL2" 1408160 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1401599 1406287 1406341 "KDAGG" 1406718 NIL KDAGG (NIL T T) -9 NIL 1406924 NIL) (-607 1401128 1401252 1401457 "KDAGG-" 1401462 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1394303 1400789 1400944 "KAFILE" 1401006 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1388758 1393814 1394042 "JORDAN" 1394124 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1388164 1388407 1388528 "JOINAST" 1388657 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1388010 1388069 1388124 "JAVACODE" 1388129 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1384309 1386215 1386269 "IXAGG" 1387198 NIL IXAGG (NIL T T) -9 NIL 1387657 NIL) (-601 1383228 1383534 1383953 "IXAGG-" 1383958 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1378808 1383150 1383209 "IVECTOR" 1383214 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1377574 1377811 1378077 "ITUPLE" 1378575 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1376010 1376187 1376493 "ITRIGMNP" 1377396 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1374755 1374959 1375242 "ITFUN3" 1375786 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1374387 1374444 1374553 "ITFUN2" 1374692 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1372216 1373249 1373548 "ITAYLOR" 1374121 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1361188 1366353 1367516 "ISUPS" 1371086 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1360292 1360432 1360668 "ISUMP" 1361035 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1355556 1360093 1360172 "ISTRING" 1360245 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1355059 1355277 1355369 "ISAST" 1355484 T ISAST (NIL) -8 NIL NIL NIL) (-590 1354269 1354350 1354566 "IRURPK" 1354973 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1353205 1353406 1353646 "IRSN" 1354049 T IRSN (NIL) -7 NIL NIL NIL) (-588 1351234 1351589 1352025 "IRRF2F" 1352843 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1350981 1351019 1351095 "IRREDFFX" 1351190 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1349596 1349855 1350154 "IROOT" 1350714 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1346227 1347280 1347972 "IR" 1348936 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1343840 1344335 1344901 "IR2" 1345705 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1342912 1343025 1343246 "IR2F" 1343723 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1342703 1342737 1342797 "IPRNTPK" 1342872 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1339310 1342592 1342661 "IPF" 1342666 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1337664 1339235 1339292 "IPADIC" 1339297 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1337003 1337224 1337354 "IP4ADDR" 1337554 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1336503 1336707 1336817 "IOMODE" 1336913 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1335576 1336100 1336227 "IOBFILE" 1336396 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1335064 1335480 1335508 "IOBCON" 1335513 T IOBCON (NIL) -9 NIL 1335534 NIL) (-575 1334561 1334619 1334809 "INVLAPLA" 1335000 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1324209 1326563 1328949 "INTTR" 1332225 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1320553 1321295 1322159 "INTTOOLS" 1323394 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1320139 1320230 1320347 "INTSLPE" 1320456 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1318120 1320062 1320121 "INTRVL" 1320126 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1315722 1316234 1316809 "INTRF" 1317605 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1315133 1315230 1315372 "INTRET" 1315620 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1313130 1313519 1313989 "INTRAT" 1314741 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1310358 1310941 1311567 "INTPM" 1312615 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1307060 1307660 1308405 "INTPAF" 1309744 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1302239 1303201 1304252 "INTPACK" 1306029 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1299143 1301968 1302095 "INT" 1302132 T INT (NIL) -8 NIL NIL NIL) (-563 1298395 1298547 1298755 "INTHERTR" 1298985 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1297834 1297914 1298102 "INTHERAL" 1298309 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1295680 1296123 1296580 "INTHEORY" 1297397 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1286988 1288609 1290388 "INTG0" 1294032 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1267561 1272351 1277161 "INTFTBL" 1282198 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1266810 1266948 1267121 "INTFACT" 1267420 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1264195 1264641 1265205 "INTEF" 1266364 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1262654 1263367 1263395 "INTDOM" 1263696 T INTDOM (NIL) -9 NIL 1263903 NIL) (-555 1262023 1262197 1262439 "INTDOM-" 1262444 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1258510 1260407 1260461 "INTCAT" 1261260 NIL INTCAT (NIL T) -9 NIL 1261580 NIL) (-553 1257982 1258085 1258213 "INTBIT" 1258402 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1256653 1256807 1257121 "INTALG" 1257827 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1256110 1256200 1256370 "INTAF" 1256557 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1249564 1255920 1256060 "INTABL" 1256065 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1248895 1249334 1249399 "INT8" 1249433 T INT8 (NIL) -8 NIL NIL 1249478) (-548 1248225 1248664 1248729 "INT64" 1248763 T INT64 (NIL) -8 NIL NIL 1248808) (-547 1247555 1247994 1248059 "INT32" 1248093 T INT32 (NIL) -8 NIL NIL 1248138) (-546 1246885 1247324 1247389 "INT16" 1247423 T INT16 (NIL) -8 NIL NIL 1247468) (-545 1241892 1244574 1244602 "INS" 1245536 T INS (NIL) -9 NIL 1246201 NIL) (-544 1239132 1239903 1240877 "INS-" 1240950 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1237907 1238134 1238432 "INPSIGN" 1238885 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1237025 1237142 1237339 "INPRODPF" 1237787 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1235919 1236036 1236273 "INPRODFF" 1236905 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1234919 1235071 1235331 "INNMFACT" 1235755 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1234116 1234213 1234401 "INMODGCD" 1234818 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1232624 1232869 1233193 "INFSP" 1233861 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1231808 1231925 1232108 "INFPROD0" 1232504 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1228690 1229873 1230388 "INFORM" 1231301 T INFORM (NIL) -8 NIL NIL NIL) (-535 1228300 1228360 1228458 "INFORM1" 1228625 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1227823 1227912 1228026 "INFINITY" 1228206 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1226999 1227543 1227644 "INETCLTS" 1227742 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1225615 1225865 1226186 "INEP" 1226747 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1224891 1225512 1225577 "INDE" 1225582 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1224455 1224523 1224640 "INCRMAPS" 1224818 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1223273 1223724 1223930 "INBFILE" 1224269 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1218573 1219509 1220453 "INBFF" 1222361 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1217481 1217750 1217778 "INBCON" 1218291 T INBCON (NIL) -9 NIL 1218557 NIL) (-526 1216733 1216956 1217232 "INBCON-" 1217237 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1216239 1216457 1216548 "INAST" 1216662 T INAST (NIL) -8 NIL NIL NIL) (-524 1215693 1215918 1216024 "IMPTAST" 1216153 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1212187 1215537 1215641 "IMATRIX" 1215646 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1210899 1211022 1211337 "IMATQF" 1212043 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1209119 1209346 1209683 "IMATLIN" 1210655 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1203745 1209043 1209101 "ILIST" 1209106 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1201698 1203605 1203718 "IIARRAY2" 1203723 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1197123 1201609 1201673 "IFF" 1201678 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1196497 1196740 1196856 "IFAST" 1197027 T IFAST (NIL) -8 NIL NIL NIL) (-516 1191540 1195789 1195977 "IFARRAY" 1196354 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1190747 1191444 1191517 "IFAMON" 1191522 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1190331 1190396 1190450 "IEVALAB" 1190657 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1190006 1190074 1190234 "IEVALAB-" 1190239 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1189664 1189920 1189983 "IDPO" 1189988 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1188941 1189553 1189628 "IDPOAMS" 1189633 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1188275 1188830 1188905 "IDPOAM" 1188910 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1187360 1187610 1187663 "IDPC" 1188076 NIL IDPC (NIL T T) -9 NIL 1188225 NIL) (-508 1186856 1187252 1187325 "IDPAM" 1187330 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1186259 1186748 1186821 "IDPAG" 1186826 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1186027 1186174 1186224 "IDENT" 1186229 T IDENT (NIL) -8 NIL NIL NIL) (-505 1182282 1183130 1184025 "IDECOMP" 1185184 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1175146 1176205 1177252 "IDEAL" 1181318 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1174310 1174422 1174621 "ICDEN" 1175030 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1173408 1173790 1173937 "ICARD" 1174183 T ICARD (NIL) -8 NIL NIL NIL) (-501 1171468 1171781 1172186 "IBPTOOLS" 1173085 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1167102 1171088 1171201 "IBITS" 1171387 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1163825 1164401 1165096 "IBATOOL" 1166519 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1161604 1162066 1162599 "IBACHIN" 1163360 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1159481 1161450 1161553 "IARRAY2" 1161558 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1155634 1159407 1159464 "IARRAY1" 1159469 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1149618 1154046 1154527 "IAN" 1155173 T IAN (NIL) -8 NIL NIL NIL) (-494 1149129 1149186 1149359 "IALGFACT" 1149555 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1148657 1148770 1148798 "HYPCAT" 1149005 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1148195 1148312 1148498 "HYPCAT-" 1148503 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1147817 1147990 1148073 "HOSTNAME" 1148132 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1147662 1147699 1147740 "HOMOTOP" 1147745 NIL HOMOTOP (NIL T) -9 NIL 1147778 NIL) (-489 1144341 1145672 1145713 "HOAGG" 1146694 NIL HOAGG (NIL T) -9 NIL 1147373 NIL) (-488 1142935 1143334 1143860 "HOAGG-" 1143865 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1136966 1142530 1142679 "HEXADEC" 1142806 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1135714 1135936 1136199 "HEUGCD" 1136743 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1134817 1135551 1135681 "HELLFDIV" 1135686 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1133044 1134594 1134682 "HEAP" 1134761 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1132334 1132596 1132730 "HEADAST" 1132930 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1126248 1132249 1132311 "HDP" 1132316 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1119991 1125883 1126035 "HDMP" 1126149 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1119315 1119455 1119619 "HB" 1119847 T HB (NIL) -7 NIL NIL NIL) (-479 1112812 1119161 1119265 "HASHTBL" 1119270 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1112315 1112533 1112625 "HASAST" 1112740 T HASAST (NIL) -8 NIL NIL NIL) (-477 1110120 1111937 1112119 "HACKPI" 1112153 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1105815 1109973 1110086 "GTSET" 1110091 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1099341 1105693 1105791 "GSTBL" 1105796 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1091646 1098372 1098637 "GSERIES" 1099132 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1090813 1091204 1091232 "GROUP" 1091435 T GROUP (NIL) -9 NIL 1091569 NIL) (-472 1090179 1090338 1090589 "GROUP-" 1090594 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1088546 1088867 1089254 "GROEBSOL" 1089856 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1087486 1087748 1087799 "GRMOD" 1088328 NIL GRMOD (NIL T T) -9 NIL 1088496 NIL) (-469 1087254 1087290 1087418 "GRMOD-" 1087423 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1082571 1083608 1084608 "GRIMAGE" 1086274 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1081037 1081298 1081622 "GRDEF" 1082267 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1080481 1080597 1080738 "GRAY" 1080916 T GRAY (NIL) -7 NIL NIL NIL) (-465 1079694 1080074 1080125 "GRALG" 1080278 NIL GRALG (NIL T T) -9 NIL 1080371 NIL) (-464 1079355 1079428 1079591 "GRALG-" 1079596 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1076159 1078940 1079118 "GPOLSET" 1079262 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1075513 1075570 1075828 "GOSPER" 1076096 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1071272 1071951 1072477 "GMODPOL" 1075212 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1070277 1070461 1070699 "GHENSEL" 1071084 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1064328 1065171 1066198 "GENUPS" 1069361 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1064025 1064076 1064165 "GENUFACT" 1064271 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1063437 1063514 1063679 "GENPGCD" 1063943 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1062911 1062946 1063159 "GENMFACT" 1063396 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1061477 1061734 1062041 "GENEEZ" 1062654 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1055378 1061088 1061250 "GDMP" 1061400 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1044747 1049149 1050255 "GCNAALG" 1054361 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1043166 1044002 1044030 "GCDDOM" 1044285 T GCDDOM (NIL) -9 NIL 1044442 NIL) (-451 1042636 1042763 1042978 "GCDDOM-" 1042983 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1041308 1041493 1041797 "GB" 1042415 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1029924 1032254 1034646 "GBINTERN" 1038999 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1027761 1028053 1028474 "GBF" 1029599 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1026542 1026707 1026974 "GBEUCLID" 1027577 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1025891 1026016 1026165 "GAUSSFAC" 1026413 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1024258 1024560 1024874 "GALUTIL" 1025610 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1022566 1022840 1023164 "GALPOLYU" 1023985 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1019931 1020221 1020628 "GALFACTU" 1022263 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1011737 1013236 1014844 "GALFACT" 1018363 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1009125 1009783 1009811 "FVFUN" 1010967 T FVFUN (NIL) -9 NIL 1011687 NIL) (-440 1008391 1008573 1008601 "FVC" 1008892 T FVC (NIL) -9 NIL 1009075 NIL) (-439 1008061 1008216 1008284 "FUNDESC" 1008343 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1007703 1007858 1007939 "FUNCTION" 1008013 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1005474 1006025 1006491 "FT" 1007257 T FT (NIL) -8 NIL NIL NIL) (-436 1004292 1004775 1004978 "FTEM" 1005291 T FTEM (NIL) -8 NIL NIL NIL) (-435 1002548 1002837 1003241 "FSUPFACT" 1003983 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1000945 1001234 1001566 "FST" 1002236 T FST (NIL) -8 NIL NIL NIL) (-433 1000116 1000222 1000417 "FSRED" 1000827 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 998794 999050 999404 "FSPRMELT" 999831 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 995879 996317 996816 "FSPECF" 998357 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 977933 986382 986422 "FS" 990270 NIL FS (NIL T) -9 NIL 992559 NIL) (-429 966580 969573 973629 "FS-" 973926 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 966094 966148 966325 "FSINT" 966521 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 964413 965087 965390 "FSERIES" 965873 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 963427 963543 963774 "FSCINT" 964293 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 959661 962371 962412 "FSAGG" 962782 NIL FSAGG (NIL T) -9 NIL 963041 NIL) (-424 957423 958024 958820 "FSAGG-" 958915 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 956465 956608 956835 "FSAGG2" 957276 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 954119 954399 954953 "FS2UPS" 956183 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 953701 953744 953899 "FS2" 954070 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 952558 952729 953038 "FS2EXPXP" 953526 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 951984 952099 952251 "FRUTIL" 952438 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 943424 947479 948837 "FR" 950658 NIL FR (NIL T) -8 NIL NIL NIL) (-417 938499 941142 941182 "FRNAALG" 942578 NIL FRNAALG (NIL T) -9 NIL 943185 NIL) (-416 934172 935248 936523 "FRNAALG-" 937273 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 933810 933853 933980 "FRNAAF2" 934123 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 932217 932664 932959 "FRMOD" 933622 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 929995 930600 930917 "FRIDEAL" 932008 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 929190 929277 929566 "FRIDEAL2" 929902 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 928323 928737 928778 "FRETRCT" 928783 NIL FRETRCT (NIL T) -9 NIL 928959 NIL) (-410 927435 927666 928017 "FRETRCT-" 928022 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 924639 925823 925882 "FRAMALG" 926764 NIL FRAMALG (NIL T T) -9 NIL 927056 NIL) (-408 922773 923228 923858 "FRAMALG-" 924081 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 916721 922248 922524 "FRAC" 922529 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 916357 916414 916521 "FRAC2" 916658 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 915993 916050 916157 "FR2" 916294 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 910658 913518 913546 "FPS" 914665 T FPS (NIL) -9 NIL 915222 NIL) (-403 910107 910216 910380 "FPS-" 910526 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 907553 909196 909224 "FPC" 909449 T FPC (NIL) -9 NIL 909591 NIL) (-401 907346 907386 907483 "FPC-" 907488 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 906224 906834 906875 "FPATMAB" 906880 NIL FPATMAB (NIL T) -9 NIL 907032 NIL) (-399 903924 904400 904826 "FPARFRAC" 905861 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 899317 899816 900498 "FORTRAN" 903356 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 897033 897533 898072 "FORT" 898798 T FORT (NIL) -7 NIL NIL NIL) (-396 894709 895271 895299 "FORTFN" 896359 T FORTFN (NIL) -9 NIL 896983 NIL) (-395 894473 894523 894551 "FORTCAT" 894610 T FORTCAT (NIL) -9 NIL 894672 NIL) (-394 892606 893089 893479 "FORMULA" 894103 T FORMULA (NIL) -8 NIL NIL NIL) (-393 892394 892424 892493 "FORMULA1" 892570 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 891917 891969 892142 "FORDER" 892336 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 891013 891177 891370 "FOP" 891744 T FOP (NIL) -7 NIL NIL NIL) (-390 889621 890293 890467 "FNLA" 890895 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 888376 888765 888793 "FNCAT" 889253 T FNCAT (NIL) -9 NIL 889513 NIL) (-388 887942 888335 888363 "FNAME" 888368 T FNAME (NIL) -8 NIL NIL NIL) (-387 886597 887534 887562 "FMTC" 887567 T FMTC (NIL) -9 NIL 887603 NIL) (-386 882957 884120 884749 "FMONOID" 886001 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 882176 882699 882848 "FM" 882853 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 879600 880246 880274 "FMFUN" 881418 T FMFUN (NIL) -9 NIL 882126 NIL) (-383 878869 879050 879078 "FMC" 879368 T FMC (NIL) -9 NIL 879550 NIL) (-382 876063 876897 876951 "FMCAT" 878146 NIL FMCAT (NIL T T) -9 NIL 878641 NIL) (-381 874956 875829 875929 "FM1" 876008 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 872730 873146 873640 "FLOATRP" 874507 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 866331 870459 871080 "FLOAT" 872129 T FLOAT (NIL) -8 NIL NIL NIL) (-378 863769 864269 864847 "FLOATCP" 865798 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 862570 863382 863423 "FLINEXP" 863428 NIL FLINEXP (NIL T) -9 NIL 863521 NIL) (-376 861724 861959 862287 "FLINEXP-" 862292 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 860800 860944 861168 "FLASORT" 861576 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 858017 858859 858911 "FLALG" 860138 NIL FLALG (NIL T T) -9 NIL 860605 NIL) (-373 851801 855503 855544 "FLAGG" 856806 NIL FLAGG (NIL T) -9 NIL 857458 NIL) (-372 850527 850866 851356 "FLAGG-" 851361 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 849569 849712 849939 "FLAGG2" 850380 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 846536 847518 847577 "FINRALG" 848705 NIL FINRALG (NIL T T) -9 NIL 849213 NIL) (-369 845696 845925 846264 "FINRALG-" 846269 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 845102 845315 845343 "FINITE" 845539 T FINITE (NIL) -9 NIL 845646 NIL) (-367 837560 839721 839761 "FINAALG" 843428 NIL FINAALG (NIL T) -9 NIL 844881 NIL) (-366 832892 833942 835086 "FINAALG-" 836465 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 832287 832647 832750 "FILE" 832822 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 830971 831283 831337 "FILECAT" 832021 NIL FILECAT (NIL T T) -9 NIL 832237 NIL) (-363 828831 830333 830361 "FIELD" 830401 T FIELD (NIL) -9 NIL 830481 NIL) (-362 827451 827836 828347 "FIELD-" 828352 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 825328 826086 826433 "FGROUP" 827137 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 824418 824582 824802 "FGLMICPK" 825160 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 820277 824343 824400 "FFX" 824405 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 819878 819939 820074 "FFSLPE" 820210 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 815867 816650 817446 "FFPOLY" 819114 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 815371 815407 815616 "FFPOLY2" 815825 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 811241 815290 815353 "FFP" 815358 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 806666 811152 811216 "FF" 811221 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 801819 806009 806199 "FFNBX" 806520 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 796775 800954 801212 "FFNBP" 801673 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 791435 796059 796270 "FFNB" 796608 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 790267 790465 790780 "FFINTBAS" 791232 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 786487 788674 788702 "FFIELDC" 789322 T FFIELDC (NIL) -9 NIL 789698 NIL) (-348 785149 785520 786017 "FFIELDC-" 786022 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 784718 784764 784888 "FFHOM" 785091 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 782413 782900 783417 "FFF" 784233 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778058 782155 782256 "FFCGX" 782356 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 773706 777790 777897 "FFCGP" 778001 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 768916 773433 773541 "FFCG" 773642 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 750741 759787 759873 "FFCAT" 765038 NIL FFCAT (NIL T T T) -9 NIL 766489 NIL) (-341 745939 746986 748300 "FFCAT-" 749530 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 745350 745393 745628 "FFCAT2" 745890 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 734547 738322 739542 "FEXPR" 744202 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 733547 733982 734023 "FEVALAB" 734107 NIL FEVALAB (NIL T) -9 NIL 734368 NIL) (-337 732706 732916 733254 "FEVALAB-" 733259 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 731299 732089 732292 "FDIV" 732605 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 728365 729080 729195 "FDIVCAT" 730763 NIL FDIVCAT (NIL T T T T) -9 NIL 731200 NIL) (-334 728127 728154 728324 "FDIVCAT-" 728329 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 727347 727434 727711 "FDIV2" 728034 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726033 726292 726581 "FCPAK1" 727078 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725159 725533 725674 "FCOMP" 725924 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 708888 712309 715847 "FC" 721641 T FC (NIL) -8 NIL NIL NIL) (-329 701459 705452 705492 "FAXF" 707294 NIL FAXF (NIL T) -9 NIL 707986 NIL) (-328 698735 699393 700218 "FAXF-" 700683 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 693835 698111 698287 "FARRAY" 698592 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689080 691120 691173 "FAMR" 692196 NIL FAMR (NIL T T) -9 NIL 692656 NIL) (-325 687970 688272 688707 "FAMR-" 688712 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687166 687892 687945 "FAMONOID" 687950 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 684978 685662 685715 "FAMONC" 686656 NIL FAMONC (NIL T T) -9 NIL 687042 NIL) (-322 683670 684732 684869 "FAGROUP" 684874 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 681465 681784 682187 "FACUTIL" 683351 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 680564 680749 680971 "FACTFUNC" 681275 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 672961 679815 680027 "EXPUPXS" 680420 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 670444 670984 671570 "EXPRTUBE" 672395 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 666638 667230 667967 "EXPRODE" 669783 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 652004 665293 665721 "EXPR" 666242 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 646411 646998 647811 "EXPR2UPS" 651302 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646047 646104 646211 "EXPR2" 646348 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 637444 645179 645476 "EXPEXPAN" 645884 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 637271 637401 637430 "EXIT" 637435 T EXIT (NIL) -8 NIL NIL NIL) (-311 636778 636995 637086 "EXITAST" 637200 T EXITAST (NIL) -8 NIL NIL NIL) (-310 636405 636467 636580 "EVALCYC" 636710 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 635946 636064 636105 "EVALAB" 636275 NIL EVALAB (NIL T) -9 NIL 636379 NIL) (-308 635427 635549 635770 "EVALAB-" 635775 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 632887 634163 634191 "EUCDOM" 634746 T EUCDOM (NIL) -9 NIL 635096 NIL) (-306 631292 631734 632324 "EUCDOM-" 632329 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 618830 621590 624340 "ESTOOLS" 628562 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 618462 618519 618628 "ESTOOLS2" 618767 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618213 618255 618335 "ESTOOLS1" 618414 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612118 613846 613874 "ES" 616642 T ES (NIL) -9 NIL 618051 NIL) (-301 607065 608352 610169 "ES-" 610333 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 603439 604200 604980 "ESCONT" 606305 T ESCONT (NIL) -7 NIL NIL NIL) (-299 603184 603216 603298 "ESCONT1" 603401 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 602859 602909 603009 "ES2" 603128 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 602489 602547 602656 "ES1" 602795 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 601705 601834 602010 "ERROR" 602333 T ERROR (NIL) -7 NIL NIL NIL) (-295 595208 601564 601655 "EQTBL" 601660 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 587759 590522 591971 "EQ" 593792 NIL -3301 (NIL T) -8 NIL NIL NIL) (-293 587391 587448 587557 "EQ2" 587696 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 582680 583729 584822 "EP" 586330 NIL EP (NIL T) -7 NIL NIL NIL) (-291 581258 581555 581867 "ENV" 582388 T ENV (NIL) -8 NIL NIL NIL) (-290 580429 580957 580985 "ENTIRER" 580990 T ENTIRER (NIL) -9 NIL 581036 NIL) (-289 576923 578384 578754 "EMR" 580228 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576067 576252 576306 "ELTAGG" 576686 NIL ELTAGG (NIL T T) -9 NIL 576897 NIL) (-287 575786 575848 575989 "ELTAGG-" 575994 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 575575 575604 575658 "ELTAB" 575742 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 574701 574847 575046 "ELFUTS" 575426 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 574443 574499 574527 "ELEMFUN" 574632 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 574313 574334 574402 "ELEMFUN-" 574407 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569204 572413 572454 "ELAGG" 573394 NIL ELAGG (NIL T) -9 NIL 573857 NIL) (-281 567489 567923 568586 "ELAGG-" 568591 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566146 566426 566721 "ELABEXPR" 567214 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559010 560813 561640 "EFUPXS" 565422 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 552460 554261 555071 "EFULS" 558286 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 549882 550240 550719 "EFSTRUC" 552092 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 538953 540519 542079 "EF" 548397 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 538054 538438 538587 "EAB" 538824 T EAB (NIL) -8 NIL NIL NIL) (-274 537263 538013 538041 "E04UCFA" 538046 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 536472 537222 537250 "E04NAFA" 537255 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 535681 536431 536459 "E04MBFA" 536464 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 534890 535640 535668 "E04JAFA" 535673 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 534101 534849 534877 "E04GCFA" 534882 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 533312 534060 534088 "E04FDFA" 534093 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 532521 533271 533299 "E04DGFA" 533304 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 526694 528046 529410 "E04AGNT" 531177 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 525400 525880 525920 "DVARCAT" 526395 NIL DVARCAT (NIL T) -9 NIL 526594 NIL) (-265 524604 524816 525130 "DVARCAT-" 525135 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 517496 524403 524532 "DSMP" 524537 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 512305 513441 514509 "DROPT" 516448 T DROPT (NIL) -8 NIL NIL NIL) (-262 511970 512029 512127 "DROPT1" 512240 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 507085 508211 509348 "DROPT0" 510853 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 505430 505755 506141 "DRAWPT" 506719 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 500017 500940 502019 "DRAW" 504404 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 499650 499703 499821 "DRAWHACK" 499958 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 498381 498650 498941 "DRAWCX" 499379 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 497896 497965 498116 "DRAWCURV" 498307 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 488364 490326 492441 "DRAWCFUN" 495801 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 485177 487059 487100 "DQAGG" 487729 NIL DQAGG (NIL T) -9 NIL 488002 NIL) (-253 473448 480155 480238 "DPOLCAT" 482090 NIL DPOLCAT (NIL T T T T) -9 NIL 482635 NIL) (-252 468284 469633 471591 "DPOLCAT-" 471596 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 461433 468145 468243 "DPMO" 468248 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 454485 461213 461380 "DPMM" 461385 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 454117 454404 454452 "DOMCTOR" 454457 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 453412 453639 453776 "DOMAIN" 454000 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 447155 453047 453199 "DMP" 453313 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 446755 446811 446955 "DLP" 447093 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 440625 446082 446272 "DLIST" 446597 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 437469 439478 439519 "DLAGG" 440069 NIL DLAGG (NIL T) -9 NIL 440299 NIL) (-243 436274 436912 436940 "DIVRING" 437032 T DIVRING (NIL) -9 NIL 437115 NIL) (-242 435511 435701 436001 "DIVRING-" 436006 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 433613 433970 434376 "DISPLAY" 435125 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 427549 433527 433590 "DIRPROD" 433595 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 426397 426600 426865 "DIRPROD2" 427342 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 415654 421612 421665 "DIRPCAT" 422075 NIL DIRPCAT (NIL NIL T) -9 NIL 422915 NIL) (-237 412980 413622 414503 "DIRPCAT-" 414840 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 412267 412427 412613 "DIOSP" 412814 T DIOSP (NIL) -7 NIL NIL NIL) (-235 408969 411179 411220 "DIOPS" 411654 NIL DIOPS (NIL T) -9 NIL 411883 NIL) (-234 408518 408632 408823 "DIOPS-" 408828 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 407402 408004 408032 "DIFRING" 408219 T DIFRING (NIL) -9 NIL 408329 NIL) (-232 407048 407125 407277 "DIFRING-" 407282 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 404845 406091 406132 "DIFEXT" 406495 NIL DIFEXT (NIL T) -9 NIL 406789 NIL) (-230 403130 403558 404224 "DIFEXT-" 404229 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 400452 402662 402703 "DIAGG" 402708 NIL DIAGG (NIL T) -9 NIL 402728 NIL) (-228 399836 399993 400245 "DIAGG-" 400250 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 395301 398795 399072 "DHMATRIX" 399605 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 390913 391822 392832 "DFSFUN" 394311 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 386018 389844 390156 "DFLOAT" 390621 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 384246 384527 384923 "DFINTTLS" 385726 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 381302 382267 382667 "DERHAM" 383912 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 379151 381077 381166 "DEQUEUE" 381246 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 378366 378499 378695 "DEGRED" 379013 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 374761 375506 376359 "DEFINTRF" 377594 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 372288 372757 373356 "DEFINTEF" 374280 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 371665 371908 372023 "DEFAST" 372193 T DEFAST (NIL) -8 NIL NIL NIL) (-217 365696 371260 371409 "DECIMAL" 371536 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 363206 363666 364172 "DDFACT" 365240 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 362802 362845 362996 "DBLRESP" 363157 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 360701 361035 361395 "DBASE" 362569 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 359970 360181 360327 "DATAARY" 360600 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 359103 359929 359957 "D03FAFA" 359962 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 358237 359062 359090 "D03EEFA" 359095 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 356187 356653 357142 "D03AGNT" 357768 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 355503 356146 356174 "D02EJFA" 356179 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 354819 355462 355490 "D02CJFA" 355495 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 354135 354778 354806 "D02BHFA" 354811 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 353451 354094 354122 "D02BBFA" 354127 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 346648 348237 349843 "D02AGNT" 351865 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 344416 344939 345485 "D01WGTS" 346122 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 343510 344375 344403 "D01TRNS" 344408 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 342605 343469 343497 "D01GBFA" 343502 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 341700 342564 342592 "D01FCFA" 342597 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 340795 341659 341687 "D01ASFA" 341692 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 339890 340754 340782 "D01AQFA" 340787 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 338985 339849 339877 "D01APFA" 339882 T D01APFA (NIL) -8 NIL NIL NIL) (-197 338080 338944 338972 "D01ANFA" 338977 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 337175 338039 338067 "D01AMFA" 338072 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 336270 337134 337162 "D01ALFA" 337167 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 335365 336229 336257 "D01AKFA" 336262 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 334460 335324 335352 "D01AJFA" 335357 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 327755 329308 330869 "D01AGNT" 332919 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327092 327220 327372 "CYCLOTOM" 327623 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 323827 324540 325267 "CYCLES" 326385 T CYCLES (NIL) -7 NIL NIL NIL) (-189 323139 323273 323444 "CVMP" 323688 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 320910 321168 321544 "CTRIGMNP" 322867 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 320401 320701 320775 "CTOR" 320856 T CTOR (NIL) -8 NIL NIL NIL) (-186 319937 320132 320233 "CTORKIND" 320320 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 319285 319544 319572 "CTORCAT" 319754 T CTORCAT (NIL) -9 NIL 319867 NIL) (-184 318883 318994 319153 "CTORCAT-" 319158 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 318399 318586 318684 "CTORCALL" 318805 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 317773 317872 318025 "CSTTOOLS" 318296 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 313572 314229 314987 "CRFP" 317085 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 313074 313293 313385 "CRCEAST" 313500 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 312121 312306 312534 "CRAPACK" 312878 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 311505 311606 311810 "CPMATCH" 311997 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 311230 311258 311364 "CPIMA" 311471 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 307594 308266 308984 "COORDSYS" 310565 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307002 307124 307267 "CONTOUR" 307471 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 302920 305005 305497 "CONTFRAC" 306542 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 302800 302821 302849 "CONDUIT" 302886 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 301965 302493 302521 "COMRING" 302526 T COMRING (NIL) -9 NIL 302578 NIL) (-171 301046 301323 301507 "COMPPROP" 301801 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 300707 300742 300870 "COMPLPAT" 301005 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 290756 300516 300625 "COMPLEX" 300630 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 290392 290449 290556 "COMPLEX2" 290693 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 290110 290145 290243 "COMPFACT" 290351 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 274264 284492 284532 "COMPCAT" 285536 NIL COMPCAT (NIL T) -9 NIL 286932 NIL) (-165 263775 266703 270330 "COMPCAT-" 270686 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 263504 263532 263635 "COMMUPC" 263741 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 263299 263332 263391 "COMMONOP" 263465 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 262882 263050 263137 "COMM" 263232 T COMM (NIL) -8 NIL NIL NIL) (-161 262485 262686 262761 "COMMAAST" 262827 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 261734 261928 261956 "COMBOPC" 262294 T COMBOPC (NIL) -9 NIL 262469 NIL) (-159 260630 260840 261082 "COMBINAT" 261524 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 256827 257401 258041 "COMBF" 260052 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 255612 255943 256178 "COLOR" 256612 T COLOR (NIL) -8 NIL NIL NIL) (-156 255115 255333 255425 "COLONAST" 255540 T COLONAST (NIL) -8 NIL NIL NIL) (-155 254755 254802 254927 "CMPLXRT" 255062 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 254230 254455 254554 "CLLCTAST" 254676 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 249730 250760 251840 "CLIP" 253170 T CLIP (NIL) -7 NIL NIL NIL) (-152 248103 248836 249075 "CLIF" 249557 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 244325 246249 246290 "CLAGG" 247219 NIL CLAGG (NIL T) -9 NIL 247755 NIL) (-150 242747 243204 243787 "CLAGG-" 243792 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 242291 242376 242516 "CINTSLPE" 242656 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 239792 240263 240811 "CHVAR" 241819 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 239027 239555 239583 "CHARZ" 239588 T CHARZ (NIL) -9 NIL 239603 NIL) (-146 238781 238821 238899 "CHARPOL" 238981 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 237900 238461 238489 "CHARNZ" 238536 T CHARNZ (NIL) -9 NIL 238592 NIL) (-144 235889 236590 236925 "CHAR" 237585 T CHAR (NIL) -8 NIL NIL NIL) (-143 235615 235676 235704 "CFCAT" 235815 T CFCAT (NIL) -9 NIL NIL NIL) (-142 234860 234971 235153 "CDEN" 235499 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 230852 234013 234293 "CCLASS" 234600 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230159 230302 230465 "CATEGORY" 230709 T -10 (NIL) -8 NIL NIL NIL) (-139 229791 230078 230126 "CATCTOR" 230131 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 229269 229494 229592 "CATAST" 229713 T CATAST (NIL) -8 NIL NIL NIL) (-137 228772 228990 229082 "CASEAST" 229197 T CASEAST (NIL) -8 NIL NIL NIL) (-136 223808 224801 225554 "CARTEN" 228075 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 222916 223064 223285 "CARTEN2" 223655 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 221258 222066 222323 "CARD" 222679 T CARD (NIL) -8 NIL NIL NIL) (-133 220861 221062 221137 "CAPSLAST" 221203 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220233 220561 220589 "CACHSET" 220721 T CACHSET (NIL) -9 NIL 220798 NIL) (-131 219729 220025 220053 "CABMON" 220103 T CABMON (NIL) -9 NIL 220159 NIL) (-130 219229 219433 219543 "BYTEORD" 219639 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 218232 218763 218905 "BYTE" 219068 T BYTE (NIL) -8 NIL NIL 219190) (-128 213632 217737 217909 "BYTEBUF" 218080 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211189 213324 213431 "BTREE" 213558 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 208686 210837 210959 "BTOURN" 211099 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 206103 208156 208197 "BTCAT" 208265 NIL BTCAT (NIL T) -9 NIL 208342 NIL) (-124 205770 205850 205999 "BTCAT-" 206004 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201062 204913 204941 "BTAGG" 205163 T BTAGG (NIL) -9 NIL 205324 NIL) (-122 200552 200677 200883 "BTAGG-" 200888 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197595 199830 200045 "BSTREE" 200369 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 196733 196859 197043 "BRILL" 197451 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193432 195459 195500 "BRAGG" 196149 NIL BRAGG (NIL T) -9 NIL 196407 NIL) (-118 191961 192367 192922 "BRAGG-" 192927 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185217 191307 191491 "BPADICRT" 191809 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183559 185154 185199 "BPADIC" 185204 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183257 183287 183401 "BOUNDZRO" 183523 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178772 179863 180730 "BOP" 182410 T BOP (NIL) -8 NIL NIL NIL) (-113 176393 176837 177357 "BOP1" 178285 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175095 175817 176010 "BOOLEAN" 176220 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174457 174835 174889 "BMODULE" 174894 NIL BMODULE (NIL T T) -9 NIL 174959 NIL) (-110 170285 174255 174328 "BITS" 174404 T BITS (NIL) -8 NIL NIL NIL) (-109 169697 169819 169961 "BINDING" 170163 T BINDING (NIL) -8 NIL NIL NIL) (-108 163731 169294 169442 "BINARY" 169569 T BINARY (NIL) -8 NIL NIL NIL) (-107 161558 162986 163027 "BGAGG" 163287 NIL BGAGG (NIL T) -9 NIL 163424 NIL) (-106 161389 161421 161512 "BGAGG-" 161517 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160487 160773 160978 "BFUNCT" 161204 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159177 159355 159643 "BEZOUT" 160311 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155694 158029 158359 "BBTREE" 158880 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155428 155481 155509 "BASTYPE" 155628 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155281 155309 155382 "BASTYPE-" 155387 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154715 154791 154943 "BALFACT" 155192 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153598 154130 154316 "AUTOMOR" 154560 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153324 153329 153355 "ATTREG" 153360 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151603 152021 152373 "ATTRBUT" 152990 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151238 151431 151497 "ATTRAST" 151555 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150774 150887 150913 "ATRIG" 151114 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150583 150624 150711 "ATRIG-" 150716 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150254 150414 150440 "ASTCAT" 150445 T ASTCAT (NIL) -9 NIL 150475 NIL) (-92 149981 150040 150159 "ASTCAT-" 150164 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148178 149757 149845 "ASTACK" 149924 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146683 146980 147345 "ASSOCEQ" 147860 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145715 146342 146466 "ASP9" 146590 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145478 145663 145702 "ASP8" 145707 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144346 145083 145225 "ASP80" 145367 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143244 143981 144113 "ASP7" 144245 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142198 142921 143039 "ASP78" 143157 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141167 141878 141995 "ASP77" 142112 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140079 140805 140936 "ASP74" 141067 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 138979 139714 139846 "ASP73" 139978 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138083 138805 138905 "ASP6" 138910 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137027 137760 137878 "ASP55" 137996 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 135976 136701 136820 "ASP50" 136939 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135064 135677 135787 "ASP4" 135897 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134152 134765 134875 "ASP49" 134985 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 132936 133691 133859 "ASP42" 134041 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131712 132469 132639 "ASP41" 132823 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130662 131389 131507 "ASP35" 131625 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130427 130610 130649 "ASP34" 130654 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130164 130231 130307 "ASP33" 130382 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129057 129799 129931 "ASP31" 130063 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 128822 129005 129044 "ASP30" 129049 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128557 128626 128702 "ASP29" 128777 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128322 128505 128544 "ASP28" 128549 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128087 128270 128309 "ASP27" 128314 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127171 127785 127896 "ASP24" 128007 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126247 126973 127085 "ASP20" 127090 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125335 125948 126058 "ASP1" 126168 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124277 125009 125128 "ASP19" 125247 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124014 124081 124157 "ASP12" 124232 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 122866 123613 123757 "ASP10" 123901 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 120765 122710 122801 "ARRAY2" 122806 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116579 120413 120527 "ARRAY1" 120682 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115611 115784 116005 "ARRAY12" 116402 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 109970 111841 111916 "ARR2CAT" 114546 NIL ARR2CAT (NIL T T T) -9 NIL 115304 NIL) (-56 107404 108148 109102 "ARR2CAT-" 109107 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106996 107231 107310 "ARITY" 107343 T ARITY (NIL) -8 NIL NIL NIL) (-54 105744 105896 106202 "APPRULE" 106832 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105395 105443 105562 "APPLYORE" 105690 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104369 104660 104855 "ANY" 105218 T ANY (NIL) -8 NIL NIL NIL) (-51 103647 103770 103927 "ANY1" 104243 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101204 102084 102411 "ANTISYM" 103371 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100723 100911 101007 "ANON" 101126 T ANON (NIL) -8 NIL NIL NIL) (-48 94847 99262 99716 "AN" 100287 T AN (NIL) -8 NIL NIL NIL) (-47 91095 92457 92508 "AMR" 93256 NIL AMR (NIL T T) -9 NIL 93856 NIL) (-46 90207 90428 90791 "AMR-" 90796 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74757 90124 90185 "ALIST" 90190 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71586 74351 74520 "ALGSC" 74675 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68141 68696 69303 "ALGPKG" 71026 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67418 67519 67703 "ALGMFACT" 68027 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63155 63842 64497 "ALGMANIP" 66941 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54552 62781 62931 "ALGFF" 63088 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53748 53879 54058 "ALGFACT" 54410 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52805 53379 53417 "ALGEBRA" 53422 NIL ALGEBRA (NIL T) -9 NIL 53463 NIL) (-37 52523 52582 52714 "ALGEBRA-" 52719 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34782 50525 50577 "ALAGG" 50713 NIL ALAGG (NIL T T) -9 NIL 50874 NIL) (-35 34318 34431 34457 "AHYP" 34658 T AHYP (NIL) -9 NIL NIL NIL) (-34 33249 33497 33523 "AGG" 34022 T AGG (NIL) -9 NIL 34301 NIL) (-33 32683 32845 33059 "AGG-" 33064 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30359 30782 31200 "AF" 32325 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29866 30084 30174 "ADDAST" 30287 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29134 29393 29549 "ACPLOT" 29728 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18418 26347 26398 "ACFS" 27109 NIL ACFS (NIL T) -9 NIL 27348 NIL) (-28 16432 16922 17697 "ACFS-" 17702 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14599 14625 "ACF" 15504 T ACF (NIL) -9 NIL 15916 NIL) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351 NIL) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804 NIL) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812 NIL) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 8167b9ec..51130142 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,66 +1,55 @@ -(735973 . 3449148019) -(((*1 *1 *1) - (-12 (-4 *1 (-1060 *2 *3 *4)) (-4 *2 (-1046)) (-4 *3 (-790)) - (-4 *4 (-847))))) -(((*1 *2 *2) - (-12 (-5 *2 (-641 (-949 *3))) (-4 *3 (-452)) (-5 *1 (-360 *3 *4)) - (-14 *4 (-641 (-1170))))) - ((*1 *2 *2) - (-12 (-5 *2 (-641 *6)) (-4 *6 (-946 *3 *4 *5)) (-4 *3 (-452)) - (-4 *4 (-790)) (-4 *5 (-847)) (-5 *1 (-450 *3 *4 *5 *6)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-641 *7)) (-5 *3 (-1152)) (-4 *7 (-946 *4 *5 *6)) - (-4 *4 (-452)) (-4 *5 (-790)) (-4 *6 (-847)) - (-5 *1 (-450 *4 *5 *6 *7)))) - ((*1 *2 *2 *3 *3) - (-12 (-5 *2 (-641 *7)) (-5 *3 (-1152)) (-4 *7 (-946 *4 *5 *6)) - (-4 *4 (-452)) (-4 *5 (-790)) (-4 *6 (-847)) - (-5 *1 (-450 *4 *5 *6 *7)))) - ((*1 *1 *1) - (-12 (-4 *2 (-363)) (-4 *3 (-790)) (-4 *4 (-847)) - (-5 *1 (-504 *2 *3 *4 *5)) (-4 *5 (-946 *2 *3 *4)))) - ((*1 *2 *2) - (-12 (-5 *2 (-641 (-777 *3 (-861 *4)))) (-4 *3 (-452)) - (-14 *4 (-641 (-1170))) (-5 *1 (-626 *3 *4))))) -(((*1 *2 *3 *4 *4 *5 *6) - (-12 (-5 *3 (-641 (-641 (-940 (-225))))) (-5 *4 (-871)) - (-5 *5 (-918)) (-5 *6 (-641 (-263))) (-5 *2 (-1260)) - (-5 *1 (-1263)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-641 (-641 (-940 (-225))))) (-5 *4 (-641 (-263))) - (-5 *2 (-1260)) (-5 *1 (-1263))))) -(((*1 *2 *2 *2 *2) - (-12 (-4 *2 (-13 (-363) (-10 -8 (-15 ** ($ $ (-407 (-564))))))) - (-5 *1 (-1122 *3 *2)) (-4 *3 (-1235 *2))))) -(((*1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-924))))) +(735965 . 3449227613) (((*1 *2 *1) - (|partial| -12 (-4 *3 (-25)) (-4 *3 (-847)) (-5 *2 (-641 *1)) - (-4 *1 (-430 *3)))) - ((*1 *2 *1) - (|partial| -12 (-5 *2 (-641 (-889 *3))) (-5 *1 (-889 *3)) - (-4 *3 (-1094)))) - ((*1 *2 *1) - (|partial| -12 (-4 *3 (-1046)) (-4 *4 (-790)) (-4 *5 (-847)) - (-5 *2 (-641 *1)) (-4 *1 (-946 *3 *4 *5)))) + (-12 (-4 *1 (-329 *3)) (-4 *3 (-363)) (-4 *3 (-368)) (-5 *2 (-112)))) ((*1 *2 *3) - (|partial| -12 (-4 *4 (-790)) (-4 *5 (-847)) (-4 *6 (-1046)) - (-4 *7 (-946 *6 *4 *5)) (-5 *2 (-641 *3)) - (-5 *1 (-947 *4 *5 *6 *7 *3)) - (-4 *3 - (-13 (-363) - (-10 -8 (-15 -3742 ($ *7)) (-15 -1625 (*7 $)) - (-15 -1634 (*7 $)))))))) + (-12 (-5 *3 (-1166 *4)) (-4 *4 (-349)) (-5 *2 (-112)) + (-5 *1 (-357 *4)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1259 *4)) (-4 *4 (-349)) (-5 *2 (-112)) + (-5 *1 (-528 *4))))) (((*1 *2 *3) - (-12 (-4 *4 (-38 (-407 (-564)))) - (-5 *2 (-2 (|:| -2297 (-1150 *4)) (|:| -2309 (-1150 *4)))) - (-5 *1 (-1156 *4)) (-5 *3 (-1150 *4))))) -(((*1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-1003)))) - ((*1 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-1003))))) + (-12 (-4 *4 (-349)) (-5 *2 (-418 (-1166 (-1166 *4)))) + (-5 *1 (-1207 *4)) (-5 *3 (-1166 (-1166 *4)))))) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *4) + (-12 (-5 *3 (-1152)) (-5 *4 (-564)) (-5 *5 (-685 (-225))) + (-5 *2 (-1032)) (-5 *1 (-751))))) +(((*1 *1 *1) + (-12 (-5 *1 (-594 *2)) (-4 *2 (-38 (-407 (-564)))) (-4 *2 (-1046))))) +(((*1 *2 *1) (-12 (-5 *2 (-1152)) (-5 *1 (-536))))) +(((*1 *1 *1) + (-12 (-5 *1 (-1135 *2 *3)) (-4 *2 (-13 (-1094) (-34))) + (-4 *3 (-13 (-1094) (-34)))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-1 *5 *5)) (-4 *5 (-1235 *4)) (-4 *4 (-1213)) + (-4 *6 (-1235 (-407 *5))) + (-5 *2 + (-2 (|:| |num| *1) (|:| |den| *5) (|:| |derivden| *5) + (|:| |gd| *5))) + (-4 *1 (-342 *4 *5 *6))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-980 *2)) (-4 *2 (-1194))))) +(((*1 *1 *1 *1) (-5 *1 (-859))) ((*1 *1 *1) (-5 *1 (-859))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1166 (-564))) (-5 *3 (-564)) (-4 *1 (-866 *4))))) (((*1 *2 *1) - (-12 (-4 *1 (-326 *3 *4)) (-4 *3 (-1046)) (-4 *4 (-789)) - (-5 *2 (-112)))) - ((*1 *2 *1) (-12 (-4 *1 (-430 *3)) (-4 *3 (-847)) (-5 *2 (-112))))) + (-12 (-5 *2 (-641 (-641 (-940 (-225))))) (-5 *1 (-1204 *3)) + (-4 *3 (-971))))) +(((*1 *1 *1) (-4 *1 (-243))) + ((*1 *1 *1) + (-12 (-4 *2 (-172)) (-5 *1 (-289 *2 *3 *4 *5 *6 *7)) + (-4 *3 (-1235 *2)) (-4 *4 (-23)) (-14 *5 (-1 *3 *3 *4)) + (-14 *6 (-1 (-3 *4 "failed") *4 *4)) + (-14 *7 (-1 (-3 *3 "failed") *3 *3 *4)))) + ((*1 *1 *1) + (-4007 (-12 (-5 *1 (-294 *2)) (-4 *2 (-363)) (-4 *2 (-1209))) + (-12 (-5 *1 (-294 *2)) (-4 *2 (-473)) (-4 *2 (-1209))))) + ((*1 *1 *1) (-4 *1 (-473))) + ((*1 *2 *2) (-12 (-5 *2 (-1259 *3)) (-4 *3 (-349)) (-5 *1 (-528 *3)))) + ((*1 *1 *1) + (-12 (-5 *1 (-712 *2 *3 *4 *5 *6)) (-4 *2 (-172)) (-4 *3 (-23)) + (-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 *1) (-12 (-4 *1 (-794 *2)) (-4 *2 (-172)) (-4 *2 (-363))))) (((*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)))) @@ -92,14 +81,14 @@ (-12 (-5 *3 (-1170)) (-5 *2 (-245 (-1152))) (-5 *1 (-214 *4)) (-4 *4 (-13 (-847) - (-10 -8 (-15 -4382 ((-1152) $ *3)) (-15 -3589 ((-1264) $)) - (-15 -2096 ((-1264) $))))))) + (-10 -8 (-15 -4380 ((-1152) $ *3)) (-15 -3519 ((-1264) $)) + (-15 -3620 ((-1264) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-986)) (-5 *1 (-214 *3)) (-4 *3 (-13 (-847) - (-10 -8 (-15 -4382 ((-1152) $ (-1170))) (-15 -3589 ((-1264) $)) - (-15 -2096 ((-1264) $))))))) + (-10 -8 (-15 -4380 ((-1152) $ (-1170))) (-15 -3519 ((-1264) $)) + (-15 -3620 ((-1264) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-768)) (-5 *1 (-245 *4)) (-4 *4 (-847)))) ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-245 *3)) (-4 *3 (-847)))) @@ -185,141 +174,94 @@ (-12 (-5 *2 "rest") (-4 *1 (-1247 *3)) (-4 *3 (-1209)))) ((*1 *2 *1 *3) (-12 (-5 *3 "first") (-4 *1 (-1247 *2)) (-4 *2 (-1209))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-452)) (-4 *6 (-790)) (-4 *7 (-847)) - (-4 *3 (-1060 *5 *6 *7)) - (-5 *2 (-641 (-2 (|:| |val| (-112)) (|:| -2084 *4)))) - (-5 *1 (-1102 *5 *6 *7 *3 *4)) (-4 *4 (-1066 *5 *6 *7 *3))))) -(((*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 *2 *1) - (-12 (-5 *2 (-641 (-294 *3))) (-5 *1 (-294 *3)) (-4 *3 (-556)) - (-4 *3 (-1209))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1 *5 *4 *4)) (-4 *4 (-1094)) (-4 *5 (-1094)) - (-5 *2 (-1 *5 *4)) (-5 *1 (-679 *4 *5))))) -(((*1 *1 *1 *2) - (-12 (-5 *1 (-594 *2)) (-4 *2 (-38 (-407 (-564)))) (-4 *2 (-1046))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -2577 (-779 *3)) (|:| |coef1| (-779 *3)))) - (-5 *1 (-779 *3)) (-4 *3 (-556)) (-4 *3 (-1046)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-556)) (-4 *3 (-1046)) (-4 *4 (-790)) (-4 *5 (-847)) - (-5 *2 (-2 (|:| -2577 *1) (|:| |coef1| *1))) - (-4 *1 (-1060 *3 *4 *5))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-1166 *3)) (-4 *3 (-368)) (-4 *1 (-329 *3)) - (-4 *3 (-363))))) (((*1 *2 *3) (-12 (-4 *1 (-349)) (-5 *3 (-564)) (-5 *2 (-1182 (-918) (-768)))))) -(((*1 *1 *1) (-4 *1 (-243))) - ((*1 *1 *1) - (-12 (-4 *2 (-172)) (-5 *1 (-289 *2 *3 *4 *5 *6 *7)) - (-4 *3 (-1235 *2)) (-4 *4 (-23)) (-14 *5 (-1 *3 *3 *4)) - (-14 *6 (-1 (-3 *4 "failed") *4 *4)) - (-14 *7 (-1 (-3 *3 "failed") *3 *3 *4)))) - 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(-4 *5 (-373 *4)) (-4 *6 (-373 *4)) + (-4 *7 (-989 *4)) (-4 *2 (-683 *7 *8 *9)) + (-5 *1 (-522 *4 *5 *6 *3 *7 *8 *9 *2)) (-4 *3 (-683 *4 *5 *6)) + (-4 *8 (-373 *7)) (-4 *9 (-373 *7)))) + ((*1 *1 *1) + (|partial| -12 (-4 *1 (-683 *2 *3 *4)) (-4 *2 (-1046)) + (-4 *3 (-373 *2)) (-4 *4 (-373 *2)) (-4 *2 (-363)))) + ((*1 *2 *2) + (|partial| -12 (-4 *3 (-363)) (-4 *3 (-172)) (-4 *4 (-373 *3)) + (-4 *5 (-373 *3)) (-5 *1 (-684 *3 *4 *5 *2)) + (-4 *2 (-683 *3 *4 *5)))) + ((*1 *1 *1) + (|partial| -12 (-5 *1 (-685 *2)) (-4 *2 (-363)) (-4 *2 (-1046)))) + ((*1 *1 *1) + (|partial| -12 (-4 *1 (-1117 *2 *3 *4 *5)) (-4 *3 (-1046)) + (-4 *4 (-238 *2 *3)) (-4 *5 (-238 *2 *3)) (-4 *3 (-363)))) + ((*1 *2 *2) (-12 (-5 *2 (-641 *3)) (-4 *3 (-847)) (-5 *1 (-1180 *3))))) +(((*1 *2 *2) + (-12 (-5 *2 (-940 *3)) (-4 *3 (-13 (-363) (-1194) (-999))) + (-5 *1 (-176 *3))))) (((*1 *2 *3) (-12 (-5 *3 (-1170)) (-4 *4 (-13 (-452) (-847) (-1035 (-564)) (-637 (-564)))) @@ -357,36 +299,101 @@ ((*1 *1 *2 *3) (-12 (-5 *2 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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"))) + (|:| -4172 + (-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 *2 (-1032)) (-5 *1 (-305))))) +(((*1 *2 *3 *4) + (|partial| -12 (-5 *4 (-1170)) (-4 *5 (-612 (-889 (-564)))) + (-4 *5 (-883 (-564))) + (-4 *5 (-13 (-847) (-1035 (-564)) (-452) (-637 (-564)))) + (-5 *2 (-2 (|:| |special| *3) (|:| |integrand| *3))) + (-5 *1 (-567 *5 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*3) (-768))) + (-4 *6 (-238 (-2780 *3) (-768))) (-14 *7 - (-1 (-112) (-2 (|:| -1495 *5) (|:| -2515 *6)) - (-2 (|:| -1495 *5) (|:| -2515 *6)))) + (-1 (-112) (-2 (|:| -3348 *5) (|:| -4309 *6)) + (-2 (|:| -3348 *5) (|:| -4309 *6)))) (-5 *1 (-461 *3 *4 *5 *6 *7 *2)) (-4 *5 (-847)) (-4 *2 (-946 *4 *6 (-861 *3))))) ((*1 *1 *1 *2) @@ -1746,46 +2002,7 @@ (-12 (-4 *1 (-1276 *3 *2)) (-4 *3 (-847)) (-4 *2 (-1046)))) ((*1 *1 *1 *2) (-12 (-5 *1 (-1282 *2 *3)) (-4 *2 (-1046)) (-4 *3 (-843))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-641 (-1088 (-379)))) (-5 *3 (-641 (-263))) - (-5 *1 (-261)))) - ((*1 *1 *2) (-12 (-5 *2 (-641 (-1088 (-379)))) (-5 *1 (-263)))) - ((*1 *2 *1 *2) (-12 (-5 *2 (-641 (-1088 (-379)))) (-5 *1 (-468)))) - ((*1 *2 *1) (-12 (-5 *2 (-641 (-1088 (-379)))) (-5 *1 (-468))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1060 *2 *3 *4)) (-4 *2 (-1046)) (-4 *3 (-790)) - (-4 *4 (-847))))) -(((*1 *1 *2) (-12 (-5 *2 (-1114)) (-5 *1 (-818))))) -(((*1 *1 *1) - (-12 (-5 *1 (-339 *2 *3 *4)) (-14 *2 (-641 (-1170))) - (-14 *3 (-641 (-1170))) (-4 *4 (-387)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-866 *3)) (-5 *2 (-564)))) - ((*1 *1 *1) (-4 *1 (-999))) - ((*1 *1 *2) (-12 (-5 *2 (-564)) (-4 *1 (-1009)))) - ((*1 *1 *2) (-12 (-5 *2 (-407 (-564))) (-4 *1 (-1009)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-1009)) (-5 *2 (-918)))) - ((*1 *1 *1) (-4 *1 (-1009)))) -(((*1 *2 *2) - (-12 (-5 *2 (-940 *3)) (-4 *3 (-13 (-363) (-1194) (-999))) - (-5 *1 (-176 *3))))) -(((*1 *1) (-5 *1 (-130)))) -(((*1 *2 *2) (-12 (-5 *2 (-379)) (-5 *1 (-1261)))) - ((*1 *2) (-12 (-5 *2 (-379)) (-5 *1 (-1261))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-13 (-363) (-147) (-1035 (-564)))) (-4 *5 (-1235 *4)) - (-5 *2 (-2 (|:| |ans| (-407 *5)) (|:| |nosol| (-112)))) - (-5 *1 (-1012 *4 *5)) (-5 *3 (-407 *5))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-1235 *2)) (-4 *2 (-1046))))) -(((*1 *2 *2) (-12 (-5 *2 (-685 *3)) (-4 *3 (-307)) (-5 *1 (-696 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-847) (-556))) (-5 *1 (-276 *3 *2)) - (-4 *2 (-13 (-430 *3) (-999)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-564)) (|has| *1 (-6 -4402)) (-4 *1 (-404)) - (-5 *2 (-918))))) -(((*1 *1 *2) - (-12 (-5 *2 (-641 (-918))) (-5 *1 (-1095 *3 *4)) (-14 *3 (-918)) - (-14 *4 (-918))))) +(((*1 *1 *1 *1 *1) (-4 *1 (-545)))) (((*1 *2 *3 *4) (-12 (-5 *4 (-641 (-48))) (-5 *2 (-418 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1235 (-48))))) @@ -1834,8 +2051,8 @@ (-12 (-4 *4 (-13 (-847) - (-10 -8 (-15 -2235 ((-1170) $)) - (-15 -3851 ((-3 $ "failed") (-1170)))))) + (-10 -8 (-15 -2373 ((-1170) $)) + (-15 -3826 ((-3 $ "failed") (-1170)))))) (-4 *5 (-790)) (-4 *7 (-556)) (-5 *2 (-418 *3)) (-5 *1 (-456 *4 *5 *6 *7 *3)) (-4 *6 (-556)) (-4 *3 (-946 *7 *5 *4)))) @@ -1884,13 +2101,13 @@ (-12 (-4 *4 (-790)) (-4 *5 (-13 (-847) - (-10 -8 (-15 -2235 ((-1170) $)) - (-15 -3851 ((-3 $ "failed") (-1170)))))) + (-10 -8 (-15 -2373 ((-1170) $)) + (-15 -3826 ((-3 $ "failed") (-1170)))))) (-4 *6 (-307)) (-5 *2 (-418 *3)) (-5 *1 (-727 *4 *5 *6 *3)) (-4 *3 (-946 (-949 *6) *4 *5)))) ((*1 *2 *3) (-12 (-4 *4 (-790)) - (-4 *5 (-13 (-847) (-10 -8 (-15 -2235 ((-1170) $))))) (-4 *6 (-556)) + (-4 *5 (-13 (-847) (-10 -8 (-15 -2373 ((-1170) $))))) (-4 *6 (-556)) (-5 *2 (-418 *3)) (-5 *1 (-729 *4 *5 *6 *3)) (-4 *3 (-946 (-407 (-949 *6)) *4 *5)))) ((*1 *2 *3) @@ -1926,27 +2143,30 @@ ((*1 *2 *1) (-12 (-5 *2 (-418 *1)) (-4 *1 (-1213)))) ((*1 *2 *3) (-12 (-5 *2 (-418 *3)) (-5 *1 (-1224 *3)) (-4 *3 (-1235 (-564)))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1202 *3 *4 *5 *6)) (-4 *3 (-556)) (-4 *4 (-790)) - (-4 *5 (-847)) (-4 *6 (-1060 *3 *4 *5)) (-5 *2 (-641 *5))))) +(((*1 *1 *2 *1 *1) + (-12 (-5 *2 (-1170)) (-5 *1 (-671 *3)) (-4 *3 (-1094))))) +(((*1 *2 *1 *2) (-12 (-5 *1 (-1023 *2)) (-4 *2 (-1209))))) +(((*1 *2 *2) + (-12 (-4 *3 (-452)) (-4 *4 (-790)) (-4 *5 (-847)) + (-5 *1 (-449 *3 *4 *5 *2)) (-4 *2 (-946 *3 *4 *5))))) +(((*1 *2 *1 *2) (-12 (-5 *2 (-641 (-1152))) (-5 *1 (-394))))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1209)) (-5 *1 (-599 *3)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1209)) (-5 *1 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+ (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -1357 (-641 (-330))))) (-5 *1 (-398 *3 *4 *5 *6)) (-14 *3 (-1170)) - (-14 *4 (-3 (|:| |fst| (-434)) (|:| -2966 "void"))) + (-14 *4 (-3 (|:| |fst| (-434)) (|:| -3037 "void"))) (-14 *5 (-641 (-1170))) (-14 *6 (-1174)))) ((*1 *1 *2) (-12 (-5 *2 (-641 (-330))) (-5 *1 (-398 *3 *4 *5 *6)) - (-14 *3 (-1170)) (-14 *4 (-3 (|:| |fst| (-434)) (|:| -2966 "void"))) + (-14 *3 (-1170)) (-14 *4 (-3 (|:| |fst| (-434)) (|:| -3037 "void"))) (-14 *5 (-641 (-1170))) (-14 *6 (-1174)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-5 *1 (-398 *3 *4 *5 *6)) (-14 *3 (-1170)) - (-14 *4 (-3 (|:| |fst| (-434)) (|:| -2966 "void"))) + (-14 *4 (-3 (|:| |fst| (-434)) (|:| -3037 "void"))) (-14 *5 (-641 (-1170))) (-14 *6 (-1174)))) ((*1 *1 *2) (-12 (-5 *2 (-331 *4)) (-4 *4 (-13 (-847) (-21))) @@ -3934,14 +4329,14 @@ ((*1 *1 *2) (-12 (-5 *2 (-434)) (-5 *1 (-437)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -1328 (-641 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -1357 (-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)) (|:| -1328 (-641 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -1357 (-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)))) @@ -4010,7 +4405,7 @@ (-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 (|:| -1762 *3) (|:| -2414 *4)))) + (-12 (-5 *2 (-641 (-2 (|:| -1838 *3) (|:| -2566 *4)))) (-4 *3 (-1046)) (-4 *4 (-723)) (-5 *1 (-732 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-564)) (-4 *1 (-760)))) ((*1 *1 *2) @@ -4019,25 +4414,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -3089 (-1088 (-840 (-225)))) (|:| |abserr| (-225)) + (|:| -4172 (-1088 (-840 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| |mdnia| (-2 (|:| |fn| (-316 (-225))) - (|:| -3089 (-641 (-1088 (-840 (-225))))) + (|:| -4172 (-641 (-1088 (-840 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))))) (-5 *1 (-766)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-316 (-225))) - (|:| -3089 (-641 (-1088 (-840 (-225))))) (|:| |abserr| (-225)) + (|:| -4172 (-641 (-1088 (-840 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-766)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -3089 (-1088 (-840 (-225)))) (|:| |abserr| (-225)) + (|:| -4172 (-1088 (-840 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-766)))) ((*1 *2 *3) (-12 (-5 *2 (-771)) (-5 *1 (-770 *3)) (-4 *3 (-1209)))) @@ -4055,23 +4450,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-316 (-225))) (|:| -3258 (-641 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -3286 (-641 (-225))) (|:| |lb| (-641 (-840 (-225)))) (|:| |cf| (-641 (-316 (-225)))) (|:| |ub| (-641 (-840 (-225)))))) (|:| |lsa| (-2 (|:| |lfn| (-641 (-316 (-225)))) - (|:| -3258 (-641 (-225))))))) + (|:| -3286 (-641 (-225))))))) (-5 *1 (-838)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3258 (-641 (-225))))) + (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3286 (-641 (-225))))) (-5 *1 (-838)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-316 (-225))) (|:| -3258 (-641 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -3286 (-641 (-225))) (|:| |lb| (-641 (-840 (-225)))) (|:| |cf| (-641 (-316 (-225)))) (|:| |ub| (-641 (-840 (-225)))))) (-5 *1 (-838)))) @@ -4141,7 +4536,7 @@ ((*1 *1 *2) (-12 (-5 *2 (-1170)) (-5 *1 (-1169)))) ((*1 *2 *1) (-12 (-5 *2 (-1182 (-1170) (-437))) (-5 *1 (-1174)))) ((*1 *2 *1) (-12 (-5 *2 (-1152)) (-5 *1 (-1175)))) - ((*1 *2 *1) (-12 (-5 *2 (-1170)) (-5 *1 (-1175)))) + ((*1 *2 *1) (-12 (-5 *2 (-506)) (-5 *1 (-1175)))) ((*1 *2 *1) (-12 (-5 *2 (-225)) (-5 *1 (-1175)))) ((*1 *2 *1) (-12 (-5 *2 (-564)) 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(-349)) (-5 *2 (-418 (-1166 (-1166 *4)))) + (-5 *1 (-1207 *4)) (-5 *3 (-1166 (-1166 *4)))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-768)) (-5 *2 (-407 (-564))) (-5 *1 (-225)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-768)) (-5 *2 (-407 (-564))) (-5 *1 (-225)))) + ((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-768)) (-5 *2 (-407 (-564))) (-5 *1 (-379)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-768)) (-5 *2 (-407 (-564))) (-5 *1 (-379))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-144))))) (((*1 *1 *2) (-12 (-5 *2 (-641 *1)) (-4 *1 (-452)))) ((*1 *1 *1 *1) (-4 *1 (-452))) ((*1 *2 *3) @@ -10127,12 +9359,9 @@ ((*1 *2 *2 *1) (-12 (-4 *1 (-1060 *2 *3 *4)) (-4 *2 (-1046)) (-4 *3 (-790)) (-4 *4 (-847)) (-4 *2 (-452))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1209)) (-5 *1 (-1126 *4 *2)) - (-4 *2 (-13 (-602 (-564) *4) (-10 -7 (-6 -4411) (-6 -4412)))))) - ((*1 *2 *2) - (-12 (-4 *3 (-847)) (-4 *3 (-1209)) (-5 *1 (-1126 *3 *2)) - (-4 *2 (-13 (-602 (-564) *3) (-10 -7 (-6 -4411) (-6 -4412))))))) +(((*1 *1 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|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"))) - (|:| -3089 - (-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)))) + (-12 (-4 *1 (-691 *3)) (-4 *3 (-1094)) + (-5 *2 (-641 (-2 (|:| -2577 *3) (|:| -3861 (-768)))))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1166 *1)) (-5 *4 (-1170)) (-4 *1 (-27)) + (-5 *2 (-641 *1)))) + ((*1 *2 *3) (-12 (-5 *3 (-1166 *1)) (-4 *1 (-27)) (-5 *2 (-641 *1)))) + ((*1 *2 *3) (-12 (-5 *3 (-949 *1)) (-4 *1 (-27)) (-5 *2 (-641 *1)))) + ((*1 *2 *1 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(-5 *3 (-1152)) (-5 *2 (-1264)) (-5 *1 (-1186 *4 *5)) + (-4 *4 (-1094)) (-4 *5 (-1094))))) +(((*1 *1 *2) + (-12 (-5 *2 (-316 *3)) (-4 *3 (-13 (-1046) (-847))) + (-5 *1 (-223 *3 *4)) (-14 *4 (-641 (-1170)))))) +(((*1 *2) (-12 (-5 *2 (-1264)) (-5 *1 (-1173)))) + ((*1 *2 *3) (-12 (-5 *3 (-1170)) (-5 *2 (-1264)) (-5 *1 (-1173)))) + ((*1 *2 *3 *1) (-12 (-5 *3 (-1170)) (-5 *2 (-1264)) (-5 *1 (-1173))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-452)) (-4 *6 (-790)) (-4 *7 (-847)) + (-4 *3 (-1060 *5 *6 *7)) (-5 *2 (-641 *4)) + (-5 *1 (-1102 *5 *6 *7 *3 *4)) (-4 *4 (-1066 *5 *6 *7 *3))))) +(((*1 *2 *1) (-12 (-4 *1 (-794 *2)) (-4 *2 (-172)))) + ((*1 *2 *1) (-12 (-4 *1 (-994 *2)) (-4 *2 (-172))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-980 *2)) (-4 *2 (-1194))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1 *3 *3 (-564))) (-4 *3 (-1046)) (-5 *1 (-99 *3)))) + ((*1 *1 *2 *2) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1046)) (-5 *1 (-99 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1046)) (-5 *1 (-99 *3))))) (((*1 *2 *1) (-12 (-5 *2 (-1098)) (-5 *1 (-52))))) +(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-1210 *3)) (-4 *3 (-1094))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-847) (-556))) (-5 *1 (-276 *3 *2)) @@ -10319,45 +9560,20 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *3) (-12 (-5 *3 (-1152)) (-5 *2 (-379)) (-5 *1 (-783))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-847) (-452))) (-5 *1 (-1200 *3 *2)) - (-4 *2 (-13 (-430 *3) (-1194)))))) -(((*1 *1 *1) (-12 (-4 *1 (-670 *2)) (-4 *2 (-1209))))) -(((*1 *2 *3 *4 *5 *6 *5) - (-12 (-5 *4 (-169 (-225))) (-5 *5 (-564)) (-5 *6 (-1152)) - (-5 *3 (-225)) (-5 *2 (-1032)) (-5 *1 (-755))))) (((*1 *1 *2) (-12 (-5 *2 (-641 *1)) (-4 *1 (-452)))) ((*1 *1 *1 *1) (-4 *1 (-452)))) -(((*1 *2 *1) - (-12 (-4 *1 (-329 *3)) (-4 *3 (-363)) (-4 *3 (-368)) - (-5 *2 (-1166 *3))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-849 *2)) (-4 *2 (-1046)) (-4 *2 (-363))))) -(((*1 *2 *1) (-12 (-4 *1 (-166 *2)) (-4 *2 (-172)) (-4 *2 (-1194)))) - ((*1 *2 *1) (-12 (-5 *1 (-331 *2)) (-4 *2 (-847)))) - ((*1 *2 *1) (-12 (-5 *2 (-641 *3)) (-5 *1 (-610 *3)) (-4 *3 (-847))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-768)) (-4 *1 (-374 *3 *4)) (-4 *3 (-847)) - (-4 *4 (-172)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-768)) (-4 *1 (-1280 *3 *4)) (-4 *3 (-847)) - (-4 *4 (-1046))))) -(((*1 *2 *2) - (-12 (-5 *2 (-641 *6)) (-4 *6 (-1060 *3 *4 *5)) (-4 *3 (-452)) - (-4 *3 (-556)) (-4 *4 (-790)) (-4 *5 (-847)) - (-5 *1 (-974 *3 *4 *5 *6)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-641 *7)) (-5 *3 (-112)) (-4 *7 (-1060 *4 *5 *6)) - (-4 *4 (-452)) (-4 *4 (-556)) (-4 *5 (-790)) (-4 *6 (-847)) - (-5 *1 (-974 *4 *5 *6 *7))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1166 (-949 *6))) (-4 *6 (-556)) - (-4 *2 (-946 (-407 (-949 *6)) *5 *4)) (-5 *1 (-729 *5 *4 *6 *2)) - (-4 *5 (-790)) - (-4 *4 (-13 (-847) (-10 -8 (-15 -2235 ((-1170) $)))))))) -(((*1 *2 *2) - (-12 (-5 *2 (-940 *3)) (-4 *3 (-13 (-363) (-1194) (-999))) - (-5 *1 (-176 *3))))) +(((*1 *2) (-12 (-5 *2 (-1264)) 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*2 *2) (-12 (-4 *3 (-13 (-847) (-556))) (-5 *1 (-276 *3 *2)) @@ -10441,45 +9632,40 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *3 *3 *4 *4 *5 *5 *3 *3 *4 *4 *5 *5 *3 *3 *4 *4 *5 *5 *3 *4 *4 - *4 *6 *4) - (-12 (-5 *4 (-564)) (-5 *5 (-685 (-225))) (-5 *6 (-671 (-225))) - (-5 *3 (-225)) (-5 *2 (-1032)) (-5 *1 (-747))))) -(((*1 *2 *1 *3) - (-12 (-4 *1 (-342 *4 *3 *5)) (-4 *4 (-1213)) (-4 *3 (-1235 *4)) - (-4 *5 (-1235 (-407 *3))) (-5 *2 (-112)))) - ((*1 *2 *1 *3) - (-12 (-4 *1 (-342 *3 *4 *5)) (-4 *3 (-1213)) (-4 *4 (-1235 *3)) - (-4 *5 (-1235 (-407 *4))) (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-4 *1 (-342 *3 *4 *5)) (-4 *3 (-1213)) (-4 *4 (-1235 *3)) - (-4 *5 (-1235 (-407 *4))) (-5 *2 (-112))))) -(((*1 *1 *2 *3) (-12 (-5 *2 (-768)) (-5 *3 (-112)) (-5 *1 (-110)))) - ((*1 *2 *2) (-12 (-5 *2 (-918)) (|has| *1 (-6 -4402)) (-4 *1 (-404)))) - ((*1 *2) (-12 (-4 *1 (-404)) (-5 *2 (-918))))) -(((*1 *2 *3) - (-12 (-5 *3 (-294 (-949 (-564)))) - 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(-316 (-225)))) (|:| |yinit| (-641 (-225))) + (|:| |intvals| (-641 (-225))) (|:| |g| (-316 (-225))) + (|:| |abserr| (-225)) (|:| |relerr| (-225)))) + (-5 *2 (-1032))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-641 *3)) (-4 *3 (-307)) (-5 *1 (-179 *3))))) +(((*1 *2 *3 *4 *4 *4 *3 *4 *3) + (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1032)) + (-5 *1 (-748))))) +(((*1 *2) + (-12 (-4 *1 (-342 *3 *4 *5)) (-4 *3 (-1213)) (-4 *4 (-1235 *3)) + (-4 *5 (-1235 (-407 *4))) (-5 *2 (-112))))) +(((*1 *2 *2 *1) + (-12 (-4 *1 (-1202 *3 *4 *5 *2)) (-4 *3 (-556)) (-4 *4 (-790)) + (-4 *5 (-847)) (-4 *2 (-1060 *3 *4 *5))))) +(((*1 *1) (-5 *1 (-157)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1 *2 *2)) (-4 *2 (-1250 *4)) (-5 *1 (-1252 *4 *2)) + (-4 *4 (-38 (-407 (-564))))))) +(((*1 *1 *1) (-4 *1 (-95))) + ((*1 *2 *2) (-12 (-4 *3 (-13 (-847) (-556))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-999))))) ((*1 *2 *2) @@ -11114,16 +9998,16 @@ ((*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 (-980 *4)))) - ((*1 *1 *1) - (-12 (-5 *1 (-339 *2 *3 *4)) (-14 *2 (-641 (-1170))) - (-14 *3 (-641 (-1170))) (-4 *4 (-387)))) - ((*1 *1 *1) (-4 *1 (-493))) ((*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 *1) + (-12 (-4 *1 (-1035 (-564))) (-4 *1 (-302)) (-5 *2 (-112)))) + ((*1 *2 *1) (-12 (-4 *1 (-545)) (-5 *2 (-112)))) + ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-902 *3)) (-4 *3 (-1094))))) (((*1 *1 *1) (-12 (-4 *1 (-119 *2)) (-4 *2 (-1209)))) ((*1 *1 *1) (-12 (-5 *1 (-668 *2)) (-4 *2 (-847)))) ((*1 *1 *1) (-12 (-5 *1 (-673 *2)) (-4 *2 (-847)))) @@ -11132,80 +10016,38 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-845) (-363))) (-5 *1 (-1056 *2 *3)) (-4 *3 (-1235 *2))))) -(((*1 *2 *1) - (-12 (-5 *2 (-174 (-407 (-564)))) (-5 *1 (-117 *3)) (-14 *3 (-564)))) - ((*1 *1 *2 *3 *3) - (-12 (-5 *3 (-1150 *2)) (-4 *2 (-307)) (-5 *1 (-174 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(|:| |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"))) - (|:| -3089 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated"))))) - (-5 *1 (-559))))) -(((*1 *2 *2) - (|partial| -12 (-5 *2 (-1166 *3)) (-4 *3 (-349)) (-5 *1 (-357 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1242 *3 *4)) (-4 *3 (-1046)) (-4 *4 (-1219 *3)) - (-5 *2 (-407 (-564)))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-980 *2)) (-4 *2 (-1194))))) -(((*1 *2 *3) - (-12 (-5 *3 (-481 *4 *5)) (-14 *4 (-641 (-1170))) (-4 *5 (-1046)) - (-5 *2 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*3 (-407 *5)) (-4 *4 (-1213)) (-4 *5 (-1235 *4)) (-5 *1 (-148 *4 *5 *2)) (-4 *2 (-1235 *3)))) @@ -11321,14 +10163,9 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *1 *2 *3) - (-12 (-4 *1 (-382 *3 *2)) (-4 *3 (-1046)) (-4 *2 (-1094)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-564)) (-5 *2 (-1150 *3)) (-5 *1 (-1154 *3)) - (-4 *3 (-1046)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-816 *4)) (-4 *4 (-847)) (-4 *1 (-1276 *4 *3)) - (-4 *3 (-1046))))) +(((*1 *2 *3) + (-12 (-4 *4 (-847)) (-5 *2 (-641 (-641 *4))) (-5 *1 (-1180 *4)) + (-5 *3 (-641 *4))))) (((*1 *1 *1) (-12 (-4 *1 (-119 *2)) (-4 *2 (-1209)))) ((*1 *1 *1) (-12 (-5 *1 (-668 *2)) (-4 *2 (-847)))) ((*1 *1 *1) (-12 (-5 *1 (-673 *2)) (-4 *2 (-847)))) @@ -11337,56 +10174,66 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-845) (-363))) (-5 *1 (-1056 *2 *3)) (-4 *3 (-1235 *2))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-849 *2)) (-4 *2 (-1046)) (-4 *2 (-363))))) (((*1 *2 *3) - (-12 (-5 *3 (-316 *4)) (-4 *4 (-13 (-825) (-847) (-1046))) - (-5 *2 (-1152)) (-5 *1 (-823 *4)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-316 *5)) (-5 *4 (-112)) - (-4 *5 (-13 (-825) (-847) (-1046))) (-5 *2 (-1152)) - (-5 *1 (-823 *5)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-819)) (-5 *4 (-316 *5)) - (-4 *5 (-13 (-825) (-847) (-1046))) (-5 *2 (-1264)) - (-5 *1 (-823 *5)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-819)) (-5 *4 (-316 *6)) (-5 *5 (-112)) - (-4 *6 (-13 (-825) (-847) (-1046))) (-5 *2 (-1264)) - (-5 *1 (-823 *6)))) - ((*1 *2 *1) (-12 (-4 *1 (-825)) (-5 *2 (-1152)))) - ((*1 *2 *1 *3) (-12 (-4 *1 (-825)) (-5 *3 (-112)) (-5 *2 (-1152)))) - ((*1 *2 *3 *1) (-12 (-4 *1 (-825)) (-5 *3 (-819)) (-5 *2 (-1264)))) - ((*1 *2 *3 *1 *4) - (-12 (-4 *1 (-825)) (-5 *3 (-819)) (-5 *4 (-112)) (-5 *2 (-1264))))) + (-12 + (-5 *3 + (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) + (|:| -4172 (-1088 (-840 (-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"))) + (|:| -4172 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))) + (-5 *1 (-559))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-1259 (-1259 (-564)))) (-5 *3 (-918)) (-5 *1 (-466))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-407 (-564))) (-4 *5 (-790)) (-4 *6 (-847)) - (-4 *7 (-556)) (-4 *8 (-946 *7 *5 *6)) - (-5 *2 (-2 (|:| -2515 (-768)) (|:| -1762 *9) (|:| |radicand| *9))) - (-5 *1 (-950 *5 *6 *7 *8 *9)) (-5 *4 (-768)) - (-4 *9 - (-13 (-363) - (-10 -8 (-15 -3742 ($ *8)) (-15 -1625 (*8 $)) (-15 -1634 (*8 $)))))))) -(((*1 *2 *3 *2) (-12 (-5 *3 (-768)) (-5 *1 (-853 *2)) (-4 *2 (-172))))) + (-12 (-5 *3 (-641 (-564))) (-5 *4 (-902 (-564))) + (-5 *2 (-685 (-564))) (-5 *1 (-589)))) + ((*1 *2 *3) + (-12 (-5 *3 (-641 (-564))) (-5 *2 (-641 (-685 (-564)))) + (-5 *1 (-589)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-641 (-564))) (-5 *4 (-641 (-902 (-564)))) + (-5 *2 (-641 (-685 (-564)))) (-5 *1 (-589))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-641 *3)) (-4 *3 (-307)) (-5 *1 (-179 *3))))) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) + (-12 (-5 *3 (-1 (-379) (-379))) (-5 *4 (-379)) + (-5 *2 + (-2 (|:| -3393 *4) (|:| -2039 *4) (|:| |totalpts| (-564)) + (|:| |success| (-112)))) + (-5 *1 (-786)) (-5 *5 (-564))))) +(((*1 *2 *3) (-12 (-5 *3 (-1152)) (-5 *2 (-918)) (-5 *1 (-783))))) (((*1 *2 *3 *4) - (-12 (-4 *5 (-1094)) (-4 *3 (-897 *5)) (-5 *2 (-685 *3)) - (-5 *1 (-688 *5 *3 *6 *4)) (-4 *6 (-373 *3)) - (-4 *4 (-13 (-373 *5) (-10 -7 (-6 -4411))))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-641 (-859))) (-5 *1 (-859)))) + (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1032)) (-5 *1 (-755))))) +(((*1 *2 *1) (-12 (-5 *2 (-407 (-564))) (-5 *1 (-108)))) + ((*1 *2 *1) (-12 (-5 *2 (-407 (-564))) (-5 *1 (-217)))) + ((*1 *2 *1) (-12 (-5 *2 (-407 (-564))) (-5 *1 (-487)))) + ((*1 *1 *1) (-12 (-4 *1 (-989 *2)) (-4 *2 (-556)) (-4 *2 (-307)))) ((*1 *2 *1) - (-12 - (-5 *2 - (-2 (|:| -1550 (-641 (-859))) (|:| -2850 (-641 (-859))) - (|:| |presup| (-641 (-859))) (|:| -1797 (-641 (-859))) - (|:| |args| (-641 (-859))))) - (-5 *1 (-1170))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-452)) (-4 *4 (-556)) - (-5 *2 (-2 (|:| |coef2| *3) (|:| -2060 *4))) (-5 *1 (-966 *4 *3)) - (-4 *3 (-1235 *4))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-363)) (-5 *1 (-763 *2 *3)) (-4 *2 (-705 *3)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-849 *2)) (-4 *2 (-1046)) (-4 *2 (-363))))) -(((*1 *2 *3) - (-12 (-5 *2 (-564)) (-5 *1 (-445 *3)) (-4 *3 (-404)) (-4 *3 (-1046))))) + (-12 (-5 *2 (-407 (-564))) (-5 *1 (-1001 *3)) (-14 *3 (-564)))) + ((*1 *1 *1) (-4 *1 (-1055)))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-847) (-556))) (-5 *1 (-276 *3 *2)) @@ -11403,78 +10250,51 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *1) (-12 (-4 *1 (-1128 *3)) (-4 *3 (-1046)) (-5 *2 (-112))))) -(((*1 *1 *1) - (-12 (|has| *1 (-6 -4412)) (-4 *1 (-373 *2)) (-4 *2 (-1209)) - (-4 *2 (-847)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3 *3)) (|has| *1 (-6 -4412)) - (-4 *1 (-373 *3)) (-4 *3 (-1209))))) -(((*1 *1 *1 *2) - (-12 (-4 *1 (-973 *3 *4 *2 *5)) (-4 *3 (-1046)) (-4 *4 (-790)) - (-4 *2 (-847)) (-4 *5 (-1060 *3 *4 *2))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-641 (-564))) (-5 *4 (-902 (-564))) - (-5 *2 (-685 (-564))) (-5 *1 (-589)))) - ((*1 *2 *3) - (-12 (-5 *3 (-641 (-564))) (-5 *2 (-641 (-685 (-564)))) - (-5 *1 (-589)))) + (-12 (-4 *5 (-452)) (-4 *6 (-790)) (-4 *7 (-847)) + (-4 *3 (-1060 *5 *6 *7)) + (-5 *2 (-641 (-2 (|:| |val| (-112)) (|:| -3991 *4)))) + (-5 *1 (-1102 *5 *6 *7 *3 *4)) (-4 *4 (-1066 *5 *6 *7 *3))))) +(((*1 *1 *2 *3) + (-12 (-5 *1 (-961 *2 *3)) (-4 *2 (-1094)) (-4 *3 (-1094))))) +(((*1 *1 *2 *3) + (-12 (-4 *1 (-382 *3 *2)) (-4 *3 (-1046)) (-4 *2 (-1094)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-641 (-564))) (-5 *4 (-641 (-902 (-564)))) - (-5 *2 (-641 (-685 (-564)))) (-5 *1 (-589))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *2 *6)) (-5 *4 (-1 *6 *5)) (-4 *5 (-1094)) - (-4 *6 (-1094)) (-4 *2 (-1094)) (-5 *1 (-676 *5 *6 *2))))) + (-12 (-5 *4 (-564)) (-5 *2 (-1150 *3)) (-5 *1 (-1154 *3)) + (-4 *3 (-1046)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-816 *4)) (-4 *4 (-847)) (-4 *1 (-1276 *4 *3)) + (-4 *3 (-1046))))) +(((*1 *1 *2 *3) + (-12 (-5 *3 (-641 (-506))) (-5 *2 (-506)) (-5 *1 (-483))))) (((*1 *2 *3 *1) (|partial| -12 (-4 *1 (-36 *3 *4)) (-4 *3 (-1094)) (-4 *4 (-1094)) - (-5 *2 (-2 (|:| -1327 *3) (|:| -2423 *4)))))) -(((*1 *1 *1 *1) (-5 *1 (-225))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-225)) (-5 *1 (-226)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-169 (-225))) (-5 *1 (-226)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-13 (-847) (-556))) (-5 *1 (-431 *3 *2)) - (-4 *2 (-430 *3)))) - ((*1 *2 *3 *3) - (-12 (-5 *3 (-768)) (-5 *2 (-1 (-379))) (-5 *1 (-1037)))) - ((*1 *1 *1 *1) (-4 *1 (-1133)))) + (-5 *2 (-2 (|:| -1354 *3) (|:| -2577 *4)))))) +(((*1 *2 *3) + (|partial| -12 (-5 *3 (-1259 *4)) (-4 *4 (-637 (-564))) + (-5 *2 (-1259 (-564))) (-5 *1 (-1286 *4))))) +(((*1 *2 *3) + (-12 (-5 *3 (-407 *5)) (-4 *5 (-1235 *4)) (-4 *4 (-556)) + (-4 *4 (-1046)) (-4 *2 (-1250 *4)) (-5 *1 (-1253 *4 *5 *6 *2)) + (-4 *6 (-652 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-819))))) +(((*1 *1 *1 *1 *2) + (|partial| -12 (-5 *2 (-112)) (-5 *1 (-594 *3)) (-4 *3 (-1046))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-452) (-847) (-1035 (-564)) (-637 (-564)))) (-5 *1 (-420 *3 *2 *4 *5)) (-4 *2 (-13 (-27) (-1194) (-430 *3))) (-14 *4 (-1170)) (-14 *5 *2))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-452) (-847) (-1035 (-564)) (-637 (-564)))) - (-4 *2 (-13 (-27) (-1194) (-430 *3) (-10 -8 (-15 -3742 ($ *4))))) + (-4 *2 (-13 (-27) (-1194) (-430 *3) (-10 -8 (-15 -3713 ($ *4))))) (-4 *4 (-845)) (-4 *5 (-13 (-1237 *2 *4) (-363) (-1194) - (-10 -8 (-15 -4117 ($ $)) (-15 -3128 ($ $))))) + (-10 -8 (-15 -1721 ($ $)) (-15 -2397 ($ $))))) (-5 *1 (-422 *3 *2 *4 *5 *6 *7)) (-4 *6 (-980 *5)) (-14 *7 (-1170))))) -(((*1 *2 *3) - (-12 (-4 *4 (-1046)) - (-4 *2 (-13 (-404) (-1035 *4) (-363) (-1194) (-284))) - (-5 *1 (-443 *4 *3 *2)) (-4 *3 (-1235 *4)))) - ((*1 *1 *1) (-4 *1 (-545))) - ((*1 *2 *1) (-12 (-5 *2 (-918)) (-5 *1 (-668 *3)) (-4 *3 (-847)))) - ((*1 *2 *1) (-12 (-5 *2 (-918)) (-5 *1 (-673 *3)) (-4 *3 (-847)))) - ((*1 *2 *1) (-12 (-5 *2 (-768)) (-5 *1 (-816 *3)) (-4 *3 (-847)))) - ((*1 *2 *1) (-12 (-5 *2 (-768)) (-5 *1 (-890 *3)) (-4 *3 (-847)))) - ((*1 *2 *1) (-12 (-4 *1 (-992 *3)) (-4 *3 (-1209)) (-5 *2 (-768)))) - ((*1 *2 *1) (-12 (-5 *2 (-768)) (-5 *1 (-1206 *3)) (-4 *3 (-1209)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1257 *2)) (-4 *2 (-1209)) (-4 *2 (-999)) - (-4 *2 (-1046))))) -(((*1 *2 *2) - (-12 (-4 *3 (-452)) (-4 *4 (-790)) (-4 *5 (-847)) - (-4 *6 (-1060 *3 *4 *5)) (-5 *1 (-622 *3 *4 *5 *6 *7 *2)) - (-4 *7 (-1066 *3 *4 *5 *6)) (-4 *2 (-1103 *3 *4 *5 *6))))) -(((*1 *2 *3) - (-12 (-5 *3 (-641 *4)) (-4 *4 (-847)) (-5 *2 (-641 (-660 *4 *5))) - (-5 *1 (-625 *4 *5 *6)) (-4 *5 (-13 (-172) (-714 (-407 (-564))))) - (-14 *6 (-918))))) -(((*1 *2) - (-12 (-4 *1 (-342 *3 *4 *5)) (-4 *3 (-1213)) (-4 *4 (-1235 *3)) - (-4 *5 (-1235 (-407 *4))) (-5 *2 (-685 (-407 *4)))))) -(((*1 *1 *1) (-4 *1 (-95))) +(((*1 *1 *1) + (-12 (-5 *1 (-594 *2)) (-4 *2 (-38 (-407 (-564)))) (-4 *2 (-1046))))) +(((*1 *1 *1) (-4 *1 (-95))) ((*1 *1 *1 *1) (-5 *1 (-225))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-847) (-556))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-999))))) @@ -11484,12 +10304,60 @@ ((*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 (-980 *4)))) + ((*1 *1 *1) + (-12 (-5 *1 (-339 *2 *3 *4)) (-14 *2 (-641 (-1170))) + (-14 *3 (-641 (-1170))) (-4 *4 (-387)))) + ((*1 *1 *1 *1) (-5 *1 (-379))) ((*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 *3 *4) + (-12 (-5 *3 (-649 (-407 *6))) (-5 *4 (-1 (-641 *5) *6)) + (-4 *5 (-13 (-363) (-147) (-1035 (-564)) (-1035 (-407 (-564))))) + (-4 *6 (-1235 *5)) (-5 *2 (-641 (-407 *6))) (-5 *1 (-809 *5 *6)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-649 (-407 *7))) (-5 *4 (-1 (-641 *6) *7)) + (-5 *5 (-1 (-418 *7) *7)) + (-4 *6 (-13 (-363) (-147) (-1035 (-564)) (-1035 (-407 (-564))))) + (-4 *7 (-1235 *6)) (-5 *2 (-641 (-407 *7))) (-5 *1 (-809 *6 *7)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-650 *6 (-407 *6))) (-5 *4 (-1 (-641 *5) *6)) + (-4 *5 (-13 (-363) (-147) (-1035 (-564)) (-1035 (-407 (-564))))) + (-4 *6 (-1235 *5)) (-5 *2 (-641 (-407 *6))) (-5 *1 (-809 *5 *6)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-650 *7 (-407 *7))) (-5 *4 (-1 (-641 *6) *7)) + (-5 *5 (-1 (-418 *7) *7)) + (-4 *6 (-13 (-363) (-147) (-1035 (-564)) (-1035 (-407 (-564))))) + (-4 *7 (-1235 *6)) (-5 *2 (-641 (-407 *7))) (-5 *1 (-809 *6 *7)))) + ((*1 *2 *3) + (-12 (-5 *3 (-649 (-407 *5))) (-4 *5 (-1235 *4)) (-4 *4 (-27)) + (-4 *4 (-13 (-363) (-147) (-1035 (-564)) (-1035 (-407 (-564))))) + (-5 *2 (-641 (-407 *5))) (-5 *1 (-809 *4 *5)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-649 (-407 *6))) (-5 *4 (-1 (-418 *6) *6)) + (-4 *6 (-1235 *5)) (-4 *5 (-27)) + (-4 *5 (-13 (-363) (-147) (-1035 (-564)) (-1035 (-407 (-564))))) + (-5 *2 (-641 (-407 *6))) (-5 *1 (-809 *5 *6)))) + ((*1 *2 *3) + (-12 (-5 *3 (-650 *5 (-407 *5))) (-4 *5 (-1235 *4)) (-4 *4 (-27)) + (-4 *4 (-13 (-363) (-147) (-1035 (-564)) (-1035 (-407 (-564))))) + (-5 *2 (-641 (-407 *5))) (-5 *1 (-809 *4 *5)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-650 *6 (-407 *6))) (-5 *4 (-1 (-418 *6) *6)) + (-4 *6 (-1235 *5)) (-4 *5 (-27)) + (-4 *5 (-13 (-363) (-147) (-1035 (-564)) (-1035 (-407 (-564))))) + (-5 *2 (-641 (-407 *6))) (-5 *1 (-809 *5 *6))))) +(((*1 *2 *1) (-12 (-4 *1 (-244 *2)) (-4 *2 (-1209)))) + ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-1090)))) + ((*1 *2 *1) + (|partial| -12 (-4 *1 (-1202 *3 *4 *5 *2)) (-4 *3 (-556)) + (-4 *4 (-790)) (-4 *5 (-847)) (-4 *2 (-1060 *3 *4 *5)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-768)) (-4 *1 (-1247 *3)) (-4 *3 (-1209)))) + ((*1 *2 *1) (-12 (-4 *1 (-1247 *2)) (-4 *2 (-1209))))) (((*1 *1 *1 *2 *3) (-12 (-5 *2 (-641 (-1170))) (-5 *3 (-1170)) (-5 *1 (-536)))) ((*1 *2 *3 *2) @@ -11501,36 +10369,57 @@ ((*1 *2 *3 *2 *4) (-12 (-5 *4 (-641 (-1170))) (-5 *2 (-1170)) (-5 *1 (-701 *3)) (-4 *3 (-612 (-536)))))) -(((*1 *2 *1) (-12 (-4 *1 (-244 *2)) (-4 *2 (-1209)))) - ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-1090)))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-1259 (-1170))) (-5 *3 (-1259 (-453 *4 *5 *6 *7))) + (-5 *1 (-453 *4 *5 *6 *7)) (-4 *4 (-172)) (-14 *5 (-918)) + (-14 *6 (-641 (-1170))) (-14 *7 (-1259 (-685 *4))))) + ((*1 *1 *2 *3) + (-12 (-5 *2 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(-307)) (-5 *1 (-913 *3 *4 *5 *6)))) ((*1 *2 *3) - (-12 (-5 *2 (-407 (-564))) (-5 *1 (-1005 *3)) (-4 *3 (-1035 *2))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1114)) (-5 *2 (-1264)) (-5 *1 (-828))))) + (-12 (-5 *3 (-641 *2)) (-4 *2 (-946 *6 *4 *5)) + (-5 *1 (-913 *4 *5 *6 *2)) (-4 *4 (-790)) (-4 *5 (-847)) + (-4 *6 (-307))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-847) (-556))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-999))))) @@ -11741,47 +10634,52 @@ (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3)))) ((*1 *1 *1) (-4 *1 (-1197)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-418 *5)) (-4 *5 (-556)) +(((*1 *2 *1) + (-12 (-4 *3 (-452)) (-4 *4 (-847)) (-4 *5 (-790)) (-5 *2 (-641 *6)) + (-5 *1 (-984 *3 *4 *5 *6)) (-4 *6 (-946 *3 *5 *4))))) +(((*1 *1 *1) + (-12 (-5 *1 (-594 *2)) (-4 *2 (-38 (-407 (-564)))) (-4 *2 (-1046))))) +(((*1 *2 *3) + (-12 (-5 *3 (-641 (-564))) (-5 *2 (-1172 (-407 (-564)))) + (-5 *1 (-190))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1007 *3)) (-4 *3 (-1209)) (-5 *2 (-641 *3))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-768)) + (-4 *3 (-13 (-307) (-10 -8 (-15 -3948 ((-418 $) $))))) + (-4 *4 (-1235 *3)) (-5 *1 (-499 *3 *4 *5)) (-4 *5 (-409 *3 *4))))) +(((*1 *2 *3 *1) + (-12 (-5 *3 (-641 *4)) (-4 *4 (-1094)) (-4 *4 (-1209)) (-5 *2 (-112)) + (-5 *1 (-1150 *4))))) +(((*1 *2 *2 *2 *3) + (-12 (-5 *2 (-685 *3)) (-4 *3 (-1046)) (-5 *1 (-686 *3))))) +(((*1 *2 *3) + (|partial| -12 + (-5 *3 + (-2 (|:| |xinit| (-225)) (|:| |xend| (-225)) + (|:| |fn| (-1259 (-316 (-225)))) (|:| |yinit| (-641 (-225))) + (|:| |intvals| (-641 (-225))) (|:| |g| (-316 (-225))) + (|:| |abserr| (-225)) (|:| |relerr| (-225)))) + (-5 *2 + (-2 (|:| |stiffness| (-379)) (|:| |stability| (-379)) + (|:| |expense| (-379)) (|:| |accuracy| (-379)) + (|:| |intermediateResults| (-379)))) + (-5 *1 (-800))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) + (|:| -4172 (-1088 (-840 (-225)))) (|:| |abserr| (-225)) + (|:| |relerr| (-225)))) + (-5 *2 (-564)) (-5 *1 (-204))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-685 *6)) (-5 *5 (-1 (-418 (-1166 *6)) (-1166 *6))) + (-4 *6 (-363)) (-5 *2 - (-2 (|:| -2515 (-768)) (|:| -1762 *5) (|:| |radicand| (-641 *5)))) - (-5 *1 (-320 *5)) (-5 *4 (-768)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-999)) (-5 *2 (-564))))) -(((*1 *2 *2) - (-12 (-5 *2 (-641 *3)) (-4 *3 (-1235 (-564))) (-5 *1 (-486 *3))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-683 *2 *3 *4)) (-4 *2 (-1046)) (-4 *3 (-373 *2)) - (-4 *4 (-373 *2))))) -(((*1 *2 *3 *4) - (-12 (-5 *2 (-641 (-169 *4))) (-5 *1 (-155 *3 *4)) - (-4 *3 (-1235 (-169 (-564)))) (-4 *4 (-13 (-363) (-845))))) - ((*1 *2 *3) - (-12 (-4 *4 (-13 (-363) (-845))) (-5 *2 (-641 (-169 *4))) - (-5 *1 (-181 *4 *3)) (-4 *3 (-1235 (-169 *4))))) - ((*1 *2 *3 *4) - (-12 (-4 *4 (-13 (-363) (-845))) (-5 *2 (-641 (-169 *4))) - (-5 *1 (-181 *4 *3)) (-4 *3 (-1235 (-169 *4)))))) -(((*1 *1 *2) - (-12 (-5 *2 (-685 *4)) (-4 *4 (-1046)) (-5 *1 (-1136 *3 *4)) - (-14 *3 (-768))))) -(((*1 *2) - (-12 (-4 *1 (-342 *3 *4 *5)) (-4 *3 (-1213)) (-4 *4 (-1235 *3)) - (-4 *5 (-1235 (-407 *4))) (-5 *2 (-112))))) -(((*1 *1 *1 *1) (-5 *1 (-859)))) -(((*1 *1 *2) (-12 (-5 *2 (-1259 *3)) (-4 *3 (-363)) (-4 *1 (-329 *3)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1259 *3)) (-4 *3 (-1235 *4)) (-4 *4 (-1213)) - (-4 *1 (-342 *4 *3 *5)) (-4 *5 (-1235 (-407 *3))))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1259 *4)) (-5 *3 (-1259 *1)) (-4 *4 (-172)) - (-4 *1 (-367 *4)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1259 *4)) (-5 *3 (-1259 *1)) (-4 *4 (-172)) - (-4 *1 (-370 *4 *5)) (-4 *5 (-1235 *4)))) - ((*1 *1 *2) - (-12 (-5 *2 (-1259 *3)) (-4 *3 (-172)) (-4 *1 (-409 *3 *4)) - (-4 *4 (-1235 *3)))) - ((*1 *1 *2) (-12 (-5 *2 (-1259 *3)) (-4 *3 (-172)) (-4 *1 (-417 *3))))) + (-641 + (-2 (|:| |outval| *7) (|:| |outmult| (-564)) + (|:| |outvect| (-641 (-685 *7)))))) + (-5 *1 (-532 *6 *7 *4)) (-4 *7 (-363)) (-4 *4 (-13 (-363) (-845)))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-847) (-556))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-999))))) @@ -11803,36 +10701,45 @@ ((*1 *1 *1 *2) (-12 (-5 *1 (-715 *2)) (-4 *2 (-363)))) ((*1 *1 *2) (-12 (-5 *1 (-715 *2)) (-4 *2 (-363)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-768))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-112)) (-5 *3 (-641 (-263))) (-5 *1 (-261)))) - ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-263))))) -(((*1 *1 *2) (-12 (-5 *2 (-768)) (-5 *1 (-134))))) -(((*1 *2 *1) - (-12 (-4 *1 (-683 *3 *4 *5)) (-4 *3 (-1046)) (-4 *4 (-373 *3)) - (-4 *5 (-373 *3)) (-5 *2 (-112)))) +(((*1 *2 *3 *4 *4 *5) + (|partial| -12 (-5 *4 (-610 *3)) (-5 *5 (-641 *3)) + (-4 *3 (-13 (-430 *6) (-27) (-1194))) + (-4 *6 (-13 (-452) (-1035 (-564)) (-847) (-147) (-637 (-564)))) + (-5 *2 + (-2 (|:| |mainpart| *3) + (|:| |limitedlogs| + (-641 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) + (-5 *1 (-566 *6 *3 *7)) (-4 *7 (-1094))))) +(((*1 *2 *3) + (-12 (-4 *4 (-1046)) (-5 *2 (-564)) (-5 *1 (-443 *4 *3 *5)) + (-4 *3 (-1235 *4)) + (-4 *5 (-13 (-404) (-1035 *4) (-363) (-1194) (-284)))))) +(((*1 *1) (-5 *1 (-130)))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-641 *1)) (-4 *1 (-1060 *4 *5 *6)) (-4 *4 (-1046)) + (-4 *5 (-790)) (-4 *6 (-847)) (-5 *2 (-112)))) + ((*1 *2 *1 *1) + (-12 (-4 *1 (-1060 *3 *4 *5)) (-4 *3 (-1046)) (-4 *4 (-790)) + (-4 *5 (-847)) (-5 *2 (-112)))) ((*1 *2 *1) - (-12 (-4 *1 (-1049 *3 *4 *5 *6 *7)) (-4 *5 (-1046)) - (-4 *6 (-238 *4 *5)) (-4 *7 (-238 *3 *5)) (-5 *2 (-112))))) -(((*1 *2 *1) (-12 (-5 *2 (-564)) (-5 *1 (-157)))) - ((*1 *2 *1) (-12 (-5 *2 (-157)) (-5 *1 (-871)))) - ((*1 *2 *3) (-12 (-5 *3 (-940 *2)) (-5 *1 (-979 *2)) (-4 *2 (-1046))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1007 *3)) (-4 *3 (-1209)) (-5 *2 (-641 *3))))) + (-12 (-4 *1 (-1202 *3 *4 *5 *6)) (-4 *3 (-556)) (-4 *4 (-790)) + (-4 *5 (-847)) (-4 *6 (-1060 *3 *4 *5)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-4 *1 (-1202 *4 *5 *6 *3)) (-4 *4 (-556)) (-4 *5 (-790)) + (-4 *6 (-847)) (-4 *3 (-1060 *4 *5 *6)) (-5 *2 (-112))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-685 *5)) (-5 *4 (-1259 *5)) (-4 *5 (-363)) - (-5 *2 (-112)) (-5 *1 (-663 *5)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-363)) (-4 *6 (-13 (-373 *5) (-10 -7 (-6 -4412)))) - (-4 *4 (-13 (-373 *5) (-10 -7 (-6 -4412)))) (-5 *2 (-112)) - (-5 *1 (-664 *5 *6 *4 *3)) (-4 *3 (-683 *5 *6 *4))))) + (-12 (-5 *3 (-641 (-1259 *5))) (-5 *4 (-564)) (-5 *2 (-1259 *5)) + (-5 *1 (-1026 *5)) (-4 *5 (-363)) (-4 *5 (-368)) (-4 *5 (-1046))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-1127 (-225))) (-5 *3 (-641 (-263))) (-5 *1 (-1261)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1127 (-225))) (-5 *3 (-1152)) (-5 *1 (-1261)))) + ((*1 *1 *1) (-5 *1 (-1261)))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-1209)) (-5 *1 (-182 *3 *2)) (-4 *2 (-670 *3))))) (((*1 *2 *1) - (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1046)) (-4 *4 (-847)) - (-4 *5 (-266 *4)) (-4 *6 (-790)) (-5 *2 (-641 *4))))) -(((*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 *2 *2) (|partial| -12 (-4 *1 (-980 *2)) (-4 *2 (-1194))))) + (-12 (-5 *2 (-1023 (-840 (-564)))) (-5 *1 (-594 *3)) (-4 *3 (-1046))))) +(((*1 *1 *1) (-5 *1 (-1058)))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-847) (-556))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-999))))) @@ -11842,6 +10749,9 @@ ((*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 (-980 *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)))) @@ -11849,47 +10759,71 @@ (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3)))) ((*1 *1 *1) (-4 *1 (-1197)))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-847) (-556) (-1035 (-564)))) (-5 *2 (-407 (-564))) - (-5 *1 (-433 *4 *3)) (-4 *3 (-430 *4)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-610 *3)) (-4 *3 (-430 *5)) - (-4 *5 (-13 (-847) (-556) (-1035 (-564)))) - (-5 *2 (-1166 (-407 (-564)))) (-5 *1 (-433 *5 *3))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-363)) - (-5 *2 (-641 (-2 (|:| C (-685 *5)) (|:| |g| (-1259 *5))))) - (-5 *1 (-975 *5)) (-5 *3 (-685 *5)) (-5 *4 (-1259 *5))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-641 *5)) (-5 *4 (-918)) (-4 *5 (-847)) - (-5 *2 (-641 (-668 *5))) (-5 *1 (-668 *5))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -3089 (-1088 (-840 (-225)))) (|:| |abserr| (-225)) - (|:| |relerr| (-225)))) - (-5 *2 (-1150 (-225))) (-5 *1 (-192)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-316 (-225))) (-5 *4 (-641 (-1170))) - (-5 *5 (-1088 (-840 (-225)))) (-5 *2 (-1150 (-225))) (-5 *1 (-300)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1259 (-316 (-225)))) (-5 *4 (-641 (-1170))) - (-5 *5 (-1088 (-840 (-225)))) (-5 *2 (-1150 (-225))) (-5 *1 (-300))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *3 (-1 (-641 *2) *2 *2 *2)) (-4 *2 (-1094)) - (-5 *1 (-103 *2)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1094)) (-5 *1 (-103 *2))))) +(((*1 *2) (-12 (-5 *2 (-1264)) (-5 *1 (-756))))) +(((*1 *2 *1) (-12 (-5 *2 (-641 (-835))) (-5 *1 (-140))))) (((*1 *2) - (-12 (-4 *3 (-556)) (-5 *2 (-641 *4)) (-5 *1 (-43 *3 *4)) + (-12 (-4 *3 (-556)) (-5 *2 (-641 (-685 *3))) (-5 *1 (-43 *3 *4)) (-4 *4 (-417 *3))))) +(((*1 *2 *3 *4 *2 *5 *6) + (-12 + (-5 *5 + (-2 (|:| |done| (-641 *11)) + (|:| |todo| (-641 (-2 (|:| |val| *3) (|:| -3991 *11)))))) + (-5 *6 (-768)) + (-5 *2 (-641 (-2 (|:| |val| (-641 *10)) (|:| -3991 *11)))) + (-5 *3 (-641 *10)) (-5 *4 (-641 *11)) (-4 *10 (-1060 *7 *8 *9)) + (-4 *11 (-1066 *7 *8 *9 *10)) (-4 *7 (-452)) (-4 *8 (-790)) + (-4 *9 (-847)) (-5 *1 (-1064 *7 *8 *9 *10 *11)))) + ((*1 *2 *3 *4 *2 *5 *6) + (-12 + (-5 *5 + (-2 (|:| |done| (-641 *11)) + (|:| |todo| (-641 (-2 (|:| |val| *3) (|:| -3991 *11)))))) + (-5 *6 (-768)) + (-5 *2 (-641 (-2 (|:| |val| (-641 *10)) (|:| -3991 *11)))) + (-5 *3 (-641 *10)) (-5 *4 (-641 *11)) (-4 *10 (-1060 *7 *8 *9)) + (-4 *11 (-1103 *7 *8 *9 *10)) (-4 *7 (-452)) (-4 *8 (-790)) + (-4 *9 (-847)) (-5 *1 (-1139 *7 *8 *9 *10 *11))))) +(((*1 *2 *1 *1) + (-12 (-4 *1 (-1007 *3)) (-4 *3 (-1209)) (-4 *3 (-1094)) + (-5 *2 (-112))))) +(((*1 *2) (-12 (-5 *2 (-641 (-1152))) (-5 *1 (-1262))))) (((*1 *2 *3) - (-12 (-4 *4 (-556)) (-5 *2 (-768)) (-5 *1 (-43 *4 *3)) - (-4 *3 (-417 *4))))) + (-12 (-5 *3 (-585 *2)) (-4 *2 (-13 (-29 *4) (-1194))) + (-5 *1 (-583 *4 *2)) + (-4 *4 (-13 (-452) (-1035 (-564)) (-847) (-637 (-564)))))) + ((*1 *2 *3) + (-12 (-5 *3 (-585 (-407 (-949 *4)))) + (-4 *4 (-13 (-452) (-1035 (-564)) (-847) (-637 (-564)))) + (-5 *2 (-316 *4)) (-5 *1 (-588 *4))))) +(((*1 *1 *2) (-12 (-5 *2 (-641 *3)) (-4 *3 (-1209)) (-5 *1 (-327 *3)))) + ((*1 *1 *2) + (-12 (-5 *2 (-641 *3)) (-4 *3 (-1209)) (-5 *1 (-516 *3 *4)) + (-14 *4 (-564))))) +(((*1 *2 *2 *3) + (-12 (-4 *4 (-790)) + (-4 *3 (-13 (-847) (-10 -8 (-15 -2373 ((-1170) $))))) (-4 *5 (-556)) + (-5 *1 (-729 *4 *3 *5 *2)) (-4 *2 (-946 (-407 (-949 *5)) *4 *3)))) + ((*1 *2 *2 *3) + (-12 (-4 *4 (-1046)) (-4 *5 (-790)) + (-4 *3 + (-13 (-847) + (-10 -8 (-15 -2373 ((-1170) $)) + (-15 -3826 ((-3 $ "failed") (-1170)))))) + (-5 *1 (-981 *4 *5 *3 *2)) (-4 *2 (-946 (-949 *4) *5 *3)))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-641 *6)) + (-4 *6 + (-13 (-847) + (-10 -8 (-15 -2373 ((-1170) $)) + (-15 -3826 ((-3 $ "failed") (-1170)))))) + (-4 *4 (-1046)) (-4 *5 (-790)) (-5 *1 (-981 *4 *5 *6 *2)) + (-4 *2 (-946 (-949 *4) *5 *6))))) (((*1 *2 *2) - (-12 (-4 *3 (-13 (-847) (-452))) (-5 *1 (-1200 *3 *2)) - (-4 *2 (-13 (-430 *3) (-1194)))))) + (-12 (-5 *2 (-1150 *3)) (-4 *3 (-1046)) (-5 *1 (-1154 *3)))) + ((*1 *1 *1) + (-12 (-5 *1 (-1251 *2 *3 *4)) (-4 *2 (-1046)) (-14 *3 (-1170)) + (-14 *4 *2)))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-847) (-556))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-999))))) @@ -11899,6 +10833,7 @@ ((*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 (-980 *4)))) + ((*1 *1 *2) (-12 (-5 *1 (-331 *2)) (-4 *2 (-847)))) ((*1 *1 *1) (-12 (-5 *1 (-339 *2 *3 *4)) (-14 *2 (-641 (-1170))) (-14 *3 (-641 (-1170))) (-4 *4 (-387)))) @@ -11909,33 +10844,39 @@ (-12 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(-816 *3)))) + (-5 *1 (-816 *3)) (-4 *3 (-847))))) +(((*1 *2 *3) + (-12 (-4 *4 (-452)) (-4 *5 (-790)) (-4 *6 (-847)) (-5 *2 (-564)) + (-5 *1 (-449 *4 *5 *6 *3)) (-4 *3 (-946 *4 *5 *6))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-379)) (-5 *2 (-1264)) (-5 *1 (-1261))))) +(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-442 *3)) (-4 *3 (-1235 (-564)))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-641 (-407 (-949 *5)))) (-5 *4 (-641 (-1170))) - (-4 *5 (-556)) (-5 *2 (-641 (-641 (-949 *5)))) (-5 *1 (-1178 *5))))) -(((*1 *2 *3 *4 *4 *4) - (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1060 *5 *6 *7)) - (-4 *5 (-452)) (-4 *6 (-790)) (-4 *7 (-847)) - (-5 *2 (-641 (-1024 *5 *6 *7 *8))) (-5 *1 (-1024 *5 *6 *7 *8)))) - ((*1 *2 *3 *4 *4 *4) - (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1060 *5 *6 *7)) - (-4 *5 (-452)) (-4 *6 (-790)) (-4 *7 (-847)) - (-5 *2 (-641 (-1140 *5 *6 *7 *8))) (-5 *1 (-1140 *5 *6 *7 *8))))) -(((*1 *2 *3 *3 *3 *4 *4 *3) - (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1032)) - (-5 *1 (-752))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-225)) (-5 *1 (-226)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-169 (-225))) (-5 *1 (-226)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-13 (-847) (-556))) (-5 *1 (-431 *3 *2)) - (-4 *2 (-430 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1133)))) -(((*1 *2 *2 *2 *3 *3) - (-12 (-5 *3 (-768)) (-4 *4 (-1046)) (-5 *1 (-1231 *4 *2)) - (-4 *2 (-1235 *4))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1032)) (-5 *1 (-755))))) +(((*1 *2 *2 *2) + (|partial| -12 (-4 *3 (-13 (-556) (-147))) (-5 *1 (-1229 *3 *2)) + (-4 *2 (-1235 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-434))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-847) (-556))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-999))))) @@ -12738,7 +11777,7 @@ ((*1 *1 *1) (-4 *1 (-284))) ((*1 *2 *3) (-12 (-5 *3 (-418 *4)) (-4 *4 (-556)) - (-5 *2 (-641 (-2 (|:| -1762 (-768)) (|:| |logand| *4)))) + (-5 *2 (-641 (-2 (|:| -1838 (-768)) (|:| |logand| *4)))) (-5 *1 (-320 *4)))) ((*1 *1 *1) (-12 (-5 *1 (-339 *2 *3 *4)) (-14 *2 (-641 (-1170))) @@ -12758,18 +11797,76 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-768)) (-5 *1 (-1279 *3 *4)) (-4 *4 (-714 (-407 (-564)))) (-4 *3 (-847)) (-4 *4 (-172))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-768)) (-4 *6 (-1094)) (-4 *3 (-897 *6)) - (-5 *2 (-685 *3)) (-5 *1 (-688 *6 *3 *7 *4)) (-4 *7 (-373 *3)) - (-4 *4 (-13 (-373 *6) (-10 -7 (-6 -4411))))))) +(((*1 *2 *3) (-12 (-5 *3 (-918)) (-5 *2 (-901 (-564))) (-5 *1 (-914)))) + ((*1 *2 *3) + (-12 (-5 *3 (-641 (-564))) (-5 *2 (-901 (-564))) (-5 *1 (-914))))) +(((*1 *2 *1 *2) + (-12 (-4 *1 (-364 *3 *2)) (-4 *3 (-1094)) (-4 *2 (-1094))))) (((*1 *2 *3) - (-12 (-5 *3 (-1166 *4)) (-4 *4 (-349)) - (-5 *2 (-1259 (-641 (-2 (|:| -3426 *4) (|:| -1495 (-1114)))))) - (-5 *1 (-346 *4))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-980 *2)) (-4 *2 (-1194))))) -(((*1 *2) - (-12 (-5 *2 (-1259 (-1095 *3 *4))) (-5 *1 (-1095 *3 *4)) - (-14 *3 (-918)) (-14 *4 (-918))))) + (-12 (|has| *2 (-6 (-4413 "*"))) (-4 *5 (-373 *2)) (-4 *6 (-373 *2)) + (-4 *2 (-1046)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1235 *2)) + (-4 *4 (-683 *2 *5 *6))))) +(((*1 *1 *2 *2 *2) + (-12 (-5 *1 (-227 *2)) (-4 *2 (-13 (-363) (-1194))))) + ((*1 *1 *1 *2) (-12 (-5 *1 (-715 *2)) (-4 *2 (-363)))) + ((*1 *1 *2) (-12 (-5 *1 (-715 *2)) (-4 *2 (-363)))) + ((*1 *2 *1 *3 *4 *4) + (-12 (-5 *3 (-918)) (-5 *4 (-379)) (-5 *2 (-1264)) (-5 *1 (-1260))))) +(((*1 *1) (-5 *1 (-820)))) +(((*1 *2 *1) + (-12 (-5 *2 (-1088 *3)) (-5 *1 (-1086 *3)) (-4 *3 (-1209)))) + ((*1 *1 *2 *2) (-12 (-4 *1 (-1087 *2)) (-4 *2 (-1209)))) + ((*1 *1 *2) (-12 (-5 *1 (-1226 *2)) (-4 *2 (-1209))))) +(((*1 *2 *3 *3) + (-12 (-4 *2 (-556)) (-5 *1 (-966 *2 *3)) (-4 *3 (-1235 *2))))) +(((*1 *1 *2 *3 *1) + (-12 (-5 *2 (-889 *4)) (-4 *4 (-1094)) (-5 *1 (-886 *4 *3)) + (-4 *3 (-1094))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-847) (-452))) (-5 *1 (-1200 *3 *2)) + (-4 *2 (-13 (-430 *3) (-1194)))))) +(((*1 *2 *3 *3 *3) + (-12 (-5 *3 (-641 (-564))) (-5 *2 (-685 (-564))) (-5 *1 (-1104))))) +(((*1 *2 *3) + (-12 (-5 *3 (-564)) (-4 *4 (-1235 (-407 *3))) (-5 *2 (-918)) + (-5 *1 (-910 *4 *5)) (-4 *5 (-1235 (-407 *4)))))) +(((*1 *2 *1 *1) + (-12 (-4 *1 (-1060 *3 *4 *5)) (-4 *3 (-1046)) (-4 *4 (-790)) + (-4 *5 (-847)) (-5 *2 (-112))))) +(((*1 *1 *2) + (-12 + (-5 *2 + (-641 + (-2 + (|:| -1354 + (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) + (|:| -4172 (-1088 (-840 (-225)))) (|:| |abserr| (-225)) + (|:| |relerr| (-225)))) + (|:| -2577 + (-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"))) + (|:| -4172 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-559))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-47 *3 *4)) (-4 *3 (-1046)) (-4 *4 (-789)))) @@ -12877,9 +11974,9 @@ (-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 (|:| -2118 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -2839 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-363)) (-4 *6 (-363)) - (-5 *2 (-2 (|:| -2118 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -2839 *6) (|:| |coeff| *6))) (-5 *1 (-584 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -12998,7 +12095,7 @@ (-4 *8 (-1046)) (-4 *6 (-790)) (-4 *2 (-13 (-1094) - (-10 -8 (-15 -1780 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-768)))))) + (-10 -8 (-15 -1848 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-768)))))) (-5 *1 (-948 *6 *7 *8 *5 *2)) (-4 *5 (-946 *8 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-955 *5)) (-4 *5 (-1209)) @@ -13011,8 +12108,8 @@ (-4 *2 (-946 (-949 *4) *5 *6)) (-4 *5 (-790)) (-4 *6 (-13 (-847) - (-10 -8 (-15 -2235 ((-1170) $)) - (-15 -3851 ((-3 $ "failed") (-1170)))))) + (-10 -8 (-15 -2373 ((-1170) $)) + (-15 -3826 ((-3 $ "failed") (-1170)))))) (-5 *1 (-981 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-556)) (-4 *6 (-556)) @@ -13099,77 +12196,193 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1046)) (-5 *1 (-1282 *3 *4)) (-4 *4 (-843))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-556) (-147))) (-5 *1 (-537 *3 *2)) - (-4 *2 (-1250 *3)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-363) (-368) (-612 (-564)))) (-4 *4 (-1235 *3)) - (-4 *5 (-721 *3 *4)) (-5 *1 (-541 *3 *4 *5 *2)) (-4 *2 (-1250 *5)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-363) (-368) (-612 (-564)))) (-5 *1 (-542 *3 *2)) - (-4 *2 (-1250 *3)))) - ((*1 *2 *2) - (-12 (-5 *2 (-1150 *3)) (-4 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*2 (-901 (-564))) (-5 *1 (-914)))) + ((*1 *2) (-12 (-5 *2 (-901 (-564))) (-5 *1 (-914))))) +(((*1 *1 *2) + (|partial| -12 (-5 *2 (-816 *3)) (-4 *3 (-847)) (-5 *1 (-668 *3))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-13 (-307) (-147))) (-4 *5 (-790)) (-4 *6 (-847)) (-4 *7 (-946 *4 *5 *6)) (-5 *2 (-641 (-641 *7))) @@ -13186,246 +12399,38 @@ (-12 (-5 *4 (-112)) (-4 *5 (-13 (-307) (-147))) (-4 *6 (-790)) (-4 *7 (-847)) (-4 *8 (-946 *5 *6 *7)) (-5 *2 (-641 (-641 *8))) (-5 *1 (-448 *5 *6 *7 *8)) (-5 *3 (-641 *8))))) -(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-1152)) (-5 *3 (-771)) (-5 *1 (-114))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-821))))) -(((*1 *1 *2) (-12 (-5 *2 (-1152)) (-5 *1 (-529)))) - ((*1 *1 *2) (-12 (-5 *2 (-388)) (-5 *1 (-529))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-373 *2)) (-4 *2 (-1209)) (-4 *2 (-847)))) - ((*1 *1 *2 *1 *1) - (-12 (-5 *2 (-1 (-112) *3 *3)) (-4 *1 (-373 *3)) (-4 *3 (-1209)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-965 *2)) (-4 *2 (-847)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-1128 *2)) (-4 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*4 (-452)) (-4 *4 (-556)) + (-5 *2 (-2 (|:| |coef2| *3) (|:| -2215 *4))) (-5 *1 (-966 *4 *3)) + (-4 *3 (-1235 *4))))) +(((*1 *2 *2) (-12 (-5 *2 (-1152)) (-5 *1 (-1187))))) +(((*1 *2 *3 *2) + (-12 (-5 *1 (-675 *3 *2)) (-4 *3 (-1094)) (-4 *2 (-1094))))) +(((*1 *2 *3) + (-12 (-4 *2 (-363)) (-4 *2 (-845)) (-5 *1 (-942 *2 *3)) + (-4 *3 (-1235 *2))))) (((*1 *2 *1) (-12 (-5 *2 @@ -17370,7 +17263,7 @@ (-2 (|:| |var| (-1170)) (|:| |arrayIndex| (-641 (-949 (-564)))) (|:| |rand| - (-2 (|:| |ints2Floats?| (-112)) (|:| -3808 (-859)))))) + (-2 (|:| |ints2Floats?| (-112)) (|:| -3780 (-859)))))) (|:| |arrayAssignmentBranch| (-2 (|:| |var| (-1170)) (|:| |rand| (-859)) (|:| |ints2Floats?| (-112)))) @@ -17378,41 +17271,54 @@ (-2 (|:| |switch| (-1169)) (|:| |thenClause| (-330)) (|:| |elseClause| (-330)))) (|:| |returnBranch| - (-2 (|:| -4003 (-112)) - (|:| -3426 - (-2 (|:| |ints2Floats?| (-112)) (|:| -3808 (-859)))))) + (-2 (|:| -4127 (-112)) + (|:| -3393 + (-2 (|:| |ints2Floats?| (-112)) (|:| -3780 (-859)))))) (|:| |blockBranch| (-641 (-330))) (|:| |commentBranch| (-641 (-1152))) (|:| |callBranch| (-1152)) (|:| |forBranch| - (-2 (|:| -3089 (-1086 (-949 (-564)))) - (|:| |span| (-949 (-564))) (|:| -4337 (-330)))) + (-2 (|:| -4172 (-1086 (-949 (-564)))) + (|:| |span| (-949 (-564))) (|:| -4360 (-330)))) (|:| |labelBranch| (-1114)) - (|:| |loopBranch| (-2 (|:| |switch| (-1169)) (|:| -4337 (-330)))) + (|:| |loopBranch| (-2 (|:| |switch| (-1169)) (|:| -4360 (-330)))) (|:| |commonBranch| - (-2 (|:| -4324 (-1170)) (|:| |contents| (-641 (-1170))))) + (-2 (|:| -4344 (-1170)) (|:| |contents| (-641 (-1170))))) (|:| |printBranch| (-641 (-859))))) (-5 *1 (-330))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-641 (-2 (|:| |val| (-641 *8)) (|:| -3991 *9)))) + (-5 *4 (-768)) (-4 *8 (-1060 *5 *6 *7)) (-4 *9 (-1066 *5 *6 *7 *8)) + (-4 *5 (-452)) (-4 *6 (-790)) (-4 *7 (-847)) (-5 *2 (-1264)) + (-5 *1 (-1064 *5 *6 *7 *8 *9)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-641 (-2 (|:| |val| (-641 *8)) (|:| -3991 *9)))) + (-5 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(-468))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-3 + (|:| |noa| + (-2 (|:| |fn| (-316 (-225))) (|:| -3286 (-641 (-225))) + (|:| |lb| (-641 (-840 (-225)))) + (|:| |cf| (-641 (-316 (-225)))) + (|:| |ub| (-641 (-840 (-225)))))) + (|:| |lsa| + (-2 (|:| |lfn| (-641 (-316 (-225)))) + (|:| -3286 (-641 (-225))))))) + (-5 *2 (-641 (-1152))) (-5 *1 (-267))))) +(((*1 *2 *3) + (-12 (-5 *2 (-418 (-1166 *1))) (-5 *1 (-316 *4)) (-5 *3 (-1166 *1)) + (-4 *4 (-452)) (-4 *4 (-556)) (-4 *4 (-847)))) + ((*1 *2 *3) + (-12 (-4 *1 (-906)) (-5 *2 (-418 (-1166 *1))) (-5 *3 (-1166 *1))))) +(((*1 *2 *1) (-12 (-4 *1 (-952)) (-5 *2 (-1088 (-225))))) + ((*1 *2 *1) (-12 (-4 *1 (-971)) (-5 *2 (-1088 (-225)))))) +(((*1 *2 *3 *3 *4 *3) + (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1032)) + (-5 *1 (-744))))) +(((*1 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-1186 *3 *4)) (-4 *3 (-1094)) + (-4 *4 (-1094))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-641 (-1 (-112) *8))) (-4 *8 (-1060 *5 *6 *7)) + (-4 *5 (-556)) (-4 *6 (-790)) (-4 *7 (-847)) + (-5 *2 (-2 (|:| |goodPols| (-641 *8)) (|:| |badPols| (-641 *8)))) + (-5 *1 (-974 *5 *6 *7 *8)) (-5 *4 (-641 *8))))) +(((*1 *2 *3) (-12 (-5 *3 (-949 (-225))) (-5 *2 (-225)) (-5 *1 (-305))))) +(((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-819))))) +(((*1 *1) (-5 *1 (-437)))) (((*1 *2 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-789)) (-4 *2 (-1046)))) ((*1 *2 *1) (-12 (-4 *2 (-1046)) (-5 *1 (-50 *2 *3)) (-14 *3 (-641 (-1170))))) @@ -17443,10 +17403,10 @@ ((*1 *2 *1) (-12 (-4 *1 (-382 *2 *3)) (-4 *3 (-1094)) (-4 *2 (-1046)))) ((*1 *2 *1) - (-12 (-14 *3 (-641 (-1170))) (-4 *5 (-238 (-2641 *3) (-768))) + (-12 (-14 *3 (-641 (-1170))) (-4 *5 (-238 (-2780 *3) (-768))) (-14 *6 - (-1 (-112) (-2 (|:| -1495 *4) (|:| -2515 *5)) - (-2 (|:| -1495 *4) (|:| -2515 *5)))) + (-1 (-112) (-2 (|:| -3348 *4) (|:| -4309 *5)) + (-2 (|:| -3348 *4) (|:| -4309 *5)))) (-4 *2 (-172)) (-5 *1 (-461 *3 *2 *4 *5 *6 *7)) (-4 *4 (-847)) (-4 *7 (-946 *2 *5 (-861 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-509 *2 *3)) (-4 *3 (-847)) (-4 *2 (-1094)))) @@ -17463,50 +17423,43 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1060 *3 *4 *2)) (-4 *3 (-1046)) (-4 *4 (-790)) (-4 *2 (-847))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *7 *7)) (-4 *7 (-1235 *6)) - (-4 *6 (-13 (-27) (-430 *5))) - (-4 *5 (-13 (-847) (-556) (-1035 (-564)))) (-4 *8 (-1235 (-407 *7))) - (-5 *2 (-585 *3)) (-5 *1 (-552 *5 *6 *7 *8 *3)) - (-4 *3 (-342 *6 *7 *8))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -1935 *1) (|:| -1363 *1))) (-4 *1 (-307)))) - ((*1 *2 *1 *1) - (|partial| -12 (-5 *2 (-2 (|:| |lm| (-386 *3)) (|:| |rm| (-386 *3)))) - (-5 *1 (-386 *3)) (-4 *3 (-1094)))) - ((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -1935 (-768)) (|:| -1363 (-768)))) - (-5 *1 (-768)))) - ((*1 *2 *3 *3) - (-12 (-4 *4 (-556)) (-5 *2 (-2 (|:| -1935 *3) (|:| -1363 *3))) - (-5 *1 (-966 *4 *3)) (-4 *3 (-1235 *4))))) -(((*1 *2 *3 *4 *3) - (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1235 *5)) (-4 *5 (-363)) - (-5 *2 (-2 (|:| -2118 (-407 *6)) (|:| |coeff| (-407 *6)))) - (-5 *1 (-574 *5 *6)) (-5 *3 (-407 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(-768))) (-14 *7 - (-1 (-112) (-2 (|:| -1495 *5) (|:| -2515 *6)) - (-2 (|:| -1495 *5) (|:| -2515 *6)))) + (-1 (-112) (-2 (|:| -3348 *5) (|:| -4309 *6)) + (-2 (|:| -3348 *5) (|:| -4309 *6)))) (-5 *2 (-710 *5 *6 *7)) (-5 *1 (-461 *3 *4 *5 *6 *7 *8)) (-4 *5 (-847)) (-4 *8 (-946 *4 *6 (-861 *3))))) ((*1 *2 *1) @@ -17515,859 +17468,906 @@ ((*1 *1 *1) (-12 (-4 *1 (-970 *2 *3 *4)) (-4 *2 (-1046)) (-4 *3 (-789)) (-4 *4 (-847))))) -(((*1 *1 *2) (-12 (-5 *2 (-1114)) (-5 *1 (-951))))) -(((*1 *2 *3) - (-12 (-5 *3 (-247 *4 *5)) (-14 *4 (-641 (-1170))) (-4 *5 (-1046)) - (-5 *2 (-481 *4 *5)) (-5 *1 (-941 *4 *5))))) -(((*1 *2 *1) - (|partial| -12 (-4 *1 (-946 *3 *4 *2)) (-4 *3 (-1046)) (-4 *4 (-790)) - (-4 *2 (-847)))) - ((*1 *2 *3) - (|partial| -12 (-4 *4 (-790)) (-4 *5 (-1046)) (-4 *6 (-946 *5 *4 *2)) - (-4 *2 (-847)) (-5 *1 (-947 *4 *2 *5 *6 *3)) - (-4 *3 - (-13 (-363) - (-10 -8 (-15 -3742 ($ *6)) (-15 -1625 (*6 $)) - (-15 -1634 (*6 $))))))) +(((*1 *2 *1 *1) + (|partial| -12 (-4 *1 (-329 *3)) (-4 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\ No newline at end of file |