diff options
| -rw-r--r-- | src/ChangeLog | 5 | ||||
| -rw-r--r-- | src/algebra/indexedp.spad.pamphlet | 12 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 296 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 8 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1331 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 7300 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 25382 |
7 files changed, 17173 insertions, 17161 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 2887db40..e8bb54fb 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,10 @@ 2010-06-28 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/indexedp.spad.pamphlet (IndexedDirectProductCategory) + [terms]: Rename from support. + +2010-06-28 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/indexedp.spad.pamphlet (IndexedDirectProductCategory): Rework implementation. diff --git a/src/algebra/indexedp.spad.pamphlet b/src/algebra/indexedp.spad.pamphlet index 1e1a569f..34b61d1f 100644 --- a/src/algebra/indexedp.spad.pamphlet +++ b/src/algebra/indexedp.spad.pamphlet @@ -46,9 +46,9 @@ IndexedDirectProductCategory(A:SetCategory,S:OrderedSet): Category == ++ reductum(z) returns a new element created by removing the ++ leading coefficient/support pair from the element z. ++ Error: if z has no support. - support: % -> List Pair(S,A) - ++ \spad{support x} returns the list of terms in \spad{x}. - ++ Each term is a pair of an index (the first component) + terms: % -> List Pair(S,A) + ++ \spad{terms x} returns the list of terms in \spad{x}. + ++ Each term is a pair of a support (the first component) ++ and the corresponding value (the second component). @ @@ -104,7 +104,7 @@ IndexedDirectProductObject(A,S): Public == Private where error "Can't take leadingCoefficient of empty product element" termIndex first rep x - support x == rep x + terms x == rep x @ \section{domain IDPAM IndexedDirectProductAbelianMonoid} @@ -322,7 +322,9 @@ IndexedDirectProductAbelianGroup(A:AbelianGroup,S:OrderedSet): @ \section{License} <<license>>= ---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. +--Copyright (C) 1991-2002, The Numerical ALgorithms Group Ltd. +--All rights reserved. +--Copyright (C) 2007-2010, Gabriel Dos Reis. --All rights reserved. -- --Redistribution and use in source and binary forms, with or without diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index b8ba4119..c2422e8e 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2293439 . 3486762004) +(2293386 . 3486768660) (-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 -1955) +(-32 R -1956) ((|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 -1057) (QUOTE (-576))))) @@ -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 -1955 UP UPUP -3878) +(-40 -1956 UP UPUP -1415) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4455 |has| (-419 |#2|) (-374)) (-4460 |has| (-419 |#2|) (-374)) (-4454 |has| (-419 |#2|) (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2755 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2755 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2755 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2755 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2755 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2755 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) -(-41 R -1955) +(-41 R -1956) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -442) (|devaluate| |#1|))))) @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1955) +(-54 |Base| R -1956) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -392,7 +392,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-116 -1955 UP) +(-116 -1956 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 @@ -524,7 +524,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4459 . T)) NIL -(-149 -1955 UP UPUP) +(-149 -1956 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 @@ -564,7 +564,7 @@ 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 -(-159 R -1955) +(-159 R -1956) ((|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 @@ -688,7 +688,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -1955) +(-190 R -1956) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -796,11 +796,11 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -(-217 -1955 UP UPUP R) +(-217 -1956 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 -(-218 -1955 FP) +(-218 -1956 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 @@ -812,7 +812,7 @@ NIL ((|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 -(-221 R -1955) +(-221 R -1956) ((|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 @@ -832,7 +832,7 @@ NIL ((|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}."))) ((-4459 . T)) NIL -(-226 R -1955) +(-226 R -1956) ((|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 @@ -958,11 +958,11 @@ NIL NIL (-257 |n| R M S) ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) -((-4459 -2755 (-2669 (|has| |#4| (-1068)) (|has| |#4| (-238))) (|has| |#4| (-6 -4459)) (-2669 (|has| |#4| (-1068)) (|has| |#4| (-915 (-1195))))) (-4456 |has| |#4| (-1068)) (-4457 |has| |#4| (-1068)) (-4462 . T)) +((-4459 -2755 (-2670 (|has| |#4| (-1068)) (|has| |#4| (-238))) (|has| |#4| (-6 -4459)) (-2670 (|has| |#4| (-1068)) (|has| |#4| (-915 (-1195))))) (-4456 |has| |#4| (-1068)) (-4457 |has| |#4| (-1068)) (-4462 . T)) ((-2755 (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-238))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-374))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-738))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-805))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-862))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1068))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST 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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."))) @@ -1068,11 +1068,11 @@ 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 -(-285 R -1955) +(-285 R -1956) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-286 R -1955) +(-286 R -1956) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1124,7 +1124,7 @@ 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 -(-299 S R |Mod| -2634 -2331 |exactQuo|) +(-299 S R |Mod| -2313 -2404 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL @@ -1156,11 +1156,11 @@ NIL ((|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 -(-307 -1955 S) +(-307 -1956 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 -(-308 E -1955) +(-308 E -1956) ((|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 @@ -1208,7 +1208,7 @@ 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 -(-320 -1955) +(-320 -1956) ((|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 @@ -1236,7 +1236,7 @@ NIL ((|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."))) ((-4459 -2755 (-12 (|has| |#1| (-568)) (-2755 (|has| |#1| (-1068)) (|has| |#1| (-485)))) (|has| |#1| (-1068)) (|has| |#1| (-485))) (-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) ((-4464 "*") |has| |#1| (-568)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-568)) (-4454 |has| |#1| (-568))) ((-2755 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))))) (|HasCategory| |#1| (QUOTE (-568))) (-2755 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (QUOTE (-21))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (QUOTE (-1068))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))))) (-2755 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (-2755 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1068)))) (-2755 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1068)))) (-2755 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1068)))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-2755 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))))) (-2755 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2755 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))))) (-2755 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1068)))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| $ (QUOTE (-1068))) (|HasCategory| $ (LIST (QUOTE -1057) (QUOTE (-576))))) -(-327 R -1955) +(-327 R -1956) ((|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{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1247,7 +1247,7 @@ NIL (-329 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."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . 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(|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 @@ -1280,11 +1280,11 @@ NIL ((|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."))) ((-4463 . T) (-4462 . T)) ((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-338 S -1955) +(-338 S -1956) ((|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 (-379)))) -(-339 -1955) +(-339 -1956) ((|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."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL @@ -1308,15 +1308,15 @@ 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 -(-345 S -1955 UP UPUP R) +(-345 S -1956 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 -(-346 -1955 UP UPUP R) +(-346 -1956 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 -(-347 -1955 UP UPUP R) +(-347 -1956 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 @@ -1336,11 +1336,11 @@ 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 -(-352 S -1955 UP UPUP) +(-352 S -1956 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(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 (-379))) (|HasCategory| |#2| (QUOTE (-374)))) -(-353 -1955 UP UPUP) +(-353 -1956 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(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."))) ((-4455 |has| (-419 |#2|) (-374)) (-4460 |has| (-419 |#2|) (-374)) (-4454 |has| (-419 |#2|) (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL @@ -1372,7 +1372,7 @@ 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."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL -(-361 R UP -1955) +(-361 R UP -1956) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1396,7 +1396,7 @@ NIL ((|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."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) ((-2755 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) -(-367 -1955 GF) +(-367 -1956 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 @@ -1404,7 +1404,7 @@ 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 -(-369 -1955 FP FPP) +(-369 -1956 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL @@ -1544,7 +1544,7 @@ 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 -(-404 -1955 UP UPUP R) +(-404 -1956 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 @@ -1572,7 +1572,7 @@ NIL ((|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 -(-411 -1955 UP) +(-411 -1956 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1628,11 +1628,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-425 R -1955 UP A) +(-425 R -1956 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4459 . T)) NIL -(-426 R -1955 UP A |ibasis|) +(-426 R -1956 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 -1057) (|devaluate| |#2|)))) @@ -1680,7 +1680,7 @@ 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4462 . T) (-4452 . T) (-4463 . T)) NIL -(-438 R -1955) +(-438 R -1956) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1688,7 +1688,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4449 -12 (|has| |#1| (-6 -4449)) (|has| |#2| (-6 -4449))) (-4456 . T) (-4457 . T) (-4459 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4449)) (|HasAttribute| |#2| (QUOTE -4449)))) -(-440 R -1955) +(-440 R -1956) ((|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 @@ -1700,15 +1700,15 @@ NIL ((|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| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\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}."))) ((-4459 -2755 (|has| |#1| (-1068)) (|has| |#1| (-485))) (-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) ((-4464 "*") |has| |#1| (-568)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-568)) (-4454 |has| |#1| (-568))) NIL -(-443 R -1955) +(-443 R -1956) ((|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 -(-444 R -1955) +(-444 R -1956) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for 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{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-445 R -1955) +(-445 R -1956) ((|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 @@ -1716,7 +1716,7 @@ 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 -(-447 R -1955 UP) +(-447 R -1956 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 -1057) (QUOTE (-48))))) @@ -1748,7 +1748,7 @@ 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 -(-455 R UP -1955) +(-455 R UP -1956) ((|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 @@ -1860,7 +1860,7 @@ 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 -(-483 |lv| -1955 R) +(-483 |lv| -1956 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 @@ -1875,7 +1875,7 @@ NIL (-486 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1589) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1962) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2610) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1961) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) (-487 |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."))) ((-4463 . T)) @@ -1916,7 +1916,7 @@ NIL ((|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}."))) ((-4462 . T) (-4463 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-497 -1955 UP UPUP R) +(-497 -1956 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 @@ -1952,7 +1952,7 @@ 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 -(-506 -1955 UP |AlExt| |AlPol|) +(-506 -1956 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 @@ -1972,7 +1972,7 @@ NIL ((|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 -(-511 R UP -1955) +(-511 R UP -1956) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the \\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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1992,7 +1992,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-516 -1955 |Expon| |VarSet| |DPoly|) +(-516 -1956 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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 -626) (QUOTE (-1195))))) @@ -2013,7 +2013,7 @@ NIL NIL NIL (-521 A S) -((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|support| (((|List| (|Pair| |#2| |#1|)) $) "\\spad{support x} returns the list of terms in \\spad{x}. Each term is a pair of an index (the first component) and the corresponding value (the second component).")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) +((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|terms| (((|List| (|Pair| |#2| |#1|)) $) "\\spad{terms x} returns the list of terms in \\spad{x}. Each term is a pair of a support (the first component) and the corresponding value (the second component).")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) NIL NIL (-522 A S) @@ -2025,7 +2025,7 @@ NIL NIL NIL (-524 A S) -((|constructor| (NIL "\\indented{1}{Data Last Updated: June 28,{} 2010} Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) +((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) NIL NIL (-525 S A B) @@ -2104,7 +2104,7 @@ 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 -(-544 K -1955 |Par|) +(-544 K -1956 |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 @@ -2128,7 +2128,7 @@ 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 -(-550 K -1955 |Par|) +(-550 K -1956 |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 @@ -2180,11 +2180,11 @@ NIL ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4462 . T) (-4463 . T)) ((-12 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#2|)))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102)))) -(-563 R -1955) +(-563 R -1956) ((|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 -(-564 R0 -1955 UP UPUP R) +(-564 R0 -1956 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 @@ -2204,7 +2204,7 @@ 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."))) ((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL -(-569 R -1955) +(-569 R -1956) ((|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,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2216,7 +2216,7 @@ 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 -(-572 R -1955 L) +(-572 R -1956 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -668) (|devaluate| |#2|)))) @@ -2224,11 +2224,11 @@ 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 -(-574 -1955 UP UPUP R) +(-574 -1956 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 -(-575 -1955 UP) +(-575 -1956 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 @@ -2240,15 +2240,15 @@ 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 -(-578 R -1955 L) +(-578 R -1956 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -668) (|devaluate| |#2|)))) -(-579 R -1955) +(-579 R -1956) ((|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 -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1158)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-641))))) -(-580 -1955 UP) +(-580 -1956 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2256,7 +2256,7 @@ 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 -(-582 -1955) +(-582 -1956) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL @@ -2268,15 +2268,15 @@ NIL ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-585 R -1955) +(-585 R -1956) ((|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 -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-294))) (|HasCategory| |#2| (QUOTE (-641))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-294)))) (|HasCategory| |#1| (QUOTE (-568)))) -(-586 -1955 UP) +(-586 -1956 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-587 R -1955) +(-587 R -1956) ((|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 @@ -2308,11 +2308,11 @@ 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 -(-595 R -1955) +(-595 R -1956) ((|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 -(-596 E -1955) +(-596 E -1956) ((|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 @@ -2320,7 +2320,7 @@ NIL ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL -(-598 -1955) +(-598 -1956) ((|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}."))) ((-4457 . T) (-4456 . T)) ((|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-1195))))) @@ -2376,7 +2376,7 @@ 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 -(-612 R -1955 FG) +(-612 R -1956 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{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2406,7 +2406,7 @@ NIL NIL (-619 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)."))) -((-4459 -2755 (-2669 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4457 . T) (-4456 . T)) +((-4459 -2755 (-2670 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4457 . T) (-4456 . T)) ((-2755 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-620 |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."))) @@ -2436,7 +2436,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-627 -1955 UP) +(-627 -1956 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2464,7 +2464,7 @@ 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}."))) ((-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-860)))) -(-634 R -1955) +(-634 R -1956) ((|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 @@ -2496,11 +2496,11 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-642 R -1955) +(-642 R -1956) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-643 |lv| -1955) +(-643 |lv| -1956) ((|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 @@ -2518,7 +2518,7 @@ NIL NIL (-647 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)."))) -((-4459 -2755 (-2669 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4457 . T) (-4456 . T)) +((-4459 -2755 (-2670 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4457 . T) (-4456 . T)) ((-2755 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-648 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))}."))) @@ -2584,7 +2584,7 @@ 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,{}..))}.")) (|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 -(-664 R -1955 L) +(-664 R -1956 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 @@ -2604,11 +2604,11 @@ 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}."))) ((-4456 . T) (-4457 . T) (-4459 . T)) NIL -(-669 -1955 UP) +(-669 -1956 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)))) -(-670 A -3801) +(-670 A -1878) ((|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}}"))) ((-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) @@ -2644,11 +2644,11 @@ 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}."))) ((-4463 . T) (-4462 . T)) NIL -(-679 -1955) +(-679 -1956) ((|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 -(-680 -1955 |Row| |Col| M) +(-680 -1956 |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 @@ -2744,7 +2744,7 @@ 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 -(-704 S -1955 FLAF FLAS) +(-704 S -1956 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 @@ -2768,7 +2768,7 @@ 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 -(-710 OV E -1955 PG) +(-710 OV E -1956 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 @@ -2820,7 +2820,7 @@ 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 -(-723 R |Mod| -2634 -2331 |exactQuo|) +(-723 R |Mod| -2313 -2404 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL @@ -2836,7 +2836,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-727 R |Mod| -2634 -2331 |exactQuo|) +(-727 R |Mod| -2313 -2404 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4459 . T)) NIL @@ -2848,7 +2848,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4457 . T) (-4456 . T)) NIL -(-730 -1955) +(-730 -1956) ((|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]]}."))) ((-4459 . T)) NIL @@ -2884,7 +2884,7 @@ 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 -(-739 -1955 UP) +(-739 -1956 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 @@ -3036,11 +3036,11 @@ 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 -(-777 -1955) +(-777 -1956) ((|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 -(-778 P -1955) +(-778 P -1956) ((|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 @@ -3048,7 +3048,7 @@ NIL NIL NIL NIL -(-780 UP -1955) +(-780 UP -1956) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3064,7 +3064,7 @@ 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."))) (((-4464 "*") . T)) NIL -(-784 R -1955) +(-784 R -1956) ((|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 @@ -3084,7 +3084,7 @@ 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 -(-789 -1955 |ExtF| |SUEx| |ExtP| |n|) +(-789 -1956 |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 @@ -3180,11 +3180,11 @@ NIL ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-813 R -1955 L) +(-813 R -1956 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-814 R -1955) +(-814 R -1956) ((|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 @@ -3192,7 +3192,7 @@ 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 -(-816 R -1955) +(-816 R -1956) ((|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 @@ -3200,11 +3200,11 @@ 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 -(-818 -1955 UP UPUP R) +(-818 -1956 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 -(-819 -1955 UP L LQ) +(-819 -1956 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 @@ -3212,27 +3212,27 @@ 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 -(-821 -1955 UP L LQ) +(-821 -1956 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}\\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{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 ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\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 -(-822 -1955 UP) +(-822 -1956 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 -(-823 -1955 L UP A LO) +(-823 -1956 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 -(-824 -1955 UP) +(-824 -1956 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{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 ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-825 -1955 LO) +(-825 -1956 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 -(-826 -1955 LODO) +(-826 -1956 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) NIL NIL @@ -3572,7 +3572,7 @@ 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 -(-911 UP -1955) +(-911 UP -1956) ((|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 @@ -3640,7 +3640,7 @@ 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."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-379)))) -(-928 R0 -1955 UP UPUP R) +(-928 R0 -1956 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 @@ -3668,7 +3668,7 @@ 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(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-935 -1955) +(-935 -1956) ((|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 @@ -3684,11 +3684,11 @@ 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}."))) (((-4464 "*") . T)) NIL -(-939 -1955 P) +(-939 -1956 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-940 |xx| -1955) +(-940 |xx| -1956) ((|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 @@ -3712,7 +3712,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-946 R -1955) +(-946 R -1956) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3724,7 +3724,7 @@ 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 -(-949 S R -1955) +(-949 S R -1956) ((|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 @@ -3744,7 +3744,7 @@ 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 -899) (|devaluate| |#1|)))) -(-954 R -1955 -2014) +(-954 R -1956 -2014) ((|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 @@ -3796,7 +3796,7 @@ 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}."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) NIL -(-967 E V R P -1955) +(-967 E V R P -1956) ((|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 @@ -3808,7 +3808,7 @@ NIL ((|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}."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-926))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-970 E V R P -1955) +(-970 E V R P -1956) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-464)))) @@ -3836,7 +3836,7 @@ NIL ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-977 -1955) +(-977 -1956) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\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{ai = 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 @@ -3944,7 +3944,7 @@ 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 -(-1004 K R UP -1955) +(-1004 K R UP -1956) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -4016,7 +4016,7 @@ 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 -(-1022 -1955 UP UPUP |radicnd| |n|) +(-1022 -1956 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4455 |has| (-419 |#2|) (-374)) (-4460 |has| (-419 |#2|) (-374)) (-4454 |has| (-419 |#2|) (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2755 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2755 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2755 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2755 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2755 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2755 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) @@ -4056,19 +4056,19 @@ 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}}"))) ((-4455 . T) (-4460 . T) (-4454 . T) (-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4459 . T)) NIL -(-1032 R -1955) +(-1032 R -1956) ((|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 -(-1033 R -1955) +(-1033 R -1956) ((|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 -(-1034 -1955 UP) +(-1034 -1956 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 -(-1035 -1955 UP) +(-1035 -1956 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 @@ -4104,7 +4104,7 @@ NIL ((|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"))) ((-4455 . T) (-4460 . T) (-4454 . T) (-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4459 . T)) ((-2755 (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (QUOTE (-576))))) -(-1044 -1955 L) +(-1044 -1956 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4140,7 +4140,7 @@ 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 -(-1053 -1955 |Expon| |VarSet| |FPol| |LFPol|) +(-1053 -1956 |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"))) (((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL @@ -4204,7 +4204,7 @@ 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."))) ((-4459 . T)) NIL -(-1069 |xx| -1955) +(-1069 |xx| -1956) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4308,11 +4308,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1095 |Base| R -1955) +(-1095 |Base| R -1956) ((|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 -(-1096 |Base| R -1955) +(-1096 |Base| R -1956) ((|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 @@ -4468,7 +4468,7 @@ 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 -(-1135 R -1955) +(-1135 R -1956) ((|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 @@ -4516,7 +4516,7 @@ NIL ((|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}"))) ((-4463 . T) (-4462 . T)) NIL -(-1147 UP -1955) +(-1147 UP -1956) ((|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.")) 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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL @@ -4699,11 +4699,11 @@ NIL (-1192 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) 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We may integrate a series when we can divide coefficients by integers.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . 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(NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4828,7 +4828,7 @@ 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 -(-1225 R -1955) +(-1225 R -1956) ((|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 @@ -4836,7 +4836,7 @@ 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 -(-1227 R -1955) +(-1227 R -1956) ((|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 -626) (LIST (QUOTE -905) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -899) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -899) (|devaluate| |#1|))))) @@ -4864,7 +4864,7 @@ 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 (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) -(-1234 -1955) +(-1234 -1956) ((|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 @@ -4927,11 +4927,11 @@ NIL (-1249 |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)}."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . 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The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -5011,11 +5011,11 @@ NIL (-1270 |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)}."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1589) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1962) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) +((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2610) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1961) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-1271 |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."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1589) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1962) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2610) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1961) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) (-1272 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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) (((-4464 "*") |has| (-1271 |#2| |#3| |#4|) (-174)) (-4455 |has| (-1271 |#2| |#3| |#4|) (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) @@ -5035,7 +5035,7 @@ NIL (-1276 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-576)))) (|HasCategory| |#2| (QUOTE (-976))) (|HasCategory| |#2| (QUOTE (-1221))) (|HasSignature| |#2| (LIST (QUOTE -1962) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1589) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1195))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-976))) (|HasCategory| |#2| (QUOTE (-1221))) (|HasSignature| |#2| (LIST (QUOTE -1961) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2610) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1195))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) (-1277 |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."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) @@ -5043,12 +5043,12 @@ NIL (-1278 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1131))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1589) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1962) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1131))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2610) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1961) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) (-1279 |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 -(-1280 -1955 UP L UTS) +(-1280 -1956 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 (-568)))) @@ -5108,7 +5108,7 @@ 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 -(-1295 K R UP -1955) +(-1295 K R UP -1956) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -5144,11 +5144,11 @@ 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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) NIL -(-1304 S -1955) +(-1304 S -1956) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1305 -1955) +(-1305 -1956) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL @@ -5208,4 +5208,4 @@ NIL NIL NIL NIL -((-3 NIL 2293419 2293424 2293429 2293434) (-2 NIL 2293399 2293404 2293409 2293414) (-1 NIL 2293379 2293384 2293389 2293394) (0 NIL 2293359 2293364 2293369 2293374) (-1315 "ZMOD.spad" 2293168 2293181 2293297 2293354) (-1314 "ZLINDEP.spad" 2292234 2292245 2293158 2293163) (-1313 "ZDSOLVE.spad" 2282179 2282201 2292224 2292229) (-1312 "YSTREAM.spad" 2281674 2281685 2282169 2282174) (-1311 "YDIAGRAM.spad" 2281308 2281317 2281664 2281669) (-1310 "XRPOLY.spad" 2280528 2280548 2281164 2281233) (-1309 "XPR.spad" 2278323 2278336 2280246 2280345) (-1308 "XPOLY.spad" 2277878 2277889 2278179 2278248) (-1307 "XPOLYC.spad" 2277197 2277213 2277804 2277873) (-1306 "XPBWPOLY.spad" 2275634 2275654 2276977 2277046) (-1305 "XF.spad" 2274097 2274112 2275536 2275629) (-1304 "XF.spad" 2272540 2272557 2273981 2273986) (-1303 "XFALG.spad" 2269588 2269604 2272466 2272535) (-1302 "XEXPPKG.spad" 2268839 2268865 2269578 2269583) (-1301 "XDPOLY.spad" 2268453 2268469 2268695 2268764) (-1300 "XALG.spad" 2268113 2268124 2268409 2268448) (-1299 "WUTSET.spad" 2263916 2263933 2267723 2267750) (-1298 "WP.spad" 2263115 2263159 2263774 2263841) (-1297 "WHILEAST.spad" 2262913 2262922 2263105 2263110) (-1296 "WHEREAST.spad" 2262584 2262593 2262903 2262908) (-1295 "WFFINTBS.spad" 2260247 2260269 2262574 2262579) (-1294 "WEIER.spad" 2258469 2258480 2260237 2260242) (-1293 "VSPACE.spad" 2258142 2258153 2258437 2258464) (-1292 "VSPACE.spad" 2257835 2257848 2258132 2258137) (-1291 "VOID.spad" 2257512 2257521 2257825 2257830) (-1290 "VIEW.spad" 2255192 2255201 2257502 2257507) (-1289 "VIEWDEF.spad" 2250393 2250402 2255182 2255187) (-1288 "VIEW3D.spad" 2234354 2234363 2250383 2250388) (-1287 "VIEW2D.spad" 2222245 2222254 2234344 2234349) (-1286 "VECTOR.spad" 2220766 2220777 2221017 2221044) (-1285 "VECTOR2.spad" 2219405 2219418 2220756 2220761) (-1284 "VECTCAT.spad" 2217309 2217320 2219373 2219400) (-1283 "VECTCAT.spad" 2215020 2215033 2217086 2217091) (-1282 "VARIABLE.spad" 2214800 2214815 2215010 2215015) (-1281 "UTYPE.spad" 2214444 2214453 2214790 2214795) (-1280 "UTSODETL.spad" 2213739 2213763 2214400 2214405) (-1279 "UTSODE.spad" 2211955 2211975 2213729 2213734) (-1278 "UTS.spad" 2206902 2206930 2210422 2210519) (-1277 "UTSCAT.spad" 2204381 2204397 2206800 2206897) (-1276 "UTSCAT.spad" 2201504 2201522 2203925 2203930) (-1275 "UTS2.spad" 2201099 2201134 2201494 2201499) (-1274 "URAGG.spad" 2195772 2195783 2201089 2201094) (-1273 "URAGG.spad" 2190409 2190422 2195728 2195733) (-1272 "UPXSSING.spad" 2188054 2188080 2189490 2189623) (-1271 "UPXS.spad" 2185350 2185378 2186186 2186335) (-1270 "UPXSCONS.spad" 2183109 2183129 2183482 2183631) (-1269 "UPXSCCA.spad" 2181680 2181700 2182955 2183104) (-1268 "UPXSCCA.spad" 2180393 2180415 2181670 2181675) (-1267 "UPXSCAT.spad" 2178982 2178998 2180239 2180388) (-1266 "UPXS2.spad" 2178525 2178578 2178972 2178977) (-1265 "UPSQFREE.spad" 2176939 2176953 2178515 2178520) (-1264 "UPSCAT.spad" 2174726 2174750 2176837 2176934) (-1263 "UPSCAT.spad" 2172219 2172245 2174332 2174337) (-1262 "UPOLYC.spad" 2167259 2167270 2172061 2172214) (-1261 "UPOLYC.spad" 2162191 2162204 2166995 2167000) (-1260 "UPOLYC2.spad" 2161662 2161681 2162181 2162186) (-1259 "UP.spad" 2158768 2158783 2159155 2159308) (-1258 "UPMP.spad" 2157668 2157681 2158758 2158763) (-1257 "UPDIVP.spad" 2157233 2157247 2157658 2157663) (-1256 "UPDECOMP.spad" 2155478 2155492 2157223 2157228) (-1255 "UPCDEN.spad" 2154687 2154703 2155468 2155473) (-1254 "UP2.spad" 2154051 2154072 2154677 2154682) (-1253 "UNISEG.spad" 2153404 2153415 2153970 2153975) (-1252 "UNISEG2.spad" 2152901 2152914 2153360 2153365) (-1251 "UNIFACT.spad" 2152004 2152016 2152891 2152896) (-1250 "ULS.spad" 2141788 2141816 2142733 2143162) (-1249 "ULSCONS.spad" 2132922 2132942 2133292 2133441) (-1248 "ULSCCAT.spad" 2130659 2130679 2132768 2132917) (-1247 "ULSCCAT.spad" 2128504 2128526 2130615 2130620) (-1246 "ULSCAT.spad" 2126736 2126752 2128350 2128499) (-1245 "ULS2.spad" 2126250 2126303 2126726 2126731) (-1244 "UINT8.spad" 2126127 2126136 2126240 2126245) (-1243 "UINT64.spad" 2126003 2126012 2126117 2126122) (-1242 "UINT32.spad" 2125879 2125888 2125993 2125998) (-1241 "UINT16.spad" 2125755 2125764 2125869 2125874) (-1240 "UFD.spad" 2124820 2124829 2125681 2125750) (-1239 "UFD.spad" 2123947 2123958 2124810 2124815) (-1238 "UDVO.spad" 2122828 2122837 2123937 2123942) (-1237 "UDPO.spad" 2120321 2120332 2122784 2122789) (-1236 "TYPE.spad" 2120253 2120262 2120311 2120316) (-1235 "TYPEAST.spad" 2120172 2120181 2120243 2120248) (-1234 "TWOFACT.spad" 2118824 2118839 2120162 2120167) (-1233 "TUPLE.spad" 2118310 2118321 2118723 2118728) (-1232 "TUBETOOL.spad" 2115177 2115186 2118300 2118305) (-1231 "TUBE.spad" 2113824 2113841 2115167 2115172) (-1230 "TS.spad" 2112423 2112439 2113389 2113486) (-1229 "TSETCAT.spad" 2099550 2099567 2112391 2112418) (-1228 "TSETCAT.spad" 2086663 2086682 2099506 2099511) (-1227 "TRMANIP.spad" 2081029 2081046 2086369 2086374) (-1226 "TRIMAT.spad" 2079992 2080017 2081019 2081024) (-1225 "TRIGMNIP.spad" 2078519 2078536 2079982 2079987) (-1224 "TRIGCAT.spad" 2078031 2078040 2078509 2078514) (-1223 "TRIGCAT.spad" 2077541 2077552 2078021 2078026) (-1222 "TREE.spad" 2075999 2076010 2077031 2077058) (-1221 "TRANFUN.spad" 2075838 2075847 2075989 2075994) (-1220 "TRANFUN.spad" 2075675 2075686 2075828 2075833) (-1219 "TOPSP.spad" 2075349 2075358 2075665 2075670) (-1218 "TOOLSIGN.spad" 2075012 2075023 2075339 2075344) (-1217 "TEXTFILE.spad" 2073573 2073582 2075002 2075007) (-1216 "TEX.spad" 2070719 2070728 2073563 2073568) (-1215 "TEX1.spad" 2070275 2070286 2070709 2070714) (-1214 "TEMUTL.spad" 2069830 2069839 2070265 2070270) (-1213 "TBCMPPK.spad" 2067923 2067946 2069820 2069825) (-1212 "TBAGG.spad" 2066973 2066996 2067903 2067918) (-1211 "TBAGG.spad" 2066031 2066056 2066963 2066968) (-1210 "TANEXP.spad" 2065439 2065450 2066021 2066026) (-1209 "TALGOP.spad" 2065163 2065174 2065429 2065434) (-1208 "TABLE.spad" 2063132 2063155 2063402 2063429) (-1207 "TABLEAU.spad" 2062613 2062624 2063122 2063127) (-1206 "TABLBUMP.spad" 2059416 2059427 2062603 2062608) (-1205 "SYSTEM.spad" 2058644 2058653 2059406 2059411) (-1204 "SYSSOLP.spad" 2056127 2056138 2058634 2058639) (-1203 "SYSPTR.spad" 2056026 2056035 2056117 2056122) (-1202 "SYSNNI.spad" 2055208 2055219 2056016 2056021) (-1201 "SYSINT.spad" 2054612 2054623 2055198 2055203) (-1200 "SYNTAX.spad" 2050818 2050827 2054602 2054607) (-1199 "SYMTAB.spad" 2048886 2048895 2050808 2050813) (-1198 "SYMS.spad" 2044909 2044918 2048876 2048881) (-1197 "SYMPOLY.spad" 2043916 2043927 2043998 2044125) (-1196 "SYMFUNC.spad" 2043417 2043428 2043906 2043911) (-1195 "SYMBOL.spad" 2040920 2040929 2043407 2043412) (-1194 "SWITCH.spad" 2037691 2037700 2040910 2040915) (-1193 "SUTS.spad" 2034739 2034767 2036158 2036255) (-1192 "SUPXS.spad" 2032022 2032050 2032871 2033020) (-1191 "SUP.spad" 2028742 2028753 2029515 2029668) (-1190 "SUPFRACF.spad" 2027847 2027865 2028732 2028737) (-1189 "SUP2.spad" 2027239 2027252 2027837 2027842) (-1188 "SUMRF.spad" 2026213 2026224 2027229 2027234) (-1187 "SUMFS.spad" 2025850 2025867 2026203 2026208) (-1186 "SULS.spad" 2015621 2015649 2016579 2017008) (-1185 "SUCHTAST.spad" 2015390 2015399 2015611 2015616) (-1184 "SUCH.spad" 2015072 2015087 2015380 2015385) (-1183 "SUBSPACE.spad" 2007187 2007202 2015062 2015067) (-1182 "SUBRESP.spad" 2006357 2006371 2007143 2007148) (-1181 "STTF.spad" 2002456 2002472 2006347 2006352) (-1180 "STTFNC.spad" 1998924 1998940 2002446 2002451) (-1179 "STTAYLOR.spad" 1991559 1991570 1998805 1998810) (-1178 "STRTBL.spad" 1989610 1989627 1989759 1989786) (-1177 "STRING.spad" 1988397 1988406 1988618 1988645) (-1176 "STREAM.spad" 1985198 1985209 1987805 1987820) (-1175 "STREAM3.spad" 1984771 1984786 1985188 1985193) (-1174 "STREAM2.spad" 1983899 1983912 1984761 1984766) (-1173 "STREAM1.spad" 1983605 1983616 1983889 1983894) (-1172 "STINPROD.spad" 1982541 1982557 1983595 1983600) (-1171 "STEP.spad" 1981742 1981751 1982531 1982536) (-1170 "STEPAST.spad" 1980976 1980985 1981732 1981737) (-1169 "STBL.spad" 1979060 1979088 1979227 1979242) (-1168 "STAGG.spad" 1978135 1978146 1979050 1979055) (-1167 "STAGG.spad" 1977208 1977221 1978125 1978130) (-1166 "STACK.spad" 1976448 1976459 1976698 1976725) (-1165 "SREGSET.spad" 1974116 1974133 1976058 1976085) (-1164 "SRDCMPK.spad" 1972677 1972697 1974106 1974111) (-1163 "SRAGG.spad" 1967820 1967829 1972645 1972672) (-1162 "SRAGG.spad" 1962983 1962994 1967810 1967815) (-1161 "SQMATRIX.spad" 1960526 1960544 1961442 1961529) (-1160 "SPLTREE.spad" 1954922 1954935 1959806 1959833) (-1159 "SPLNODE.spad" 1951510 1951523 1954912 1954917) (-1158 "SPFCAT.spad" 1950319 1950328 1951500 1951505) (-1157 "SPECOUT.spad" 1948871 1948880 1950309 1950314) (-1156 "SPADXPT.spad" 1940466 1940475 1948861 1948866) (-1155 "spad-parser.spad" 1939931 1939940 1940456 1940461) (-1154 "SPADAST.spad" 1939632 1939641 1939921 1939926) (-1153 "SPACEC.spad" 1923831 1923842 1939622 1939627) (-1152 "SPACE3.spad" 1923607 1923618 1923821 1923826) (-1151 "SORTPAK.spad" 1923156 1923169 1923563 1923568) (-1150 "SOLVETRA.spad" 1920919 1920930 1923146 1923151) (-1149 "SOLVESER.spad" 1919447 1919458 1920909 1920914) (-1148 "SOLVERAD.spad" 1915473 1915484 1919437 1919442) (-1147 "SOLVEFOR.spad" 1913935 1913953 1915463 1915468) (-1146 "SNTSCAT.spad" 1913535 1913552 1913903 1913930) (-1145 "SMTS.spad" 1911807 1911833 1913100 1913197) (-1144 "SMP.spad" 1909282 1909302 1909672 1909799) (-1143 "SMITH.spad" 1908127 1908152 1909272 1909277) (-1142 "SMATCAT.spad" 1906237 1906267 1908071 1908122) (-1141 "SMATCAT.spad" 1904279 1904311 1906115 1906120) (-1140 "SKAGG.spad" 1903242 1903253 1904247 1904274) (-1139 "SINT.spad" 1902182 1902191 1903108 1903237) (-1138 "SIMPAN.spad" 1901910 1901919 1902172 1902177) (-1137 "SIG.spad" 1901240 1901249 1901900 1901905) (-1136 "SIGNRF.spad" 1900358 1900369 1901230 1901235) (-1135 "SIGNEF.spad" 1899637 1899654 1900348 1900353) (-1134 "SIGAST.spad" 1899022 1899031 1899627 1899632) (-1133 "SHP.spad" 1896950 1896965 1898978 1898983) (-1132 "SHDP.spad" 1884628 1884655 1885137 1885236) (-1131 "SGROUP.spad" 1884236 1884245 1884618 1884623) (-1130 "SGROUP.spad" 1883842 1883853 1884226 1884231) (-1129 "SGCF.spad" 1876981 1876990 1883832 1883837) (-1128 "SFRTCAT.spad" 1875911 1875928 1876949 1876976) (-1127 "SFRGCD.spad" 1874974 1874994 1875901 1875906) (-1126 "SFQCMPK.spad" 1869611 1869631 1874964 1874969) (-1125 "SFORT.spad" 1869050 1869064 1869601 1869606) (-1124 "SEXOF.spad" 1868893 1868933 1869040 1869045) (-1123 "SEX.spad" 1868785 1868794 1868883 1868888) (-1122 "SEXCAT.spad" 1866557 1866597 1868775 1868780) (-1121 "SET.spad" 1864845 1864856 1865942 1865981) (-1120 "SETMN.spad" 1863295 1863312 1864835 1864840) (-1119 "SETCAT.spad" 1862617 1862626 1863285 1863290) (-1118 "SETCAT.spad" 1861937 1861948 1862607 1862612) (-1117 "SETAGG.spad" 1858486 1858497 1861917 1861932) (-1116 "SETAGG.spad" 1855043 1855056 1858476 1858481) (-1115 "SEQAST.spad" 1854746 1854755 1855033 1855038) (-1114 "SEGXCAT.spad" 1853902 1853915 1854736 1854741) (-1113 "SEG.spad" 1853715 1853726 1853821 1853826) (-1112 "SEGCAT.spad" 1852640 1852651 1853705 1853710) (-1111 "SEGBIND.spad" 1852398 1852409 1852587 1852592) (-1110 "SEGBIND2.spad" 1852096 1852109 1852388 1852393) (-1109 "SEGAST.spad" 1851810 1851819 1852086 1852091) (-1108 "SEG2.spad" 1851245 1851258 1851766 1851771) (-1107 "SDVAR.spad" 1850521 1850532 1851235 1851240) (-1106 "SDPOL.spad" 1847854 1847865 1848145 1848272) (-1105 "SCPKG.spad" 1845943 1845954 1847844 1847849) (-1104 "SCOPE.spad" 1845096 1845105 1845933 1845938) (-1103 "SCACHE.spad" 1843792 1843803 1845086 1845091) (-1102 "SASTCAT.spad" 1843701 1843710 1843782 1843787) (-1101 "SAOS.spad" 1843573 1843582 1843691 1843696) (-1100 "SAERFFC.spad" 1843286 1843306 1843563 1843568) (-1099 "SAE.spad" 1840756 1840772 1841367 1841502) (-1098 "SAEFACT.spad" 1840457 1840477 1840746 1840751) (-1097 "RURPK.spad" 1838116 1838132 1840447 1840452) (-1096 "RULESET.spad" 1837569 1837593 1838106 1838111) (-1095 "RULE.spad" 1835809 1835833 1837559 1837564) (-1094 "RULECOLD.spad" 1835661 1835674 1835799 1835804) (-1093 "RTVALUE.spad" 1835396 1835405 1835651 1835656) (-1092 "RSTRCAST.spad" 1835113 1835122 1835386 1835391) (-1091 "RSETGCD.spad" 1831491 1831511 1835103 1835108) (-1090 "RSETCAT.spad" 1821427 1821444 1831459 1831486) (-1089 "RSETCAT.spad" 1811383 1811402 1821417 1821422) (-1088 "RSDCMPK.spad" 1809835 1809855 1811373 1811378) (-1087 "RRCC.spad" 1808219 1808249 1809825 1809830) (-1086 "RRCC.spad" 1806601 1806633 1808209 1808214) (-1085 "RPTAST.spad" 1806303 1806312 1806591 1806596) (-1084 "RPOLCAT.spad" 1785663 1785678 1806171 1806298) (-1083 "RPOLCAT.spad" 1764736 1764753 1785246 1785251) (-1082 "ROUTINE.spad" 1760157 1760166 1762921 1762948) (-1081 "ROMAN.spad" 1759485 1759494 1760023 1760152) (-1080 "ROIRC.spad" 1758565 1758597 1759475 1759480) (-1079 "RNS.spad" 1757468 1757477 1758467 1758560) (-1078 "RNS.spad" 1756457 1756468 1757458 1757463) (-1077 "RNG.spad" 1756192 1756201 1756447 1756452) (-1076 "RNGBIND.spad" 1755352 1755366 1756147 1756152) (-1075 "RMODULE.spad" 1755117 1755128 1755342 1755347) (-1074 "RMCAT2.spad" 1754537 1754594 1755107 1755112) (-1073 "RMATRIX.spad" 1753325 1753344 1753668 1753707) (-1072 "RMATCAT.spad" 1748904 1748935 1753281 1753320) (-1071 "RMATCAT.spad" 1744373 1744406 1748752 1748757) (-1070 "RLINSET.spad" 1744077 1744088 1744363 1744368) (-1069 "RINTERP.spad" 1743965 1743985 1744067 1744072) (-1068 "RING.spad" 1743435 1743444 1743945 1743960) (-1067 "RING.spad" 1742913 1742924 1743425 1743430) (-1066 "RIDIST.spad" 1742305 1742314 1742903 1742908) (-1065 "RGCHAIN.spad" 1740833 1740849 1741735 1741762) (-1064 "RGBCSPC.spad" 1740614 1740626 1740823 1740828) (-1063 "RGBCMDL.spad" 1740144 1740156 1740604 1740609) (-1062 "RF.spad" 1737786 1737797 1740134 1740139) (-1061 "RFFACTOR.spad" 1737248 1737259 1737776 1737781) (-1060 "RFFACT.spad" 1736983 1736995 1737238 1737243) (-1059 "RFDIST.spad" 1735979 1735988 1736973 1736978) (-1058 "RETSOL.spad" 1735398 1735411 1735969 1735974) (-1057 "RETRACT.spad" 1734826 1734837 1735388 1735393) (-1056 "RETRACT.spad" 1734252 1734265 1734816 1734821) (-1055 "RETAST.spad" 1734064 1734073 1734242 1734247) (-1054 "RESULT.spad" 1731662 1731671 1732249 1732276) (-1053 "RESRING.spad" 1731009 1731056 1731600 1731657) (-1052 "RESLATC.spad" 1730333 1730344 1730999 1731004) (-1051 "REPSQ.spad" 1730064 1730075 1730323 1730328) (-1050 "REP.spad" 1727618 1727627 1730054 1730059) (-1049 "REPDB.spad" 1727325 1727336 1727608 1727613) (-1048 "REP2.spad" 1716983 1716994 1727167 1727172) (-1047 "REP1.spad" 1711179 1711190 1716933 1716938) (-1046 "REGSET.spad" 1708940 1708957 1710789 1710816) (-1045 "REF.spad" 1708275 1708286 1708895 1708900) (-1044 "REDORDER.spad" 1707481 1707498 1708265 1708270) (-1043 "RECLOS.spad" 1706264 1706284 1706968 1707061) (-1042 "REALSOLV.spad" 1705404 1705413 1706254 1706259) (-1041 "REAL.spad" 1705276 1705285 1705394 1705399) (-1040 "REAL0Q.spad" 1702574 1702589 1705266 1705271) (-1039 "REAL0.spad" 1699418 1699433 1702564 1702569) (-1038 "RDUCEAST.spad" 1699139 1699148 1699408 1699413) (-1037 "RDIV.spad" 1698794 1698819 1699129 1699134) (-1036 "RDIST.spad" 1698361 1698372 1698784 1698789) (-1035 "RDETRS.spad" 1697225 1697243 1698351 1698356) (-1034 "RDETR.spad" 1695364 1695382 1697215 1697220) (-1033 "RDEEFS.spad" 1694463 1694480 1695354 1695359) (-1032 "RDEEF.spad" 1693473 1693490 1694453 1694458) (-1031 "RCFIELD.spad" 1690659 1690668 1693375 1693468) (-1030 "RCFIELD.spad" 1687931 1687942 1690649 1690654) (-1029 "RCAGG.spad" 1685859 1685870 1687921 1687926) (-1028 "RCAGG.spad" 1683714 1683727 1685778 1685783) (-1027 "RATRET.spad" 1683074 1683085 1683704 1683709) (-1026 "RATFACT.spad" 1682766 1682778 1683064 1683069) (-1025 "RANDSRC.spad" 1682085 1682094 1682756 1682761) (-1024 "RADUTIL.spad" 1681841 1681850 1682075 1682080) (-1023 "RADIX.spad" 1678665 1678679 1680211 1680304) (-1022 "RADFF.spad" 1676404 1676441 1676523 1676679) (-1021 "RADCAT.spad" 1675999 1676008 1676394 1676399) (-1020 "RADCAT.spad" 1675592 1675603 1675989 1675994) (-1019 "QUEUE.spad" 1674823 1674834 1675082 1675109) (-1018 "QUAT.spad" 1673311 1673322 1673654 1673719) (-1017 "QUATCT2.spad" 1672931 1672950 1673301 1673306) (-1016 "QUATCAT.spad" 1671101 1671112 1672861 1672926) (-1015 "QUATCAT.spad" 1669022 1669035 1670784 1670789) (-1014 "QUAGG.spad" 1667849 1667860 1668990 1669017) (-1013 "QQUTAST.spad" 1667617 1667626 1667839 1667844) (-1012 "QFORM.spad" 1667235 1667250 1667607 1667612) (-1011 "QFCAT.spad" 1665937 1665948 1667137 1667230) (-1010 "QFCAT.spad" 1664230 1664243 1665432 1665437) (-1009 "QFCAT2.spad" 1663922 1663939 1664220 1664225) (-1008 "QEQUAT.spad" 1663480 1663489 1663912 1663917) (-1007 "QCMPACK.spad" 1658226 1658246 1663470 1663475) (-1006 "QALGSET.spad" 1654304 1654337 1658140 1658145) (-1005 "QALGSET2.spad" 1652299 1652318 1654294 1654299) (-1004 "PWFFINTB.spad" 1649714 1649736 1652289 1652294) (-1003 "PUSHVAR.spad" 1649052 1649072 1649704 1649709) (-1002 "PTRANFN.spad" 1645179 1645190 1649042 1649047) (-1001 "PTPACK.spad" 1642266 1642277 1645169 1645174) (-1000 "PTFUNC2.spad" 1642088 1642103 1642256 1642261) (-999 "PTCAT.spad" 1641343 1641353 1642056 1642083) (-998 "PSQFR.spad" 1640650 1640674 1641333 1641338) (-997 "PSEUDLIN.spad" 1639536 1639546 1640640 1640645) (-996 "PSETPK.spad" 1624969 1624985 1639414 1639419) (-995 "PSETCAT.spad" 1618889 1618912 1624949 1624964) (-994 "PSETCAT.spad" 1612783 1612808 1618845 1618850) (-993 "PSCURVE.spad" 1611766 1611774 1612773 1612778) (-992 "PSCAT.spad" 1610549 1610578 1611664 1611761) (-991 "PSCAT.spad" 1609422 1609453 1610539 1610544) (-990 "PRTITION.spad" 1608120 1608128 1609412 1609417) (-989 "PRTDAST.spad" 1607839 1607847 1608110 1608115) (-988 "PRS.spad" 1597401 1597418 1607795 1607800) (-987 "PRQAGG.spad" 1596836 1596846 1597369 1597396) (-986 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1577359 1577364) (-967 "POLYCATQ.spad" 1574752 1574774 1576624 1576629) (-966 "POLYCAT.spad" 1568222 1568243 1574620 1574747) (-965 "POLYCAT.spad" 1561030 1561053 1567430 1567435) (-964 "POLY2UP.spad" 1560482 1560496 1561020 1561025) (-963 "POLY2.spad" 1560079 1560091 1560472 1560477) (-962 "POLUTIL.spad" 1559020 1559049 1560035 1560040) (-961 "POLTOPOL.spad" 1557768 1557783 1559010 1559015) (-960 "POINT.spad" 1556453 1556463 1556540 1556567) (-959 "PNTHEORY.spad" 1553155 1553163 1556443 1556448) (-958 "PMTOOLS.spad" 1551930 1551944 1553145 1553150) (-957 "PMSYM.spad" 1551479 1551489 1551920 1551925) (-956 "PMQFCAT.spad" 1551070 1551084 1551469 1551474) (-955 "PMPRED.spad" 1550549 1550563 1551060 1551065) (-954 "PMPREDFS.spad" 1550003 1550025 1550539 1550544) (-953 "PMPLCAT.spad" 1549083 1549101 1549935 1549940) (-952 "PMLSAGG.spad" 1548668 1548682 1549073 1549078) (-951 "PMKERNEL.spad" 1548247 1548259 1548658 1548663) (-950 "PMINS.spad" 1547827 1547837 1548237 1548242) (-949 "PMFS.spad" 1547404 1547422 1547817 1547822) (-948 "PMDOWN.spad" 1546694 1546708 1547394 1547399) (-947 "PMASS.spad" 1545704 1545712 1546684 1546689) (-946 "PMASSFS.spad" 1544671 1544687 1545694 1545699) (-945 "PLOTTOOL.spad" 1544451 1544459 1544661 1544666) (-944 "PLOT.spad" 1539374 1539382 1544441 1544446) (-943 "PLOT3D.spad" 1535838 1535846 1539364 1539369) (-942 "PLOT1.spad" 1534995 1535005 1535828 1535833) (-941 "PLEQN.spad" 1522285 1522312 1534985 1534990) (-940 "PINTERP.spad" 1521907 1521926 1522275 1522280) (-939 "PINTERPA.spad" 1521691 1521707 1521897 1521902) (-938 "PI.spad" 1521300 1521308 1521665 1521686) (-937 "PID.spad" 1520270 1520278 1521226 1521295) (-936 "PICOERCE.spad" 1519927 1519937 1520260 1520265) (-935 "PGROEB.spad" 1518528 1518542 1519917 1519922) (-934 "PGE.spad" 1510145 1510153 1518518 1518523) (-933 "PGCD.spad" 1509035 1509052 1510135 1510140) (-932 "PFRPAC.spad" 1508184 1508194 1509025 1509030) (-931 "PFR.spad" 1504847 1504857 1508086 1508179) (-930 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"PDECOMP.spad" 1470109 1470126 1470629 1470634) (-910 "PDECAT.spad" 1468465 1468473 1470099 1470104) (-909 "PDDOM.spad" 1467903 1467916 1468455 1468460) (-908 "PDDOM.spad" 1467339 1467354 1467893 1467898) (-907 "PCOMP.spad" 1467192 1467205 1467329 1467334) (-906 "PBWLB.spad" 1465780 1465797 1467182 1467187) (-905 "PATTERN.spad" 1460319 1460329 1465770 1465775) (-904 "PATTERN2.spad" 1460057 1460069 1460309 1460314) (-903 "PATTERN1.spad" 1458393 1458409 1460047 1460052) (-902 "PATRES.spad" 1455968 1455980 1458383 1458388) (-901 "PATRES2.spad" 1455640 1455654 1455958 1455963) (-900 "PATMATCH.spad" 1453837 1453868 1455348 1455353) (-899 "PATMAB.spad" 1453266 1453276 1453827 1453832) (-898 "PATLRES.spad" 1452352 1452366 1453256 1453261) (-897 "PATAB.spad" 1452116 1452126 1452342 1452347) (-896 "PARTPERM.spad" 1450124 1450132 1452106 1452111) (-895 "PARSURF.spad" 1449558 1449586 1450114 1450119) (-894 "PARSU2.spad" 1449355 1449371 1449548 1449553) (-893 "script-parser.spad" 1448875 1448883 1449345 1449350) (-892 "PARSCURV.spad" 1448309 1448337 1448865 1448870) (-891 "PARSC2.spad" 1448100 1448116 1448299 1448304) (-890 "PARPCURV.spad" 1447562 1447590 1448090 1448095) (-889 "PARPC2.spad" 1447353 1447369 1447552 1447557) (-888 "PARAMAST.spad" 1446481 1446489 1447343 1447348) (-887 "PAN2EXPR.spad" 1445893 1445901 1446471 1446476) (-886 "PALETTE.spad" 1444863 1444871 1445883 1445888) (-885 "PAIR.spad" 1443850 1443863 1444451 1444456) (-884 "PADICRC.spad" 1441091 1441109 1442262 1442355) (-883 "PADICRAT.spad" 1438999 1439011 1439220 1439313) (-882 "PADIC.spad" 1438694 1438706 1438925 1438994) (-881 "PADICCT.spad" 1437243 1437255 1438620 1438689) (-880 "PADEPAC.spad" 1435932 1435951 1437233 1437238) (-879 "PADE.spad" 1434684 1434700 1435922 1435927) (-878 "OWP.spad" 1433924 1433954 1434542 1434609) (-877 "OVERSET.spad" 1433497 1433505 1433914 1433919) (-876 "OVAR.spad" 1433278 1433301 1433487 1433492) (-875 "OUT.spad" 1432364 1432372 1433268 1433273) (-874 "OUTFORM.spad" 1421756 1421764 1432354 1432359) (-873 "OUTBFILE.spad" 1421174 1421182 1421746 1421751) (-872 "OUTBCON.spad" 1420180 1420188 1421164 1421169) (-871 "OUTBCON.spad" 1419184 1419194 1420170 1420175) (-870 "OSI.spad" 1418659 1418667 1419174 1419179) (-869 "OSGROUP.spad" 1418577 1418585 1418649 1418654) (-868 "ORTHPOL.spad" 1417062 1417072 1418494 1418499) (-867 "OREUP.spad" 1416515 1416543 1416742 1416781) (-866 "ORESUP.spad" 1415816 1415840 1416195 1416234) (-865 "OREPCTO.spad" 1413673 1413685 1415736 1415741) (-864 "OREPCAT.spad" 1407820 1407830 1413629 1413668) (-863 "OREPCAT.spad" 1401857 1401869 1407668 1407673) (-862 "ORDSET.spad" 1401029 1401037 1401847 1401852) (-861 "ORDSET.spad" 1400199 1400209 1401019 1401024) (-860 "ORDRING.spad" 1399589 1399597 1400179 1400194) (-859 "ORDRING.spad" 1398987 1398997 1399579 1399584) (-858 "ORDMON.spad" 1398842 1398850 1398977 1398982) (-857 "ORDFUNS.spad" 1397974 1397990 1398832 1398837) (-856 "ORDFIN.spad" 1397794 1397802 1397964 1397969) (-855 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(-836 "OMERRK.spad" 1374543 1374551 1375499 1375504) (-835 "OMENC.spad" 1373887 1373895 1374533 1374538) (-834 "OMDEV.spad" 1368196 1368204 1373877 1373882) (-833 "OMCONN.spad" 1367605 1367613 1368186 1368191) (-832 "OINTDOM.spad" 1367368 1367376 1367531 1367600) (-831 "OFMONOID.spad" 1365491 1365501 1367324 1367329) (-830 "ODVAR.spad" 1364752 1364762 1365481 1365486) (-829 "ODR.spad" 1364396 1364422 1364564 1364713) (-828 "ODPOL.spad" 1361685 1361695 1362025 1362152) (-827 "ODP.spad" 1349499 1349519 1349872 1349971) (-826 "ODETOOLS.spad" 1348148 1348167 1349489 1349494) (-825 "ODESYS.spad" 1345842 1345859 1348138 1348143) (-824 "ODERTRIC.spad" 1341851 1341868 1345799 1345804) (-823 "ODERED.spad" 1341250 1341274 1341841 1341846) (-822 "ODERAT.spad" 1338865 1338882 1341240 1341245) (-821 "ODEPRRIC.spad" 1335902 1335924 1338855 1338860) (-820 "ODEPROB.spad" 1335159 1335167 1335892 1335897) (-819 "ODEPRIM.spad" 1332493 1332515 1335149 1335154) (-818 "ODEPAL.spad" 1331879 1331903 1332483 1332488) (-817 "ODEPACK.spad" 1318545 1318553 1331869 1331874) (-816 "ODEINT.spad" 1317980 1317996 1318535 1318540) (-815 "ODEIFTBL.spad" 1315375 1315383 1317970 1317975) (-814 "ODEEF.spad" 1310866 1310882 1315365 1315370) (-813 "ODECONST.spad" 1310403 1310421 1310856 1310861) (-812 "ODECAT.spad" 1309001 1309009 1310393 1310398) (-811 "OCT.spad" 1307137 1307147 1307851 1307890) (-810 "OCTCT2.spad" 1306783 1306804 1307127 1307132) (-809 "OC.spad" 1304579 1304589 1306739 1306778) (-808 "OC.spad" 1302100 1302112 1304262 1304267) (-807 "OCAMON.spad" 1301948 1301956 1302090 1302095) (-806 "OASGP.spad" 1301763 1301771 1301938 1301943) (-805 "OAMONS.spad" 1301285 1301293 1301753 1301758) (-804 "OAMON.spad" 1301146 1301154 1301275 1301280) (-803 "OAGROUP.spad" 1301008 1301016 1301136 1301141) (-802 "NUMTUBE.spad" 1300599 1300615 1300998 1301003) (-801 "NUMQUAD.spad" 1288575 1288583 1300589 1300594) (-800 "NUMODE.spad" 1279929 1279937 1288565 1288570) (-799 "NUMINT.spad" 1277495 1277503 1279919 1279924) (-798 "NUMFMT.spad" 1276335 1276343 1277485 1277490) (-797 "NUMERIC.spad" 1268449 1268459 1276140 1276145) (-796 "NTSCAT.spad" 1266957 1266973 1268417 1268444) (-795 "NTPOLFN.spad" 1266508 1266518 1266874 1266879) (-794 "NSUP.spad" 1259461 1259471 1264001 1264154) (-793 "NSUP2.spad" 1258853 1258865 1259451 1259456) (-792 "NSMP.spad" 1255083 1255102 1255391 1255518) (-791 "NREP.spad" 1253461 1253475 1255073 1255078) (-790 "NPCOEF.spad" 1252707 1252727 1253451 1253456) (-789 "NORMRETR.spad" 1252305 1252344 1252697 1252702) (-788 "NORMPK.spad" 1250207 1250226 1252295 1252300) (-787 "NORMMA.spad" 1249895 1249921 1250197 1250202) (-786 "NONE.spad" 1249636 1249644 1249885 1249890) (-785 "NONE1.spad" 1249312 1249322 1249626 1249631) (-784 "NODE1.spad" 1248799 1248815 1249302 1249307) (-783 "NNI.spad" 1247694 1247702 1248773 1248794) (-782 "NLINSOL.spad" 1246320 1246330 1247684 1247689) (-781 "NIPROB.spad" 1244861 1244869 1246310 1246315) (-780 "NFINTBAS.spad" 1242421 1242438 1244851 1244856) (-779 "NETCLT.spad" 1242395 1242406 1242411 1242416) (-778 "NCODIV.spad" 1240611 1240627 1242385 1242390) (-777 "NCNTFRAC.spad" 1240253 1240267 1240601 1240606) (-776 "NCEP.spad" 1238419 1238433 1240243 1240248) (-775 "NASRING.spad" 1238015 1238023 1238409 1238414) (-774 "NASRING.spad" 1237609 1237619 1238005 1238010) (-773 "NARNG.spad" 1236961 1236969 1237599 1237604) (-772 "NARNG.spad" 1236311 1236321 1236951 1236956) (-771 "NAGSP.spad" 1235388 1235396 1236301 1236306) (-770 "NAGS.spad" 1225049 1225057 1235378 1235383) (-769 "NAGF07.spad" 1223480 1223488 1225039 1225044) (-768 "NAGF04.spad" 1217882 1217890 1223470 1223475) (-767 "NAGF02.spad" 1211951 1211959 1217872 1217877) (-766 "NAGF01.spad" 1207712 1207720 1211941 1211946) (-765 "NAGE04.spad" 1201412 1201420 1207702 1207707) (-764 "NAGE02.spad" 1192072 1192080 1201402 1201407) (-763 "NAGE01.spad" 1188074 1188082 1192062 1192067) (-762 "NAGD03.spad" 1186078 1186086 1188064 1188069) (-761 "NAGD02.spad" 1178825 1178833 1186068 1186073) (-760 "NAGD01.spad" 1173118 1173126 1178815 1178820) (-759 "NAGC06.spad" 1168993 1169001 1173108 1173113) (-758 "NAGC05.spad" 1167494 1167502 1168983 1168988) (-757 "NAGC02.spad" 1166761 1166769 1167484 1167489) (-756 "NAALG.spad" 1166302 1166312 1166729 1166756) (-755 "NAALG.spad" 1165863 1165875 1166292 1166297) (-754 "MULTSQFR.spad" 1162821 1162838 1165853 1165858) (-753 "MULTFACT.spad" 1162204 1162221 1162811 1162816) (-752 "MTSCAT.spad" 1160298 1160319 1162102 1162199) (-751 "MTHING.spad" 1159957 1159967 1160288 1160293) (-750 "MSYSCMD.spad" 1159391 1159399 1159947 1159952) (-749 "MSET.spad" 1157313 1157323 1159061 1159100) (-748 "MSETAGG.spad" 1157158 1157168 1157281 1157308) (-747 "MRING.spad" 1154135 1154147 1156866 1156933) (-746 "MRF2.spad" 1153705 1153719 1154125 1154130) (-745 "MRATFAC.spad" 1153251 1153268 1153695 1153700) (-744 "MPRFF.spad" 1151291 1151310 1153241 1153246) (-743 "MPOLY.spad" 1148762 1148777 1149121 1149248) (-742 "MPCPF.spad" 1148026 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1107923) (-704 "MCALCFN.spad" 1104260 1104286 1107128 1107133) (-703 "MAYBE.spad" 1103544 1103555 1104250 1104255) (-702 "MATSTOR.spad" 1100852 1100862 1103534 1103539) (-701 "MATRIX.spad" 1099439 1099449 1099923 1099950) (-700 "MATLIN.spad" 1096783 1096807 1099323 1099328) (-699 "MATCAT.spad" 1088305 1088327 1096751 1096778) (-698 "MATCAT.spad" 1079699 1079723 1088147 1088152) (-697 "MATCAT2.spad" 1078981 1079029 1079689 1079694) (-696 "MAPPKG3.spad" 1077896 1077910 1078971 1078976) (-695 "MAPPKG2.spad" 1077234 1077246 1077886 1077891) (-694 "MAPPKG1.spad" 1076062 1076072 1077224 1077229) (-693 "MAPPAST.spad" 1075377 1075385 1076052 1076057) (-692 "MAPHACK3.spad" 1075189 1075203 1075367 1075372) (-691 "MAPHACK2.spad" 1074958 1074970 1075179 1075184) (-690 "MAPHACK1.spad" 1074602 1074612 1074948 1074953) (-689 "MAGMA.spad" 1072392 1072409 1074592 1074597) (-688 "MACROAST.spad" 1071971 1071979 1072382 1072387) (-687 "M3D.spad" 1069574 1069584 1071232 1071237) (-686 "LZSTAGG.spad" 1066812 1066822 1069564 1069569) (-685 "LZSTAGG.spad" 1064048 1064060 1066802 1066807) (-684 "LWORD.spad" 1060753 1060770 1064038 1064043) (-683 "LSTAST.spad" 1060537 1060545 1060743 1060748) (-682 "LSQM.spad" 1058694 1058708 1059088 1059139) (-681 "LSPP.spad" 1058229 1058246 1058684 1058689) (-680 "LSMP.spad" 1057079 1057107 1058219 1058224) (-679 "LSMP1.spad" 1054897 1054911 1057069 1057074) (-678 "LSAGG.spad" 1054566 1054576 1054865 1054892) (-677 "LSAGG.spad" 1054255 1054267 1054556 1054561) (-676 "LPOLY.spad" 1053209 1053228 1054111 1054180) (-675 "LPEFRAC.spad" 1052480 1052490 1053199 1053204) (-674 "LO.spad" 1051881 1051895 1052414 1052441) (-673 "LOGIC.spad" 1051483 1051491 1051871 1051876) (-672 "LOGIC.spad" 1051083 1051093 1051473 1051478) (-671 "LODOOPS.spad" 1050013 1050025 1051073 1051078) (-670 "LODO.spad" 1049397 1049413 1049693 1049732) (-669 "LODOF.spad" 1048443 1048460 1049354 1049359) (-668 "LODOCAT.spad" 1047109 1047119 1048399 1048438) (-667 "LODOCAT.spad" 1045773 1045785 1047065 1047070) (-666 "LODO2.spad" 1045046 1045058 1045453 1045492) (-665 "LODO1.spad" 1044446 1044456 1044726 1044765) (-664 "LODEEF.spad" 1043248 1043266 1044436 1044441) (-663 "LNAGG.spad" 1039395 1039405 1043238 1043243) (-662 "LNAGG.spad" 1035506 1035518 1039351 1039356) (-661 "LMOPS.spad" 1032274 1032291 1035496 1035501) (-660 "LMODULE.spad" 1032042 1032052 1032264 1032269) (-659 "LMDICT.spad" 1031212 1031222 1031476 1031503) (-658 "LLINSET.spad" 1030919 1030929 1031202 1031207) (-657 "LITERAL.spad" 1030825 1030836 1030909 1030914) (-656 "LIST.spad" 1028407 1028417 1029819 1029846) (-655 "LIST3.spad" 1027718 1027732 1028397 1028402) (-654 "LIST2.spad" 1026420 1026432 1027708 1027713) (-653 "LIST2MAP.spad" 1023323 1023335 1026410 1026415) (-652 "LINSET.spad" 1023102 1023112 1023313 1023318) (-651 "LINEXP.spad" 1021845 1021855 1023092 1023097) (-650 "LINDEP.spad" 1020654 1020666 1021757 1021762) (-649 "LIMITRF.spad" 1018582 1018592 1020644 1020649) (-648 "LIMITPS.spad" 1017485 1017498 1018572 1018577) (-647 "LIE.spad" 1015501 1015513 1016775 1016920) (-646 "LIECAT.spad" 1014977 1014987 1015427 1015496) (-645 "LIECAT.spad" 1014481 1014493 1014933 1014938) (-644 "LIB.spad" 1012232 1012240 1012678 1012693) (-643 "LGROBP.spad" 1009585 1009604 1012222 1012227) (-642 "LF.spad" 1008540 1008556 1009575 1009580) (-641 "LFCAT.spad" 1007599 1007607 1008530 1008535) (-640 "LEXTRIPK.spad" 1003102 1003117 1007589 1007594) (-639 "LEXP.spad" 1001105 1001132 1003082 1003097) (-638 "LETAST.spad" 1000804 1000812 1001095 1001100) (-637 "LEADCDET.spad" 999202 999219 1000794 1000799) (-636 "LAZM3PK.spad" 997906 997928 999192 999197) (-635 "LAUPOL.spad" 996506 996519 997406 997475) (-634 "LAPLACE.spad" 996089 996105 996496 996501) (-633 "LA.spad" 995529 995543 996011 996050) (-632 "LALG.spad" 995305 995315 995509 995524) (-631 "LALG.spad" 995089 995101 995295 995300) (-630 "KVTFROM.spad" 994824 994834 995079 995084) (-629 "KTVLOGIC.spad" 994336 994344 994814 994819) (-628 "KRCFROM.spad" 994074 994084 994326 994331) (-627 "KOVACIC.spad" 992797 992814 994064 994069) (-626 "KONVERT.spad" 992519 992529 992787 992792) (-625 "KOERCE.spad" 992256 992266 992509 992514) (-624 "KERNEL.spad" 990911 990921 992040 992045) (-623 "KERNEL2.spad" 990614 990626 990901 990906) (-622 "KDAGG.spad" 989723 989745 990594 990609) (-621 "KDAGG.spad" 988840 988864 989713 989718) (-620 "KAFILE.spad" 987694 987710 987929 987956) (-619 "JORDAN.spad" 985523 985535 986984 987129) (-618 "JOINAST.spad" 985217 985225 985513 985518) (-617 "JAVACODE.spad" 985083 985091 985207 985212) (-616 "IXAGG.spad" 983216 983240 985073 985078) (-615 "IXAGG.spad" 981204 981230 983063 983068) (-614 "IVECTOR.spad" 979821 979836 979976 980003) (-613 "ITUPLE.spad" 978982 978992 979811 979816) (-612 "ITRIGMNP.spad" 977821 977840 978972 978977) (-611 "ITFUN3.spad" 977327 977341 977811 977816) (-610 "ITFUN2.spad" 977071 977083 977317 977322) (-609 "ITFORM.spad" 976426 976434 977061 977066) (-608 "ITAYLOR.spad" 974420 974435 976290 976387) (-607 "ISUPS.spad" 966857 966872 973394 973491) (-606 "ISUMP.spad" 966358 966374 966847 966852) (-605 "ISTRING.spad" 965285 965298 965366 965393) (-604 "ISAST.spad" 965004 965012 965275 965280) (-603 "IRURPK.spad" 963721 963740 964994 964999) (-602 "IRSN.spad" 961693 961701 963711 963716) (-601 "IRRF2F.spad" 960178 960188 961649 961654) (-600 "IRREDFFX.spad" 959779 959790 960168 960173) (-599 "IROOT.spad" 958118 958128 959769 959774) (-598 "IR.spad" 955919 955933 957973 958000) (-597 "IRFORM.spad" 955243 955251 955909 955914) (-596 "IR2.spad" 954271 954287 955233 955238) (-595 "IR2F.spad" 953477 953493 954261 954266) (-594 "IPRNTPK.spad" 953237 953245 953467 953472) (-593 "IPF.spad" 952802 952814 953042 953135) (-592 "IPADIC.spad" 952563 952589 952728 952797) (-591 "IP4ADDR.spad" 952120 952128 952553 952558) (-590 "IOMODE.spad" 951642 951650 952110 952115) (-589 "IOBFILE.spad" 951003 951011 951632 951637) (-588 "IOBCON.spad" 950868 950876 950993 950998) (-587 "INVLAPLA.spad" 950517 950533 950858 950863) (-586 "INTTR.spad" 943899 943916 950507 950512) (-585 "INTTOOLS.spad" 941654 941670 943473 943478) (-584 "INTSLPE.spad" 940974 940982 941644 941649) (-583 "INTRVL.spad" 940540 940550 940888 940969) (-582 "INTRF.spad" 938964 938978 940530 940535) (-581 "INTRET.spad" 938396 938406 938954 938959) (-580 "INTRAT.spad" 937123 937140 938386 938391) (-579 "INTPM.spad" 935508 935524 936766 936771) (-578 "INTPAF.spad" 933372 933390 935440 935445) (-577 "INTPACK.spad" 923746 923754 933362 933367) (-576 "INT.spad" 923194 923202 923600 923741) (-575 "INTHERTR.spad" 922468 922485 923184 923189) (-574 "INTHERAL.spad" 922138 922162 922458 922463) (-573 "INTHEORY.spad" 918577 918585 922128 922133) (-572 "INTG0.spad" 912310 912328 918509 918514) (-571 "INTFTBL.spad" 906339 906347 912300 912305) (-570 "INTFACT.spad" 905398 905408 906329 906334) (-569 "INTEF.spad" 903783 903799 905388 905393) (-568 "INTDOM.spad" 902406 902414 903709 903778) (-567 "INTDOM.spad" 901091 901101 902396 902401) (-566 "INTCAT.spad" 899350 899360 901005 901086) (-565 "INTBIT.spad" 898857 898865 899340 899345) (-564 "INTALG.spad" 898045 898072 898847 898852) (-563 "INTAF.spad" 897545 897561 898035 898040) (-562 "INTABL.spad" 895621 895652 895784 895811) (-561 "INT8.spad" 895501 895509 895611 895616) (-560 "INT64.spad" 895380 895388 895491 895496) (-559 "INT32.spad" 895259 895267 895370 895375) (-558 "INT16.spad" 895138 895146 895249 895254) (-557 "INS.spad" 892641 892649 895040 895133) (-556 "INS.spad" 890230 890240 892631 892636) (-555 "INPSIGN.spad" 889678 889691 890220 890225) (-554 "INPRODPF.spad" 888774 888793 889668 889673) (-553 "INPRODFF.spad" 887862 887886 888764 888769) (-552 "INNMFACT.spad" 886837 886854 887852 887857) (-551 "INMODGCD.spad" 886325 886355 886827 886832) (-550 "INFSP.spad" 884622 884644 886315 886320) (-549 "INFPROD0.spad" 883702 883721 884612 884617) (-548 "INFORM.spad" 880901 880909 883692 883697) (-547 "INFORM1.spad" 880526 880536 880891 880896) (-546 "INFINITY.spad" 880078 880086 880516 880521) (-545 "INETCLTS.spad" 880055 880063 880068 880073) (-544 "INEP.spad" 878593 878615 880045 880050) (-543 "INDE.spad" 878322 878339 878583 878588) (-542 "INCRMAPS.spad" 877743 877753 878312 878317) (-541 "INBFILE.spad" 876815 876823 877733 877738) (-540 "INBFF.spad" 872609 872620 876805 876810) (-539 "INBCON.spad" 870899 870907 872599 872604) (-538 "INBCON.spad" 869187 869197 870889 870894) (-537 "INAST.spad" 868848 868856 869177 869182) (-536 "IMPTAST.spad" 868556 868564 868838 868843) (-535 "IMATRIX.spad" 867384 867410 867896 867923) (-534 "IMATQF.spad" 866478 866522 867340 867345) (-533 "IMATLIN.spad" 865083 865107 866434 866439) (-532 "ILIST.spad" 863588 863603 864113 864140) (-531 "IIARRAY2.spad" 862859 862897 863078 863105) (-530 "IFF.spad" 862269 862285 862540 862633) (-529 "IFAST.spad" 861883 861891 862259 862264) (-528 "IFARRAY.spad" 859223 859238 860913 860940) (-527 "IFAMON.spad" 859085 859102 859179 859184) (-526 "IEVALAB.spad" 858490 858502 859075 859080) (-525 "IEVALAB.spad" 857893 857907 858480 858485) (-524 "IDPO.spad" 857656 857668 857883 857888) (-523 "IDPOAMS.spad" 857412 857424 857646 857651) (-522 "IDPOAM.spad" 857132 857144 857402 857407) (-521 "IDPC.spad" 855858 855870 857122 857127) (-520 "IDPAM.spad" 855603 855615 855848 855853) (-519 "IDPAG.spad" 855350 855362 855593 855598) (-518 "IDENT.spad" 855000 855008 855340 855345) (-517 "IDECOMP.spad" 852239 852257 854990 854995) (-516 "IDEAL.spad" 847188 847227 852174 852179) (-515 "ICDEN.spad" 846377 846393 847178 847183) (-514 "ICARD.spad" 845568 845576 846367 846372) (-513 "IBPTOOLS.spad" 844175 844192 845558 845563) (-512 "IBITS.spad" 843340 843353 843773 843800) (-511 "IBATOOL.spad" 840317 840336 843330 843335) (-510 "IBACHIN.spad" 838824 838839 840307 840312) (-509 "IARRAY2.spad" 837695 837721 838314 838341) (-508 "IARRAY1.spad" 836587 836602 836725 836752) (-507 "IAN.spad" 834810 834818 836403 836496) (-506 "IALGFACT.spad" 834413 834446 834800 834805) (-505 "HYPCAT.spad" 833837 833845 834403 834408) (-504 "HYPCAT.spad" 833259 833269 833827 833832) (-503 "HOSTNAME.spad" 833067 833075 833249 833254) (-502 "HOMOTOP.spad" 832810 832820 833057 833062) (-501 "HOAGG.spad" 830092 830102 832800 832805) (-500 "HOAGG.spad" 827113 827125 829823 829828) (-499 "HEXADEC.spad" 825118 825126 825483 825576) (-498 "HEUGCD.spad" 824153 824164 825108 825113) (-497 "HELLFDIV.spad" 823743 823767 824143 824148) (-496 "HEAP.spad" 823018 823028 823233 823260) (-495 "HEADAST.spad" 822551 822559 823008 823013) (-494 "HDP.spad" 810361 810377 810738 810837) (-493 "HDMP.spad" 807575 807590 808191 808318) (-492 "HB.spad" 805826 805834 807565 807570) (-491 "HASHTBL.spad" 803854 803885 804065 804092) (-490 "HASAST.spad" 803570 803578 803844 803849) (-489 "HACKPI.spad" 803061 803069 803472 803565) (-488 "GTSET.spad" 801964 801980 802671 802698) (-487 "GSTBL.spad" 800041 800076 800215 800230) (-486 "GSERIES.spad" 797354 797381 798173 798322) (-485 "GROUP.spad" 796627 796635 797334 797349) (-484 "GROUP.spad" 795908 795918 796617 796622) (-483 "GROEBSOL.spad" 794402 794423 795898 795903) (-482 "GRMOD.spad" 792973 792985 794392 794397) (-481 "GRMOD.spad" 791542 791556 792963 792968) (-480 "GRIMAGE.spad" 784431 784439 791532 791537) (-479 "GRDEF.spad" 782810 782818 784421 784426) (-478 "GRAY.spad" 781273 781281 782800 782805) (-477 "GRALG.spad" 780350 780362 781263 781268) (-476 "GRALG.spad" 779425 779439 780340 780345) (-475 "GPOLSET.spad" 778843 778866 779071 779098) (-474 "GOSPER.spad" 778112 778130 778833 778838) (-473 "GMODPOL.spad" 777260 777287 778080 778107) (-472 "GHENSEL.spad" 776343 776357 777250 777255) (-471 "GENUPS.spad" 772636 772649 776333 776338) (-470 "GENUFACT.spad" 772213 772223 772626 772631) (-469 "GENPGCD.spad" 771799 771816 772203 772208) (-468 "GENMFACT.spad" 771251 771270 771789 771794) (-467 "GENEEZ.spad" 769202 769215 771241 771246) (-466 "GDMP.spad" 766258 766275 767032 767159) (-465 "GCNAALG.spad" 760181 760208 766052 766119) (-464 "GCDDOM.spad" 759357 759365 760107 760176) (-463 "GCDDOM.spad" 758595 758605 759347 759352) (-462 "GB.spad" 756121 756159 758551 758556) (-461 "GBINTERN.spad" 752141 752179 756111 756116) (-460 "GBF.spad" 747908 747946 752131 752136) (-459 "GBEUCLID.spad" 745790 745828 747898 747903) (-458 "GAUSSFAC.spad" 745103 745111 745780 745785) (-457 "GALUTIL.spad" 743429 743439 745059 745064) (-456 "GALPOLYU.spad" 741883 741896 743419 743424) (-455 "GALFACTU.spad" 740056 740075 741873 741878) (-454 "GALFACT.spad" 730245 730256 740046 740051) (-453 "FVFUN.spad" 727268 727276 730235 730240) (-452 "FVC.spad" 726320 726328 727258 727263) (-451 "FUNDESC.spad" 725998 726006 726310 726315) (-450 "FUNCTION.spad" 725847 725859 725988 725993) (-449 "FT.spad" 724144 724152 725837 725842) (-448 "FTEM.spad" 723309 723317 724134 724139) (-447 "FSUPFACT.spad" 722209 722228 723245 723250) (-446 "FST.spad" 720295 720303 722199 722204) (-445 "FSRED.spad" 719775 719791 720285 720290) (-444 "FSPRMELT.spad" 718657 718673 719732 719737) (-443 "FSPECF.spad" 716748 716764 718647 718652) (-442 "FS.spad" 711016 711026 716523 716743) (-441 "FS.spad" 705062 705074 710571 710576) (-440 "FSINT.spad" 704722 704738 705052 705057) (-439 "FSERIES.spad" 703913 703925 704542 704641) (-438 "FSCINT.spad" 703230 703246 703903 703908) (-437 "FSAGG.spad" 702347 702357 703186 703225) (-436 "FSAGG.spad" 701426 701438 702267 702272) (-435 "FSAGG2.spad" 700169 700185 701416 701421) (-434 "FS2UPS.spad" 694660 694694 700159 700164) (-433 "FS2.spad" 694307 694323 694650 694655) (-432 "FS2EXPXP.spad" 693432 693455 694297 694302) (-431 "FRUTIL.spad" 692386 692396 693422 693427) (-430 "FR.spad" 686009 686019 691317 691386) (-429 "FRNAALG.spad" 681278 681288 685951 686004) (-428 "FRNAALG.spad" 676559 676571 681234 681239) (-427 "FRNAAF2.spad" 676015 676033 676549 676554) (-426 "FRMOD.spad" 675425 675455 675946 675951) (-425 "FRIDEAL.spad" 674650 674671 675405 675420) (-424 "FRIDEAL2.spad" 674254 674286 674640 674645) (-423 "FRETRCT.spad" 673765 673775 674244 674249) (-422 "FRETRCT.spad" 673142 673154 673623 673628) (-421 "FRAMALG.spad" 671490 671503 673098 673137) (-420 "FRAMALG.spad" 669870 669885 671480 671485) (-419 "FRAC.spad" 666876 666886 667279 667452) (-418 "FRAC2.spad" 666481 666493 666866 666871) (-417 "FR2.spad" 665817 665829 666471 666476) (-416 "FPS.spad" 662632 662640 665707 665812) (-415 "FPS.spad" 659475 659485 662552 662557) (-414 "FPC.spad" 658521 658529 659377 659470) (-413 "FPC.spad" 657653 657663 658511 658516) (-412 "FPATMAB.spad" 657415 657425 657643 657648) (-411 "FPARFRAC.spad" 656265 656282 657405 657410) (-410 "FORTRAN.spad" 654771 654814 656255 656260) (-409 "FORT.spad" 653720 653728 654761 654766) (-408 "FORTFN.spad" 650890 650898 653710 653715) (-407 "FORTCAT.spad" 650574 650582 650880 650885) (-406 "FORMULA.spad" 648048 648056 650564 650569) (-405 "FORMULA1.spad" 647527 647537 648038 648043) (-404 "FORDER.spad" 647218 647242 647517 647522) (-403 "FOP.spad" 646419 646427 647208 647213) (-402 "FNLA.spad" 645843 645865 646387 646414) (-401 "FNCAT.spad" 644438 644446 645833 645838) (-400 "FNAME.spad" 644330 644338 644428 644433) (-399 "FMTC.spad" 644128 644136 644256 644325) (-398 "FMONOID.spad" 643793 643803 644084 644089) (-397 "FMONCAT.spad" 640946 640956 643783 643788) (-396 "FM.spad" 640641 640653 640880 640907) (-395 "FMFUN.spad" 637671 637679 640631 640636) (-394 "FMC.spad" 636723 636731 637661 637666) (-393 "FMCAT.spad" 634391 634409 636691 636718) (-392 "FM1.spad" 633748 633760 634325 634352) (-391 "FLOATRP.spad" 631483 631497 633738 633743) (-390 "FLOAT.spad" 624797 624805 631349 631478) (-389 "FLOATCP.spad" 622228 622242 624787 624792) (-388 "FLINEXP.spad" 621950 621960 622218 622223) (-387 "FLINEXP.spad" 621616 621628 621886 621891) (-386 "FLASORT.spad" 620942 620954 621606 621611) (-385 "FLALG.spad" 618588 618607 620868 620937) (-384 "FLAGG.spad" 615630 615640 618568 618583) (-383 "FLAGG.spad" 612573 612585 615513 615518) (-382 "FLAGG2.spad" 611298 611314 612563 612568) (-381 "FINRALG.spad" 609359 609372 611254 611293) (-380 "FINRALG.spad" 607346 607361 609243 609248) (-379 "FINITE.spad" 606498 606506 607336 607341) (-378 "FINAALG.spad" 595619 595629 606440 606493) (-377 "FINAALG.spad" 584752 584764 595575 595580) (-376 "FILE.spad" 584335 584345 584742 584747) (-375 "FILECAT.spad" 582861 582878 584325 584330) (-374 "FIELD.spad" 582267 582275 582763 582856) (-373 "FIELD.spad" 581759 581769 582257 582262) (-372 "FGROUP.spad" 580406 580416 581739 581754) (-371 "FGLMICPK.spad" 579193 579208 580396 580401) (-370 "FFX.spad" 578568 578583 578909 579002) (-369 "FFSLPE.spad" 578071 578092 578558 578563) (-368 "FFPOLY.spad" 569333 569344 578061 578066) (-367 "FFPOLY2.spad" 568393 568410 569323 569328) (-366 "FFP.spad" 567790 567810 568109 568202) (-365 "FF.spad" 567238 567254 567471 567564) (-364 "FFNBX.spad" 565750 565770 566954 567047) (-363 "FFNBP.spad" 564263 564280 565466 565559) (-362 "FFNB.spad" 562728 562749 563944 564037) (-361 "FFINTBAS.spad" 560242 560261 562718 562723) (-360 "FFIELDC.spad" 557819 557827 560144 560237) (-359 "FFIELDC.spad" 555482 555492 557809 557814) (-358 "FFHOM.spad" 554230 554247 555472 555477) (-357 "FFF.spad" 551665 551676 554220 554225) (-356 "FFCGX.spad" 550512 550532 551381 551474) (-355 "FFCGP.spad" 549401 549421 550228 550321) (-354 "FFCG.spad" 548193 548214 549082 549175) (-353 "FFCAT.spad" 541366 541388 548032 548188) (-352 "FFCAT.spad" 534618 534642 541286 541291) (-351 "FFCAT2.spad" 534365 534405 534608 534613) (-350 "FEXPR.spad" 526082 526128 534121 534160) (-349 "FEVALAB.spad" 525790 525800 526072 526077) (-348 "FEVALAB.spad" 525283 525295 525567 525572) (-347 "FDIV.spad" 524725 524749 525273 525278) (-346 "FDIVCAT.spad" 522789 522813 524715 524720) (-345 "FDIVCAT.spad" 520851 520877 522779 522784) (-344 "FDIV2.spad" 520507 520547 520841 520846) (-343 "FCTRDATA.spad" 519515 519523 520497 520502) (-342 "FCPAK1.spad" 518082 518090 519505 519510) (-341 "FCOMP.spad" 517461 517471 518072 518077) (-340 "FC.spad" 507468 507476 517451 517456) (-339 "FAXF.spad" 500439 500453 507370 507463) (-338 "FAXF.spad" 493462 493478 500395 500400) (-337 "FARRAY.spad" 491459 491469 492492 492519) (-336 "FAMR.spad" 489595 489607 491357 491454) (-335 "FAMR.spad" 487715 487729 489479 489484) (-334 "FAMONOID.spad" 487383 487393 487669 487674) (-333 "FAMONC.spad" 485679 485691 487373 487378) (-332 "FAGROUP.spad" 485303 485313 485575 485602) (-331 "FACUTIL.spad" 483507 483524 485293 485298) (-330 "FACTFUNC.spad" 482701 482711 483497 483502) (-329 "EXPUPXS.spad" 479534 479557 480833 480982) (-328 "EXPRTUBE.spad" 476822 476830 479524 479529) (-327 "EXPRODE.spad" 473982 473998 476812 476817) (-326 "EXPR.spad" 469157 469167 469871 470166) (-325 "EXPR2UPS.spad" 465279 465292 469147 469152) (-324 "EXPR2.spad" 464984 464996 465269 465274) (-323 "EXPEXPAN.spad" 461785 461810 462417 462510) (-322 "EXIT.spad" 461456 461464 461775 461780) (-321 "EXITAST.spad" 461192 461200 461446 461451) (-320 "EVALCYC.spad" 460652 460666 461182 461187) (-319 "EVALAB.spad" 460224 460234 460642 460647) (-318 "EVALAB.spad" 459794 459806 460214 460219) (-317 "EUCDOM.spad" 457368 457376 459720 459789) (-316 "EUCDOM.spad" 455004 455014 457358 457363) (-315 "ESTOOLS.spad" 446850 446858 454994 454999) (-314 "ESTOOLS2.spad" 446453 446467 446840 446845) (-313 "ESTOOLS1.spad" 446138 446149 446443 446448) (-312 "ES.spad" 438953 438961 446128 446133) (-311 "ES.spad" 431674 431684 438851 438856) (-310 "ESCONT.spad" 428467 428475 431664 431669) (-309 "ESCONT1.spad" 428216 428228 428457 428462) (-308 "ES2.spad" 427721 427737 428206 428211) (-307 "ES1.spad" 427291 427307 427711 427716) (-306 "ERROR.spad" 424618 424626 427281 427286) (-305 "EQTBL.spad" 422648 422670 422857 422884) (-304 "EQ.spad" 417453 417463 420240 420352) (-303 "EQ2.spad" 417171 417183 417443 417448) (-302 "EP.spad" 413497 413507 417161 417166) (-301 "ENV.spad" 412175 412183 413487 413492) (-300 "ENTIRER.spad" 411843 411851 412119 412170) (-299 "EMR.spad" 411131 411172 411769 411838) (-298 "ELTAGG.spad" 409385 409404 411121 411126) (-297 "ELTAGG.spad" 407603 407624 409341 409346) (-296 "ELTAB.spad" 407078 407091 407593 407598) (-295 "ELFUTS.spad" 406465 406484 407068 407073) (-294 "ELEMFUN.spad" 406154 406162 406455 406460) (-293 "ELEMFUN.spad" 405841 405851 406144 406149) (-292 "ELAGG.spad" 403812 403822 405821 405836) (-291 "ELAGG.spad" 401720 401732 403731 403736) (-290 "ELABOR.spad" 401066 401074 401710 401715) (-289 "ELABEXPR.spad" 399998 400006 401056 401061) (-288 "EFUPXS.spad" 396774 396804 399954 399959) (-287 "EFULS.spad" 393610 393633 396730 396735) (-286 "EFSTRUC.spad" 391625 391641 393600 393605) (-285 "EF.spad" 386401 386417 391615 391620) (-284 "EAB.spad" 384677 384685 386391 386396) (-283 "E04UCFA.spad" 384213 384221 384667 384672) (-282 "E04NAFA.spad" 383790 383798 384203 384208) (-281 "E04MBFA.spad" 383370 383378 383780 383785) (-280 "E04JAFA.spad" 382906 382914 383360 383365) (-279 "E04GCFA.spad" 382442 382450 382896 382901) (-278 "E04FDFA.spad" 381978 381986 382432 382437) (-277 "E04DGFA.spad" 381514 381522 381968 381973) (-276 "E04AGNT.spad" 377364 377372 381504 381509) (-275 "DVARCAT.spad" 374254 374264 377354 377359) (-274 "DVARCAT.spad" 371142 371154 374244 374249) (-273 "DSMP.spad" 368516 368530 368821 368948) (-272 "DSEXT.spad" 367818 367828 368506 368511) (-271 "DSEXT.spad" 367027 367039 367717 367722) (-270 "DROPT.spad" 360986 360994 367017 367022) (-269 "DROPT1.spad" 360651 360661 360976 360981) (-268 "DROPT0.spad" 355508 355516 360641 360646) (-267 "DRAWPT.spad" 353681 353689 355498 355503) (-266 "DRAW.spad" 346557 346570 353671 353676) (-265 "DRAWHACK.spad" 345865 345875 346547 346552) (-264 "DRAWCX.spad" 343335 343343 345855 345860) (-263 "DRAWCURV.spad" 342882 342897 343325 343330) (-262 "DRAWCFUN.spad" 332414 332422 342872 342877) (-261 "DQAGG.spad" 330592 330602 332382 332409) (-260 "DPOLCAT.spad" 325941 325957 330460 330587) (-259 "DPOLCAT.spad" 321376 321394 325897 325902) (-258 "DPMO.spad" 313136 313152 313274 313487) (-257 "DPMM.spad" 304909 304927 305034 305247) (-256 "DOMTMPLT.spad" 304680 304688 304899 304904) (-255 "DOMCTOR.spad" 304435 304443 304670 304675) (-254 "DOMAIN.spad" 303522 303530 304425 304430) (-253 "DMP.spad" 300782 300797 301352 301479) (-252 "DMEXT.spad" 300649 300659 300750 300777) (-251 "DLP.spad" 300001 300011 300639 300644) (-250 "DLIST.spad" 298427 298437 299031 299058) (-249 "DLAGG.spad" 296844 296854 298417 298422) (-248 "DIVRING.spad" 296386 296394 296788 296839) (-247 "DIVRING.spad" 295972 295982 296376 296381) (-246 "DISPLAY.spad" 294162 294170 295962 295967) (-245 "DIRPROD.spad" 281709 281725 282349 282448) (-244 "DIRPROD2.spad" 280527 280545 281699 281704) (-243 "DIRPCAT.spad" 279720 279736 280423 280522) (-242 "DIRPCAT.spad" 278540 278558 279245 279250) (-241 "DIOSP.spad" 277365 277373 278530 278535) (-240 "DIOPS.spad" 276361 276371 277345 277360) (-239 "DIOPS.spad" 275331 275343 276317 276322) (-238 "DIFRING.spad" 275169 275177 275311 275326) (-237 "DIFFSPC.spad" 274748 274756 275159 275164) (-236 "DIFFSPC.spad" 274325 274335 274738 274743) (-235 "DIFFMOD.spad" 273814 273824 274293 274320) (-234 "DIFFDOM.spad" 272979 272990 273804 273809) (-233 "DIFFDOM.spad" 272142 272155 272969 272974) (-232 "DIFEXT.spad" 271961 271971 272122 272137) (-231 "DIAGG.spad" 271591 271601 271941 271956) (-230 "DIAGG.spad" 271229 271241 271581 271586) (-229 "DHMATRIX.spad" 269424 269434 270569 270596) (-228 "DFSFUN.spad" 263064 263072 269414 269419) (-227 "DFLOAT.spad" 259795 259803 262954 263059) (-226 "DFINTTLS.spad" 258026 258042 259785 259790) (-225 "DERHAM.spad" 255940 255972 258006 258021) (-224 "DEQUEUE.spad" 255147 255157 255430 255457) (-223 "DEGRED.spad" 254764 254778 255137 255142) (-222 "DEFINTRF.spad" 252301 252311 254754 254759) (-221 "DEFINTEF.spad" 250811 250827 252291 252296) (-220 "DEFAST.spad" 250179 250187 250801 250806) (-219 "DECIMAL.spad" 248188 248196 248549 248642) (-218 "DDFACT.spad" 246001 246018 248178 248183) (-217 "DBLRESP.spad" 245601 245625 245991 245996) (-216 "DBASE.spad" 244265 244275 245591 245596) (-215 "DATAARY.spad" 243727 243740 244255 244260) (-214 "D03FAFA.spad" 243555 243563 243717 243722) (-213 "D03EEFA.spad" 243375 243383 243545 243550) (-212 "D03AGNT.spad" 242461 242469 243365 243370) (-211 "D02EJFA.spad" 241923 241931 242451 242456) (-210 "D02CJFA.spad" 241401 241409 241913 241918) (-209 "D02BHFA.spad" 240891 240899 241391 241396) (-208 "D02BBFA.spad" 240381 240389 240881 240886) (-207 "D02AGNT.spad" 235195 235203 240371 240376) (-206 "D01WGTS.spad" 233514 233522 235185 235190) (-205 "D01TRNS.spad" 233491 233499 233504 233509) (-204 "D01GBFA.spad" 233013 233021 233481 233486) (-203 "D01FCFA.spad" 232535 232543 233003 233008) (-202 "D01ASFA.spad" 232003 232011 232525 232530) (-201 "D01AQFA.spad" 231449 231457 231993 231998) (-200 "D01APFA.spad" 230873 230881 231439 231444) (-199 "D01ANFA.spad" 230367 230375 230863 230868) (-198 "D01AMFA.spad" 229877 229885 230357 230362) (-197 "D01ALFA.spad" 229417 229425 229867 229872) (-196 "D01AKFA.spad" 228943 228951 229407 229412) (-195 "D01AJFA.spad" 228466 228474 228933 228938) (-194 "D01AGNT.spad" 224533 224541 228456 228461) (-193 "CYCLOTOM.spad" 224039 224047 224523 224528) (-192 "CYCLES.spad" 220831 220839 224029 224034) (-191 "CVMP.spad" 220248 220258 220821 220826) (-190 "CTRIGMNP.spad" 218748 218764 220238 220243) (-189 "CTOR.spad" 218439 218447 218738 218743) (-188 "CTORKIND.spad" 218042 218050 218429 218434) (-187 "CTORCAT.spad" 217291 217299 218032 218037) (-186 "CTORCAT.spad" 216538 216548 217281 217286) (-185 "CTORCALL.spad" 216127 216137 216528 216533) (-184 "CSTTOOLS.spad" 215372 215385 216117 216122) (-183 "CRFP.spad" 209096 209109 215362 215367) (-182 "CRCEAST.spad" 208816 208824 209086 209091) (-181 "CRAPACK.spad" 207867 207877 208806 208811) (-180 "CPMATCH.spad" 207371 207386 207792 207797) (-179 "CPIMA.spad" 207076 207095 207361 207366) (-178 "COORDSYS.spad" 202085 202095 207066 207071) (-177 "CONTOUR.spad" 201496 201504 202075 202080) (-176 "CONTFRAC.spad" 197246 197256 201398 201491) (-175 "CONDUIT.spad" 197004 197012 197236 197241) (-174 "COMRING.spad" 196678 196686 196942 196999) (-173 "COMPPROP.spad" 196196 196204 196668 196673) (-172 "COMPLPAT.spad" 195963 195978 196186 196191) (-171 "COMPLEX.spad" 191340 191350 191584 191845) (-170 "COMPLEX2.spad" 191055 191067 191330 191335) (-169 "COMPILER.spad" 190604 190612 191045 191050) (-168 "COMPFACT.spad" 190206 190220 190594 190599) (-167 "COMPCAT.spad" 188278 188288 189940 190201) (-166 "COMPCAT.spad" 186078 186090 187742 187747) (-165 "COMMUPC.spad" 185826 185844 186068 186073) (-164 "COMMONOP.spad" 185359 185367 185816 185821) (-163 "COMM.spad" 185170 185178 185349 185354) (-162 "COMMAAST.spad" 184933 184941 185160 185165) (-161 "COMBOPC.spad" 183848 183856 184923 184928) (-160 "COMBINAT.spad" 182615 182625 183838 183843) (-159 "COMBF.spad" 179997 180013 182605 182610) (-158 "COLOR.spad" 178834 178842 179987 179992) (-157 "COLONAST.spad" 178500 178508 178824 178829) (-156 "CMPLXRT.spad" 178211 178228 178490 178495) (-155 "CLLCTAST.spad" 177873 177881 178201 178206) (-154 "CLIP.spad" 173981 173989 177863 177868) (-153 "CLIF.spad" 172636 172652 173937 173976) (-152 "CLAGG.spad" 169141 169151 172626 172631) (-151 "CLAGG.spad" 165517 165529 169004 169009) (-150 "CINTSLPE.spad" 164848 164861 165507 165512) (-149 "CHVAR.spad" 162986 163008 164838 164843) (-148 "CHARZ.spad" 162901 162909 162966 162981) (-147 "CHARPOL.spad" 162411 162421 162891 162896) (-146 "CHARNZ.spad" 162164 162172 162391 162406) (-145 "CHAR.spad" 160038 160046 162154 162159) (-144 "CFCAT.spad" 159366 159374 160028 160033) (-143 "CDEN.spad" 158562 158576 159356 159361) (-142 "CCLASS.spad" 156673 156681 157935 157974) (-141 "CATEGORY.spad" 155715 155723 156663 156668) (-140 "CATCTOR.spad" 155606 155614 155705 155710) (-139 "CATAST.spad" 155224 155232 155596 155601) (-138 "CASEAST.spad" 154938 154946 155214 155219) (-137 "CARTEN.spad" 150305 150329 154928 154933) (-136 "CARTEN2.spad" 149695 149722 150295 150300) (-135 "CARD.spad" 146990 146998 149669 149690) (-134 "CAPSLAST.spad" 146764 146772 146980 146985) (-133 "CACHSET.spad" 146388 146396 146754 146759) (-132 "CABMON.spad" 145943 145951 146378 146383) (-131 "BYTEORD.spad" 145618 145626 145933 145938) (-130 "BYTE.spad" 145045 145053 145608 145613) (-129 "BYTEBUF.spad" 142743 142751 144053 144080) (-128 "BTREE.spad" 141699 141709 142233 142260) (-127 "BTOURN.spad" 140587 140597 141189 141216) (-126 "BTCAT.spad" 139979 139989 140555 140582) (-125 "BTCAT.spad" 139391 139403 139969 139974) (-124 "BTAGG.spad" 138857 138865 139359 139386) (-123 "BTAGG.spad" 138343 138353 138847 138852) (-122 "BSTREE.spad" 136967 136977 137833 137860) (-121 "BRILL.spad" 135164 135175 136957 136962) (-120 "BRAGG.spad" 134104 134114 135154 135159) (-119 "BRAGG.spad" 133008 133020 134060 134065) (-118 "BPADICRT.spad" 130882 130894 131137 131230) (-117 "BPADIC.spad" 130546 130558 130808 130877) (-116 "BOUNDZRO.spad" 130202 130219 130536 130541) (-115 "BOP.spad" 125384 125392 130192 130197) (-114 "BOP1.spad" 122850 122860 125374 125379) (-113 "BOOLE.spad" 122500 122508 122840 122845) (-112 "BOOLEAN.spad" 121938 121946 122490 122495) (-111 "BMODULE.spad" 121650 121662 121906 121933) (-110 "BITS.spad" 121033 121041 121248 121275) (-109 "BINDING.spad" 120446 120454 121023 121028) (-108 "BINARY.spad" 118460 118468 118816 118909) (-107 "BGAGG.spad" 117665 117675 118440 118455) (-106 "BGAGG.spad" 116878 116890 117655 117660) (-105 "BFUNCT.spad" 116442 116450 116858 116873) (-104 "BEZOUT.spad" 115582 115609 116392 116397) (-103 "BBTREE.spad" 112310 112320 115072 115099) (-102 "BASTYPE.spad" 111982 111990 112300 112305) (-101 "BASTYPE.spad" 111652 111662 111972 111977) (-100 "BALFACT.spad" 111111 111124 111642 111647) (-99 "AUTOMOR.spad" 110562 110571 111091 111106) (-98 "ATTREG.spad" 107285 107292 110314 110557) (-97 "ATTRBUT.spad" 103308 103315 107265 107280) (-96 "ATTRAST.spad" 103025 103032 103298 103303) (-95 "ATRIG.spad" 102495 102502 103015 103020) (-94 "ATRIG.spad" 101963 101972 102485 102490) (-93 "ASTCAT.spad" 101867 101874 101953 101958) (-92 "ASTCAT.spad" 101769 101778 101857 101862) (-91 "ASTACK.spad" 100991 101000 101259 101286) (-90 "ASSOCEQ.spad" 99817 99828 100947 100952) (-89 "ASP9.spad" 98898 98911 99807 99812) (-88 "ASP8.spad" 97941 97954 98888 98893) (-87 "ASP80.spad" 97263 97276 97931 97936) (-86 "ASP7.spad" 96423 96436 97253 97258) (-85 "ASP78.spad" 95874 95887 96413 96418) (-84 "ASP77.spad" 95243 95256 95864 95869) (-83 "ASP74.spad" 94335 94348 95233 95238) (-82 "ASP73.spad" 93606 93619 94325 94330) (-81 "ASP6.spad" 92473 92486 93596 93601) (-80 "ASP55.spad" 90982 90995 92463 92468) (-79 "ASP50.spad" 88799 88812 90972 90977) (-78 "ASP4.spad" 88094 88107 88789 88794) (-77 "ASP49.spad" 87093 87106 88084 88089) (-76 "ASP42.spad" 85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 47358 47371 47729 47734) (-52 "ANY.spad" 46217 46224 47348 47353) (-51 "ANY1.spad" 45288 45297 46207 46212) (-50 "ANTISYM.spad" 43733 43749 45268 45283) (-49 "ANON.spad" 43426 43433 43723 43728) (-48 "AN.spad" 41735 41742 43242 43335) (-47 "AMR.spad" 39920 39931 41633 41730) (-46 "AMR.spad" 37942 37955 39657 39662) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 "ALGSC.spad" 33977 34003 34714 34767) (-43 "ALGPKG.spad" 29760 29771 33933 33938) (-42 "ALGMFACT.spad" 28953 28967 29750 29755) (-41 "ALGMANIP.spad" 26427 26442 28786 28791) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2293366 2293371 2293376 2293381) (-2 NIL 2293346 2293351 2293356 2293361) (-1 NIL 2293326 2293331 2293336 2293341) (0 NIL 2293306 2293311 2293316 2293321) (-1315 "ZMOD.spad" 2293115 2293128 2293244 2293301) (-1314 "ZLINDEP.spad" 2292181 2292192 2293105 2293110) (-1313 "ZDSOLVE.spad" 2282126 2282148 2292171 2292176) (-1312 "YSTREAM.spad" 2281621 2281632 2282116 2282121) (-1311 "YDIAGRAM.spad" 2281255 2281264 2281611 2281616) (-1310 "XRPOLY.spad" 2280475 2280495 2281111 2281180) (-1309 "XPR.spad" 2278270 2278283 2280193 2280292) (-1308 "XPOLY.spad" 2277825 2277836 2278126 2278195) (-1307 "XPOLYC.spad" 2277144 2277160 2277751 2277820) (-1306 "XPBWPOLY.spad" 2275581 2275601 2276924 2276993) (-1305 "XF.spad" 2274044 2274059 2275483 2275576) (-1304 "XF.spad" 2272487 2272504 2273928 2273933) (-1303 "XFALG.spad" 2269535 2269551 2272413 2272482) (-1302 "XEXPPKG.spad" 2268786 2268812 2269525 2269530) (-1301 "XDPOLY.spad" 2268400 2268416 2268642 2268711) (-1300 "XALG.spad" 2268060 2268071 2268356 2268395) (-1299 "WUTSET.spad" 2263863 2263880 2267670 2267697) (-1298 "WP.spad" 2263062 2263106 2263721 2263788) (-1297 "WHILEAST.spad" 2262860 2262869 2263052 2263057) (-1296 "WHEREAST.spad" 2262531 2262540 2262850 2262855) (-1295 "WFFINTBS.spad" 2260194 2260216 2262521 2262526) (-1294 "WEIER.spad" 2258416 2258427 2260184 2260189) (-1293 "VSPACE.spad" 2258089 2258100 2258384 2258411) (-1292 "VSPACE.spad" 2257782 2257795 2258079 2258084) (-1291 "VOID.spad" 2257459 2257468 2257772 2257777) (-1290 "VIEW.spad" 2255139 2255148 2257449 2257454) (-1289 "VIEWDEF.spad" 2250340 2250349 2255129 2255134) (-1288 "VIEW3D.spad" 2234301 2234310 2250330 2250335) (-1287 "VIEW2D.spad" 2222192 2222201 2234291 2234296) (-1286 "VECTOR.spad" 2220713 2220724 2220964 2220991) (-1285 "VECTOR2.spad" 2219352 2219365 2220703 2220708) (-1284 "VECTCAT.spad" 2217256 2217267 2219320 2219347) (-1283 "VECTCAT.spad" 2214967 2214980 2217033 2217038) (-1282 "VARIABLE.spad" 2214747 2214762 2214957 2214962) (-1281 "UTYPE.spad" 2214391 2214400 2214737 2214742) (-1280 "UTSODETL.spad" 2213686 2213710 2214347 2214352) (-1279 "UTSODE.spad" 2211902 2211922 2213676 2213681) (-1278 "UTS.spad" 2206849 2206877 2210369 2210466) (-1277 "UTSCAT.spad" 2204328 2204344 2206747 2206844) (-1276 "UTSCAT.spad" 2201451 2201469 2203872 2203877) (-1275 "UTS2.spad" 2201046 2201081 2201441 2201446) (-1274 "URAGG.spad" 2195719 2195730 2201036 2201041) (-1273 "URAGG.spad" 2190356 2190369 2195675 2195680) (-1272 "UPXSSING.spad" 2188001 2188027 2189437 2189570) (-1271 "UPXS.spad" 2185297 2185325 2186133 2186282) (-1270 "UPXSCONS.spad" 2183056 2183076 2183429 2183578) (-1269 "UPXSCCA.spad" 2181627 2181647 2182902 2183051) (-1268 "UPXSCCA.spad" 2180340 2180362 2181617 2181622) (-1267 "UPXSCAT.spad" 2178929 2178945 2180186 2180335) (-1266 "UPXS2.spad" 2178472 2178525 2178919 2178924) (-1265 "UPSQFREE.spad" 2176886 2176900 2178462 2178467) (-1264 "UPSCAT.spad" 2174673 2174697 2176784 2176881) (-1263 "UPSCAT.spad" 2172166 2172192 2174279 2174284) (-1262 "UPOLYC.spad" 2167206 2167217 2172008 2172161) (-1261 "UPOLYC.spad" 2162138 2162151 2166942 2166947) (-1260 "UPOLYC2.spad" 2161609 2161628 2162128 2162133) (-1259 "UP.spad" 2158715 2158730 2159102 2159255) (-1258 "UPMP.spad" 2157615 2157628 2158705 2158710) (-1257 "UPDIVP.spad" 2157180 2157194 2157605 2157610) (-1256 "UPDECOMP.spad" 2155425 2155439 2157170 2157175) (-1255 "UPCDEN.spad" 2154634 2154650 2155415 2155420) (-1254 "UP2.spad" 2153998 2154019 2154624 2154629) (-1253 "UNISEG.spad" 2153351 2153362 2153917 2153922) (-1252 "UNISEG2.spad" 2152848 2152861 2153307 2153312) (-1251 "UNIFACT.spad" 2151951 2151963 2152838 2152843) (-1250 "ULS.spad" 2141735 2141763 2142680 2143109) (-1249 "ULSCONS.spad" 2132869 2132889 2133239 2133388) (-1248 "ULSCCAT.spad" 2130606 2130626 2132715 2132864) (-1247 "ULSCCAT.spad" 2128451 2128473 2130562 2130567) (-1246 "ULSCAT.spad" 2126683 2126699 2128297 2128446) (-1245 "ULS2.spad" 2126197 2126250 2126673 2126678) (-1244 "UINT8.spad" 2126074 2126083 2126187 2126192) (-1243 "UINT64.spad" 2125950 2125959 2126064 2126069) (-1242 "UINT32.spad" 2125826 2125835 2125940 2125945) (-1241 "UINT16.spad" 2125702 2125711 2125816 2125821) (-1240 "UFD.spad" 2124767 2124776 2125628 2125697) (-1239 "UFD.spad" 2123894 2123905 2124757 2124762) (-1238 "UDVO.spad" 2122775 2122784 2123884 2123889) (-1237 "UDPO.spad" 2120268 2120279 2122731 2122736) (-1236 "TYPE.spad" 2120200 2120209 2120258 2120263) (-1235 "TYPEAST.spad" 2120119 2120128 2120190 2120195) (-1234 "TWOFACT.spad" 2118771 2118786 2120109 2120114) (-1233 "TUPLE.spad" 2118257 2118268 2118670 2118675) (-1232 "TUBETOOL.spad" 2115124 2115133 2118247 2118252) (-1231 "TUBE.spad" 2113771 2113788 2115114 2115119) (-1230 "TS.spad" 2112370 2112386 2113336 2113433) (-1229 "TSETCAT.spad" 2099497 2099514 2112338 2112365) (-1228 "TSETCAT.spad" 2086610 2086629 2099453 2099458) (-1227 "TRMANIP.spad" 2080976 2080993 2086316 2086321) (-1226 "TRIMAT.spad" 2079939 2079964 2080966 2080971) (-1225 "TRIGMNIP.spad" 2078466 2078483 2079929 2079934) (-1224 "TRIGCAT.spad" 2077978 2077987 2078456 2078461) (-1223 "TRIGCAT.spad" 2077488 2077499 2077968 2077973) (-1222 "TREE.spad" 2075946 2075957 2076978 2077005) (-1221 "TRANFUN.spad" 2075785 2075794 2075936 2075941) (-1220 "TRANFUN.spad" 2075622 2075633 2075775 2075780) (-1219 "TOPSP.spad" 2075296 2075305 2075612 2075617) (-1218 "TOOLSIGN.spad" 2074959 2074970 2075286 2075291) (-1217 "TEXTFILE.spad" 2073520 2073529 2074949 2074954) (-1216 "TEX.spad" 2070666 2070675 2073510 2073515) (-1215 "TEX1.spad" 2070222 2070233 2070656 2070661) (-1214 "TEMUTL.spad" 2069777 2069786 2070212 2070217) (-1213 "TBCMPPK.spad" 2067870 2067893 2069767 2069772) (-1212 "TBAGG.spad" 2066920 2066943 2067850 2067865) (-1211 "TBAGG.spad" 2065978 2066003 2066910 2066915) (-1210 "TANEXP.spad" 2065386 2065397 2065968 2065973) (-1209 "TALGOP.spad" 2065110 2065121 2065376 2065381) (-1208 "TABLE.spad" 2063079 2063102 2063349 2063376) (-1207 "TABLEAU.spad" 2062560 2062571 2063069 2063074) (-1206 "TABLBUMP.spad" 2059363 2059374 2062550 2062555) (-1205 "SYSTEM.spad" 2058591 2058600 2059353 2059358) (-1204 "SYSSOLP.spad" 2056074 2056085 2058581 2058586) (-1203 "SYSPTR.spad" 2055973 2055982 2056064 2056069) (-1202 "SYSNNI.spad" 2055155 2055166 2055963 2055968) (-1201 "SYSINT.spad" 2054559 2054570 2055145 2055150) (-1200 "SYNTAX.spad" 2050765 2050774 2054549 2054554) (-1199 "SYMTAB.spad" 2048833 2048842 2050755 2050760) (-1198 "SYMS.spad" 2044856 2044865 2048823 2048828) (-1197 "SYMPOLY.spad" 2043863 2043874 2043945 2044072) (-1196 "SYMFUNC.spad" 2043364 2043375 2043853 2043858) (-1195 "SYMBOL.spad" 2040867 2040876 2043354 2043359) (-1194 "SWITCH.spad" 2037638 2037647 2040857 2040862) (-1193 "SUTS.spad" 2034686 2034714 2036105 2036202) (-1192 "SUPXS.spad" 2031969 2031997 2032818 2032967) (-1191 "SUP.spad" 2028689 2028700 2029462 2029615) (-1190 "SUPFRACF.spad" 2027794 2027812 2028679 2028684) (-1189 "SUP2.spad" 2027186 2027199 2027784 2027789) (-1188 "SUMRF.spad" 2026160 2026171 2027176 2027181) (-1187 "SUMFS.spad" 2025797 2025814 2026150 2026155) (-1186 "SULS.spad" 2015568 2015596 2016526 2016955) (-1185 "SUCHTAST.spad" 2015337 2015346 2015558 2015563) (-1184 "SUCH.spad" 2015019 2015034 2015327 2015332) (-1183 "SUBSPACE.spad" 2007134 2007149 2015009 2015014) (-1182 "SUBRESP.spad" 2006304 2006318 2007090 2007095) (-1181 "STTF.spad" 2002403 2002419 2006294 2006299) (-1180 "STTFNC.spad" 1998871 1998887 2002393 2002398) (-1179 "STTAYLOR.spad" 1991506 1991517 1998752 1998757) (-1178 "STRTBL.spad" 1989557 1989574 1989706 1989733) (-1177 "STRING.spad" 1988344 1988353 1988565 1988592) (-1176 "STREAM.spad" 1985145 1985156 1987752 1987767) (-1175 "STREAM3.spad" 1984718 1984733 1985135 1985140) (-1174 "STREAM2.spad" 1983846 1983859 1984708 1984713) (-1173 "STREAM1.spad" 1983552 1983563 1983836 1983841) (-1172 "STINPROD.spad" 1982488 1982504 1983542 1983547) (-1171 "STEP.spad" 1981689 1981698 1982478 1982483) (-1170 "STEPAST.spad" 1980923 1980932 1981679 1981684) (-1169 "STBL.spad" 1979007 1979035 1979174 1979189) (-1168 "STAGG.spad" 1978082 1978093 1978997 1979002) (-1167 "STAGG.spad" 1977155 1977168 1978072 1978077) (-1166 "STACK.spad" 1976395 1976406 1976645 1976672) (-1165 "SREGSET.spad" 1974063 1974080 1976005 1976032) (-1164 "SRDCMPK.spad" 1972624 1972644 1974053 1974058) (-1163 "SRAGG.spad" 1967767 1967776 1972592 1972619) (-1162 "SRAGG.spad" 1962930 1962941 1967757 1967762) (-1161 "SQMATRIX.spad" 1960473 1960491 1961389 1961476) (-1160 "SPLTREE.spad" 1954869 1954882 1959753 1959780) (-1159 "SPLNODE.spad" 1951457 1951470 1954859 1954864) (-1158 "SPFCAT.spad" 1950266 1950275 1951447 1951452) (-1157 "SPECOUT.spad" 1948818 1948827 1950256 1950261) (-1156 "SPADXPT.spad" 1940413 1940422 1948808 1948813) (-1155 "spad-parser.spad" 1939878 1939887 1940403 1940408) (-1154 "SPADAST.spad" 1939579 1939588 1939868 1939873) (-1153 "SPACEC.spad" 1923778 1923789 1939569 1939574) (-1152 "SPACE3.spad" 1923554 1923565 1923768 1923773) (-1151 "SORTPAK.spad" 1923103 1923116 1923510 1923515) (-1150 "SOLVETRA.spad" 1920866 1920877 1923093 1923098) (-1149 "SOLVESER.spad" 1919394 1919405 1920856 1920861) (-1148 "SOLVERAD.spad" 1915420 1915431 1919384 1919389) (-1147 "SOLVEFOR.spad" 1913882 1913900 1915410 1915415) (-1146 "SNTSCAT.spad" 1913482 1913499 1913850 1913877) (-1145 "SMTS.spad" 1911754 1911780 1913047 1913144) (-1144 "SMP.spad" 1909229 1909249 1909619 1909746) (-1143 "SMITH.spad" 1908074 1908099 1909219 1909224) (-1142 "SMATCAT.spad" 1906184 1906214 1908018 1908069) (-1141 "SMATCAT.spad" 1904226 1904258 1906062 1906067) (-1140 "SKAGG.spad" 1903189 1903200 1904194 1904221) (-1139 "SINT.spad" 1902129 1902138 1903055 1903184) (-1138 "SIMPAN.spad" 1901857 1901866 1902119 1902124) (-1137 "SIG.spad" 1901187 1901196 1901847 1901852) (-1136 "SIGNRF.spad" 1900305 1900316 1901177 1901182) (-1135 "SIGNEF.spad" 1899584 1899601 1900295 1900300) (-1134 "SIGAST.spad" 1898969 1898978 1899574 1899579) (-1133 "SHP.spad" 1896897 1896912 1898925 1898930) (-1132 "SHDP.spad" 1884575 1884602 1885084 1885183) (-1131 "SGROUP.spad" 1884183 1884192 1884565 1884570) (-1130 "SGROUP.spad" 1883789 1883800 1884173 1884178) (-1129 "SGCF.spad" 1876928 1876937 1883779 1883784) (-1128 "SFRTCAT.spad" 1875858 1875875 1876896 1876923) (-1127 "SFRGCD.spad" 1874921 1874941 1875848 1875853) (-1126 "SFQCMPK.spad" 1869558 1869578 1874911 1874916) (-1125 "SFORT.spad" 1868997 1869011 1869548 1869553) (-1124 "SEXOF.spad" 1868840 1868880 1868987 1868992) (-1123 "SEX.spad" 1868732 1868741 1868830 1868835) (-1122 "SEXCAT.spad" 1866504 1866544 1868722 1868727) (-1121 "SET.spad" 1864792 1864803 1865889 1865928) (-1120 "SETMN.spad" 1863242 1863259 1864782 1864787) (-1119 "SETCAT.spad" 1862564 1862573 1863232 1863237) (-1118 "SETCAT.spad" 1861884 1861895 1862554 1862559) (-1117 "SETAGG.spad" 1858433 1858444 1861864 1861879) (-1116 "SETAGG.spad" 1854990 1855003 1858423 1858428) (-1115 "SEQAST.spad" 1854693 1854702 1854980 1854985) (-1114 "SEGXCAT.spad" 1853849 1853862 1854683 1854688) (-1113 "SEG.spad" 1853662 1853673 1853768 1853773) (-1112 "SEGCAT.spad" 1852587 1852598 1853652 1853657) (-1111 "SEGBIND.spad" 1852345 1852356 1852534 1852539) (-1110 "SEGBIND2.spad" 1852043 1852056 1852335 1852340) (-1109 "SEGAST.spad" 1851757 1851766 1852033 1852038) (-1108 "SEG2.spad" 1851192 1851205 1851713 1851718) (-1107 "SDVAR.spad" 1850468 1850479 1851182 1851187) (-1106 "SDPOL.spad" 1847801 1847812 1848092 1848219) (-1105 "SCPKG.spad" 1845890 1845901 1847791 1847796) (-1104 "SCOPE.spad" 1845043 1845052 1845880 1845885) (-1103 "SCACHE.spad" 1843739 1843750 1845033 1845038) (-1102 "SASTCAT.spad" 1843648 1843657 1843729 1843734) (-1101 "SAOS.spad" 1843520 1843529 1843638 1843643) (-1100 "SAERFFC.spad" 1843233 1843253 1843510 1843515) (-1099 "SAE.spad" 1840703 1840719 1841314 1841449) (-1098 "SAEFACT.spad" 1840404 1840424 1840693 1840698) (-1097 "RURPK.spad" 1838063 1838079 1840394 1840399) (-1096 "RULESET.spad" 1837516 1837540 1838053 1838058) (-1095 "RULE.spad" 1835756 1835780 1837506 1837511) (-1094 "RULECOLD.spad" 1835608 1835621 1835746 1835751) (-1093 "RTVALUE.spad" 1835343 1835352 1835598 1835603) (-1092 "RSTRCAST.spad" 1835060 1835069 1835333 1835338) (-1091 "RSETGCD.spad" 1831438 1831458 1835050 1835055) (-1090 "RSETCAT.spad" 1821374 1821391 1831406 1831433) (-1089 "RSETCAT.spad" 1811330 1811349 1821364 1821369) (-1088 "RSDCMPK.spad" 1809782 1809802 1811320 1811325) (-1087 "RRCC.spad" 1808166 1808196 1809772 1809777) (-1086 "RRCC.spad" 1806548 1806580 1808156 1808161) (-1085 "RPTAST.spad" 1806250 1806259 1806538 1806543) (-1084 "RPOLCAT.spad" 1785610 1785625 1806118 1806245) (-1083 "RPOLCAT.spad" 1764683 1764700 1785193 1785198) (-1082 "ROUTINE.spad" 1760104 1760113 1762868 1762895) (-1081 "ROMAN.spad" 1759432 1759441 1759970 1760099) (-1080 "ROIRC.spad" 1758512 1758544 1759422 1759427) (-1079 "RNS.spad" 1757415 1757424 1758414 1758507) (-1078 "RNS.spad" 1756404 1756415 1757405 1757410) (-1077 "RNG.spad" 1756139 1756148 1756394 1756399) (-1076 "RNGBIND.spad" 1755299 1755313 1756094 1756099) (-1075 "RMODULE.spad" 1755064 1755075 1755289 1755294) (-1074 "RMCAT2.spad" 1754484 1754541 1755054 1755059) (-1073 "RMATRIX.spad" 1753272 1753291 1753615 1753654) (-1072 "RMATCAT.spad" 1748851 1748882 1753228 1753267) (-1071 "RMATCAT.spad" 1744320 1744353 1748699 1748704) (-1070 "RLINSET.spad" 1744024 1744035 1744310 1744315) (-1069 "RINTERP.spad" 1743912 1743932 1744014 1744019) (-1068 "RING.spad" 1743382 1743391 1743892 1743907) (-1067 "RING.spad" 1742860 1742871 1743372 1743377) (-1066 "RIDIST.spad" 1742252 1742261 1742850 1742855) (-1065 "RGCHAIN.spad" 1740780 1740796 1741682 1741709) (-1064 "RGBCSPC.spad" 1740561 1740573 1740770 1740775) (-1063 "RGBCMDL.spad" 1740091 1740103 1740551 1740556) (-1062 "RF.spad" 1737733 1737744 1740081 1740086) (-1061 "RFFACTOR.spad" 1737195 1737206 1737723 1737728) (-1060 "RFFACT.spad" 1736930 1736942 1737185 1737190) (-1059 "RFDIST.spad" 1735926 1735935 1736920 1736925) (-1058 "RETSOL.spad" 1735345 1735358 1735916 1735921) (-1057 "RETRACT.spad" 1734773 1734784 1735335 1735340) (-1056 "RETRACT.spad" 1734199 1734212 1734763 1734768) (-1055 "RETAST.spad" 1734011 1734020 1734189 1734194) (-1054 "RESULT.spad" 1731609 1731618 1732196 1732223) (-1053 "RESRING.spad" 1730956 1731003 1731547 1731604) (-1052 "RESLATC.spad" 1730280 1730291 1730946 1730951) (-1051 "REPSQ.spad" 1730011 1730022 1730270 1730275) (-1050 "REP.spad" 1727565 1727574 1730001 1730006) (-1049 "REPDB.spad" 1727272 1727283 1727555 1727560) (-1048 "REP2.spad" 1716930 1716941 1727114 1727119) (-1047 "REP1.spad" 1711126 1711137 1716880 1716885) (-1046 "REGSET.spad" 1708887 1708904 1710736 1710763) (-1045 "REF.spad" 1708222 1708233 1708842 1708847) (-1044 "REDORDER.spad" 1707428 1707445 1708212 1708217) (-1043 "RECLOS.spad" 1706211 1706231 1706915 1707008) (-1042 "REALSOLV.spad" 1705351 1705360 1706201 1706206) (-1041 "REAL.spad" 1705223 1705232 1705341 1705346) (-1040 "REAL0Q.spad" 1702521 1702536 1705213 1705218) (-1039 "REAL0.spad" 1699365 1699380 1702511 1702516) (-1038 "RDUCEAST.spad" 1699086 1699095 1699355 1699360) (-1037 "RDIV.spad" 1698741 1698766 1699076 1699081) (-1036 "RDIST.spad" 1698308 1698319 1698731 1698736) (-1035 "RDETRS.spad" 1697172 1697190 1698298 1698303) (-1034 "RDETR.spad" 1695311 1695329 1697162 1697167) (-1033 "RDEEFS.spad" 1694410 1694427 1695301 1695306) (-1032 "RDEEF.spad" 1693420 1693437 1694400 1694405) (-1031 "RCFIELD.spad" 1690606 1690615 1693322 1693415) (-1030 "RCFIELD.spad" 1687878 1687889 1690596 1690601) (-1029 "RCAGG.spad" 1685806 1685817 1687868 1687873) (-1028 "RCAGG.spad" 1683661 1683674 1685725 1685730) (-1027 "RATRET.spad" 1683021 1683032 1683651 1683656) (-1026 "RATFACT.spad" 1682713 1682725 1683011 1683016) (-1025 "RANDSRC.spad" 1682032 1682041 1682703 1682708) (-1024 "RADUTIL.spad" 1681788 1681797 1682022 1682027) (-1023 "RADIX.spad" 1678612 1678626 1680158 1680251) (-1022 "RADFF.spad" 1676351 1676388 1676470 1676626) (-1021 "RADCAT.spad" 1675946 1675955 1676341 1676346) (-1020 "RADCAT.spad" 1675539 1675550 1675936 1675941) (-1019 "QUEUE.spad" 1674770 1674781 1675029 1675056) (-1018 "QUAT.spad" 1673258 1673269 1673601 1673666) (-1017 "QUATCT2.spad" 1672878 1672897 1673248 1673253) (-1016 "QUATCAT.spad" 1671048 1671059 1672808 1672873) (-1015 "QUATCAT.spad" 1668969 1668982 1670731 1670736) (-1014 "QUAGG.spad" 1667796 1667807 1668937 1668964) (-1013 "QQUTAST.spad" 1667564 1667573 1667786 1667791) (-1012 "QFORM.spad" 1667182 1667197 1667554 1667559) (-1011 "QFCAT.spad" 1665884 1665895 1667084 1667177) (-1010 "QFCAT.spad" 1664177 1664190 1665379 1665384) (-1009 "QFCAT2.spad" 1663869 1663886 1664167 1664172) (-1008 "QEQUAT.spad" 1663427 1663436 1663859 1663864) (-1007 "QCMPACK.spad" 1658173 1658193 1663417 1663422) (-1006 "QALGSET.spad" 1654251 1654284 1658087 1658092) (-1005 "QALGSET2.spad" 1652246 1652265 1654241 1654246) 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1432306) (-873 "OUTBFILE.spad" 1421121 1421129 1421693 1421698) (-872 "OUTBCON.spad" 1420127 1420135 1421111 1421116) (-871 "OUTBCON.spad" 1419131 1419141 1420117 1420122) (-870 "OSI.spad" 1418606 1418614 1419121 1419126) (-869 "OSGROUP.spad" 1418524 1418532 1418596 1418601) (-868 "ORTHPOL.spad" 1417009 1417019 1418441 1418446) (-867 "OREUP.spad" 1416462 1416490 1416689 1416728) (-866 "ORESUP.spad" 1415763 1415787 1416142 1416181) (-865 "OREPCTO.spad" 1413620 1413632 1415683 1415688) (-864 "OREPCAT.spad" 1407767 1407777 1413576 1413615) (-863 "OREPCAT.spad" 1401804 1401816 1407615 1407620) (-862 "ORDSET.spad" 1400976 1400984 1401794 1401799) (-861 "ORDSET.spad" 1400146 1400156 1400966 1400971) (-860 "ORDRING.spad" 1399536 1399544 1400126 1400141) (-859 "ORDRING.spad" 1398934 1398944 1399526 1399531) (-858 "ORDMON.spad" 1398789 1398797 1398924 1398929) (-857 "ORDFUNS.spad" 1397921 1397937 1398779 1398784) (-856 "ORDFIN.spad" 1397741 1397749 1397911 1397916) (-855 "ORDCOMP.spad" 1396206 1396216 1397288 1397317) (-854 "ORDCOMP2.spad" 1395499 1395511 1396196 1396201) (-853 "OPTPROB.spad" 1394137 1394145 1395489 1395494) (-852 "OPTPACK.spad" 1386546 1386554 1394127 1394132) (-851 "OPTCAT.spad" 1384225 1384233 1386536 1386541) (-850 "OPSIG.spad" 1383879 1383887 1384215 1384220) (-849 "OPQUERY.spad" 1383428 1383436 1383869 1383874) (-848 "OP.spad" 1383170 1383180 1383250 1383317) (-847 "OPERCAT.spad" 1382636 1382646 1383160 1383165) (-846 "OPERCAT.spad" 1382100 1382112 1382626 1382631) (-845 "ONECOMP.spad" 1380845 1380855 1381647 1381676) (-844 "ONECOMP2.spad" 1380269 1380281 1380835 1380840) (-843 "OMSERVER.spad" 1379275 1379283 1380259 1380264) (-842 "OMSAGG.spad" 1379063 1379073 1379231 1379270) (-841 "OMPKG.spad" 1377679 1377687 1379053 1379058) (-840 "OM.spad" 1376652 1376660 1377669 1377674) (-839 "OMLO.spad" 1376077 1376089 1376538 1376577) (-838 "OMEXPR.spad" 1375911 1375921 1376067 1376072) (-837 "OMERR.spad" 1375456 1375464 1375901 1375906) (-836 "OMERRK.spad" 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(-760 "NAGD01.spad" 1173065 1173073 1178762 1178767) (-759 "NAGC06.spad" 1168940 1168948 1173055 1173060) (-758 "NAGC05.spad" 1167441 1167449 1168930 1168935) (-757 "NAGC02.spad" 1166708 1166716 1167431 1167436) (-756 "NAALG.spad" 1166249 1166259 1166676 1166703) (-755 "NAALG.spad" 1165810 1165822 1166239 1166244) (-754 "MULTSQFR.spad" 1162768 1162785 1165800 1165805) (-753 "MULTFACT.spad" 1162151 1162168 1162758 1162763) (-752 "MTSCAT.spad" 1160245 1160266 1162049 1162146) (-751 "MTHING.spad" 1159904 1159914 1160235 1160240) (-750 "MSYSCMD.spad" 1159338 1159346 1159894 1159899) (-749 "MSET.spad" 1157260 1157270 1159008 1159047) (-748 "MSETAGG.spad" 1157105 1157115 1157228 1157255) (-747 "MRING.spad" 1154082 1154094 1156813 1156880) (-746 "MRF2.spad" 1153652 1153666 1154072 1154077) (-745 "MRATFAC.spad" 1153198 1153215 1153642 1153647) (-744 "MPRFF.spad" 1151238 1151257 1153188 1153193) (-743 "MPOLY.spad" 1148709 1148724 1149068 1149195) (-742 "MPCPF.spad" 1147973 1147992 1148699 1148704) (-741 "MPC3.spad" 1147790 1147830 1147963 1147968) (-740 "MPC2.spad" 1147436 1147469 1147780 1147785) (-739 "MONOTOOL.spad" 1145787 1145804 1147426 1147431) (-738 "MONOID.spad" 1145106 1145114 1145777 1145782) (-737 "MONOID.spad" 1144423 1144433 1145096 1145101) (-736 "MONOGEN.spad" 1143171 1143184 1144283 1144418) (-735 "MONOGEN.spad" 1141941 1141956 1143055 1143060) (-734 "MONADWU.spad" 1139971 1139979 1141931 1141936) (-733 "MONADWU.spad" 1137999 1138009 1139961 1139966) (-732 "MONAD.spad" 1137159 1137167 1137989 1137994) (-731 "MONAD.spad" 1136317 1136327 1137149 1137154) (-730 "MOEBIUS.spad" 1135053 1135067 1136297 1136312) (-729 "MODULE.spad" 1134923 1134933 1135021 1135048) (-728 "MODULE.spad" 1134813 1134825 1134913 1134918) (-727 "MODRING.spad" 1134148 1134187 1134793 1134808) (-726 "MODOP.spad" 1132813 1132825 1133970 1134037) (-725 "MODMONOM.spad" 1132544 1132562 1132803 1132808) (-724 "MODMON.spad" 1129246 1129262 1129965 1130118) (-723 "MODFIELD.spad" 1128608 1128647 1129148 1129241) (-722 "MMLFORM.spad" 1127468 1127476 1128598 1128603) (-721 "MMAP.spad" 1127210 1127244 1127458 1127463) (-720 "MLO.spad" 1125669 1125679 1127166 1127205) (-719 "MLIFT.spad" 1124281 1124298 1125659 1125664) (-718 "MKUCFUNC.spad" 1123816 1123834 1124271 1124276) (-717 "MKRECORD.spad" 1123420 1123433 1123806 1123811) (-716 "MKFUNC.spad" 1122827 1122837 1123410 1123415) (-715 "MKFLCFN.spad" 1121795 1121805 1122817 1122822) (-714 "MKBCFUNC.spad" 1121290 1121308 1121785 1121790) (-713 "MINT.spad" 1120729 1120737 1121192 1121285) (-712 "MHROWRED.spad" 1119240 1119250 1120719 1120724) (-711 "MFLOAT.spad" 1117760 1117768 1119130 1119235) (-710 "MFINFACT.spad" 1117160 1117182 1117750 1117755) (-709 "MESH.spad" 1114942 1114950 1117150 1117155) (-708 "MDDFACT.spad" 1113153 1113163 1114932 1114937) (-707 "MDAGG.spad" 1112444 1112454 1113133 1113148) (-706 "MCMPLX.spad" 1107875 1107883 1108489 1108690) (-705 "MCDEN.spad" 1107085 1107097 1107865 1107870) (-704 "MCALCFN.spad" 1104207 1104233 1107075 1107080) (-703 "MAYBE.spad" 1103491 1103502 1104197 1104202) (-702 "MATSTOR.spad" 1100799 1100809 1103481 1103486) (-701 "MATRIX.spad" 1099386 1099396 1099870 1099897) (-700 "MATLIN.spad" 1096730 1096754 1099270 1099275) (-699 "MATCAT.spad" 1088252 1088274 1096698 1096725) (-698 "MATCAT.spad" 1079646 1079670 1088094 1088099) (-697 "MATCAT2.spad" 1078928 1078976 1079636 1079641) (-696 "MAPPKG3.spad" 1077843 1077857 1078918 1078923) (-695 "MAPPKG2.spad" 1077181 1077193 1077833 1077838) (-694 "MAPPKG1.spad" 1076009 1076019 1077171 1077176) (-693 "MAPPAST.spad" 1075324 1075332 1075999 1076004) (-692 "MAPHACK3.spad" 1075136 1075150 1075314 1075319) (-691 "MAPHACK2.spad" 1074905 1074917 1075126 1075131) (-690 "MAPHACK1.spad" 1074549 1074559 1074895 1074900) (-689 "MAGMA.spad" 1072339 1072356 1074539 1074544) (-688 "MACROAST.spad" 1071918 1071926 1072329 1072334) (-687 "M3D.spad" 1069521 1069531 1071179 1071184) (-686 "LZSTAGG.spad" 1066759 1066769 1069511 1069516) (-685 "LZSTAGG.spad" 1063995 1064007 1066749 1066754) (-684 "LWORD.spad" 1060700 1060717 1063985 1063990) (-683 "LSTAST.spad" 1060484 1060492 1060690 1060695) (-682 "LSQM.spad" 1058641 1058655 1059035 1059086) (-681 "LSPP.spad" 1058176 1058193 1058631 1058636) (-680 "LSMP.spad" 1057026 1057054 1058166 1058171) (-679 "LSMP1.spad" 1054844 1054858 1057016 1057021) (-678 "LSAGG.spad" 1054513 1054523 1054812 1054839) (-677 "LSAGG.spad" 1054202 1054214 1054503 1054508) (-676 "LPOLY.spad" 1053156 1053175 1054058 1054127) (-675 "LPEFRAC.spad" 1052427 1052437 1053146 1053151) (-674 "LO.spad" 1051828 1051842 1052361 1052388) (-673 "LOGIC.spad" 1051430 1051438 1051818 1051823) (-672 "LOGIC.spad" 1051030 1051040 1051420 1051425) (-671 "LODOOPS.spad" 1049960 1049972 1051020 1051025) (-670 "LODO.spad" 1049344 1049360 1049640 1049679) (-669 "LODOF.spad" 1048390 1048407 1049301 1049306) (-668 "LODOCAT.spad" 1047056 1047066 1048346 1048385) (-667 "LODOCAT.spad" 1045720 1045732 1047012 1047017) (-666 "LODO2.spad" 1044993 1045005 1045400 1045439) (-665 "LODO1.spad" 1044393 1044403 1044673 1044712) (-664 "LODEEF.spad" 1043195 1043213 1044383 1044388) (-663 "LNAGG.spad" 1039342 1039352 1043185 1043190) (-662 "LNAGG.spad" 1035453 1035465 1039298 1039303) (-661 "LMOPS.spad" 1032221 1032238 1035443 1035448) (-660 "LMODULE.spad" 1031989 1031999 1032211 1032216) (-659 "LMDICT.spad" 1031159 1031169 1031423 1031450) (-658 "LLINSET.spad" 1030866 1030876 1031149 1031154) (-657 "LITERAL.spad" 1030772 1030783 1030856 1030861) (-656 "LIST.spad" 1028354 1028364 1029766 1029793) (-655 "LIST3.spad" 1027665 1027679 1028344 1028349) (-654 "LIST2.spad" 1026367 1026379 1027655 1027660) (-653 "LIST2MAP.spad" 1023270 1023282 1026357 1026362) (-652 "LINSET.spad" 1023049 1023059 1023260 1023265) (-651 "LINEXP.spad" 1021792 1021802 1023039 1023044) (-650 "LINDEP.spad" 1020601 1020613 1021704 1021709) (-649 "LIMITRF.spad" 1018529 1018539 1020591 1020596) (-648 "LIMITPS.spad" 1017432 1017445 1018519 1018524) (-647 "LIE.spad" 1015448 1015460 1016722 1016867) (-646 "LIECAT.spad" 1014924 1014934 1015374 1015443) (-645 "LIECAT.spad" 1014428 1014440 1014880 1014885) (-644 "LIB.spad" 1012179 1012187 1012625 1012640) (-643 "LGROBP.spad" 1009532 1009551 1012169 1012174) (-642 "LF.spad" 1008487 1008503 1009522 1009527) (-641 "LFCAT.spad" 1007546 1007554 1008477 1008482) (-640 "LEXTRIPK.spad" 1003049 1003064 1007536 1007541) (-639 "LEXP.spad" 1001052 1001079 1003029 1003044) (-638 "LETAST.spad" 1000751 1000759 1001042 1001047) (-637 "LEADCDET.spad" 999149 999166 1000741 1000746) (-636 "LAZM3PK.spad" 997853 997875 999139 999144) (-635 "LAUPOL.spad" 996453 996466 997353 997422) (-634 "LAPLACE.spad" 996036 996052 996443 996448) (-633 "LA.spad" 995476 995490 995958 995997) (-632 "LALG.spad" 995252 995262 995456 995471) (-631 "LALG.spad" 995036 995048 995242 995247) (-630 "KVTFROM.spad" 994771 994781 995026 995031) (-629 "KTVLOGIC.spad" 994283 994291 994761 994766) (-628 "KRCFROM.spad" 994021 994031 994273 994278) (-627 "KOVACIC.spad" 992744 992761 994011 994016) (-626 "KONVERT.spad" 992466 992476 992734 992739) (-625 "KOERCE.spad" 992203 992213 992456 992461) (-624 "KERNEL.spad" 990858 990868 991987 991992) (-623 "KERNEL2.spad" 990561 990573 990848 990853) (-622 "KDAGG.spad" 989670 989692 990541 990556) (-621 "KDAGG.spad" 988787 988811 989660 989665) (-620 "KAFILE.spad" 987641 987657 987876 987903) (-619 "JORDAN.spad" 985470 985482 986931 987076) (-618 "JOINAST.spad" 985164 985172 985460 985465) (-617 "JAVACODE.spad" 985030 985038 985154 985159) (-616 "IXAGG.spad" 983163 983187 985020 985025) (-615 "IXAGG.spad" 981151 981177 983010 983015) (-614 "IVECTOR.spad" 979768 979783 979923 979950) (-613 "ITUPLE.spad" 978929 978939 979758 979763) (-612 "ITRIGMNP.spad" 977768 977787 978919 978924) (-611 "ITFUN3.spad" 977274 977288 977758 977763) (-610 "ITFUN2.spad" 977018 977030 977264 977269) (-609 "ITFORM.spad" 976373 976381 977008 977013) (-608 "ITAYLOR.spad" 974367 974382 976237 976334) (-607 "ISUPS.spad" 966804 966819 973341 973438) (-606 "ISUMP.spad" 966305 966321 966794 966799) (-605 "ISTRING.spad" 965232 965245 965313 965340) (-604 "ISAST.spad" 964951 964959 965222 965227) (-603 "IRURPK.spad" 963668 963687 964941 964946) (-602 "IRSN.spad" 961640 961648 963658 963663) (-601 "IRRF2F.spad" 960125 960135 961596 961601) (-600 "IRREDFFX.spad" 959726 959737 960115 960120) (-599 "IROOT.spad" 958065 958075 959716 959721) (-598 "IR.spad" 955866 955880 957920 957947) (-597 "IRFORM.spad" 955190 955198 955856 955861) (-596 "IR2.spad" 954218 954234 955180 955185) (-595 "IR2F.spad" 953424 953440 954208 954213) (-594 "IPRNTPK.spad" 953184 953192 953414 953419) (-593 "IPF.spad" 952749 952761 952989 953082) (-592 "IPADIC.spad" 952510 952536 952675 952744) (-591 "IP4ADDR.spad" 952067 952075 952500 952505) (-590 "IOMODE.spad" 951589 951597 952057 952062) (-589 "IOBFILE.spad" 950950 950958 951579 951584) (-588 "IOBCON.spad" 950815 950823 950940 950945) (-587 "INVLAPLA.spad" 950464 950480 950805 950810) (-586 "INTTR.spad" 943846 943863 950454 950459) (-585 "INTTOOLS.spad" 941601 941617 943420 943425) (-584 "INTSLPE.spad" 940921 940929 941591 941596) (-583 "INTRVL.spad" 940487 940497 940835 940916) (-582 "INTRF.spad" 938911 938925 940477 940482) (-581 "INTRET.spad" 938343 938353 938901 938906) (-580 "INTRAT.spad" 937070 937087 938333 938338) (-579 "INTPM.spad" 935455 935471 936713 936718) (-578 "INTPAF.spad" 933319 933337 935387 935392) (-577 "INTPACK.spad" 923693 923701 933309 933314) (-576 "INT.spad" 923141 923149 923547 923688) (-575 "INTHERTR.spad" 922415 922432 923131 923136) (-574 "INTHERAL.spad" 922085 922109 922405 922410) (-573 "INTHEORY.spad" 918524 918532 922075 922080) (-572 "INTG0.spad" 912257 912275 918456 918461) (-571 "INTFTBL.spad" 906286 906294 912247 912252) (-570 "INTFACT.spad" 905345 905355 906276 906281) (-569 "INTEF.spad" 903730 903746 905335 905340) (-568 "INTDOM.spad" 902353 902361 903656 903725) (-567 "INTDOM.spad" 901038 901048 902343 902348) (-566 "INTCAT.spad" 899297 899307 900952 901033) (-565 "INTBIT.spad" 898804 898812 899287 899292) (-564 "INTALG.spad" 897992 898019 898794 898799) (-563 "INTAF.spad" 897492 897508 897982 897987) (-562 "INTABL.spad" 895568 895599 895731 895758) (-561 "INT8.spad" 895448 895456 895558 895563) (-560 "INT64.spad" 895327 895335 895438 895443) (-559 "INT32.spad" 895206 895214 895317 895322) (-558 "INT16.spad" 895085 895093 895196 895201) (-557 "INS.spad" 892588 892596 894987 895080) (-556 "INS.spad" 890177 890187 892578 892583) (-555 "INPSIGN.spad" 889625 889638 890167 890172) (-554 "INPRODPF.spad" 888721 888740 889615 889620) (-553 "INPRODFF.spad" 887809 887833 888711 888716) (-552 "INNMFACT.spad" 886784 886801 887799 887804) (-551 "INMODGCD.spad" 886272 886302 886774 886779) (-550 "INFSP.spad" 884569 884591 886262 886267) (-549 "INFPROD0.spad" 883649 883668 884559 884564) (-548 "INFORM.spad" 880848 880856 883639 883644) (-547 "INFORM1.spad" 880473 880483 880838 880843) (-546 "INFINITY.spad" 880025 880033 880463 880468) (-545 "INETCLTS.spad" 880002 880010 880015 880020) (-544 "INEP.spad" 878540 878562 879992 879997) (-543 "INDE.spad" 878269 878286 878530 878535) (-542 "INCRMAPS.spad" 877690 877700 878259 878264) (-541 "INBFILE.spad" 876762 876770 877680 877685) (-540 "INBFF.spad" 872556 872567 876752 876757) (-539 "INBCON.spad" 870846 870854 872546 872551) (-538 "INBCON.spad" 869134 869144 870836 870841) (-537 "INAST.spad" 868795 868803 869124 869129) (-536 "IMPTAST.spad" 868503 868511 868785 868790) (-535 "IMATRIX.spad" 867331 867357 867843 867870) (-534 "IMATQF.spad" 866425 866469 867287 867292) (-533 "IMATLIN.spad" 865030 865054 866381 866386) (-532 "ILIST.spad" 863535 863550 864060 864087) (-531 "IIARRAY2.spad" 862806 862844 863025 863052) (-530 "IFF.spad" 862216 862232 862487 862580) (-529 "IFAST.spad" 861830 861838 862206 862211) (-528 "IFARRAY.spad" 859170 859185 860860 860887) (-527 "IFAMON.spad" 859032 859049 859126 859131) (-526 "IEVALAB.spad" 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834805) (-505 "HYPCAT.spad" 833837 833845 834403 834408) (-504 "HYPCAT.spad" 833259 833269 833827 833832) (-503 "HOSTNAME.spad" 833067 833075 833249 833254) (-502 "HOMOTOP.spad" 832810 832820 833057 833062) (-501 "HOAGG.spad" 830092 830102 832800 832805) (-500 "HOAGG.spad" 827113 827125 829823 829828) (-499 "HEXADEC.spad" 825118 825126 825483 825576) (-498 "HEUGCD.spad" 824153 824164 825108 825113) (-497 "HELLFDIV.spad" 823743 823767 824143 824148) (-496 "HEAP.spad" 823018 823028 823233 823260) (-495 "HEADAST.spad" 822551 822559 823008 823013) (-494 "HDP.spad" 810361 810377 810738 810837) (-493 "HDMP.spad" 807575 807590 808191 808318) (-492 "HB.spad" 805826 805834 807565 807570) (-491 "HASHTBL.spad" 803854 803885 804065 804092) (-490 "HASAST.spad" 803570 803578 803844 803849) (-489 "HACKPI.spad" 803061 803069 803472 803565) (-488 "GTSET.spad" 801964 801980 802671 802698) (-487 "GSTBL.spad" 800041 800076 800215 800230) (-486 "GSERIES.spad" 797354 797381 798173 798322) (-485 "GROUP.spad" 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"FSPRMELT.spad" 718657 718673 719732 719737) (-443 "FSPECF.spad" 716748 716764 718647 718652) (-442 "FS.spad" 711016 711026 716523 716743) (-441 "FS.spad" 705062 705074 710571 710576) (-440 "FSINT.spad" 704722 704738 705052 705057) (-439 "FSERIES.spad" 703913 703925 704542 704641) (-438 "FSCINT.spad" 703230 703246 703903 703908) (-437 "FSAGG.spad" 702347 702357 703186 703225) (-436 "FSAGG.spad" 701426 701438 702267 702272) (-435 "FSAGG2.spad" 700169 700185 701416 701421) (-434 "FS2UPS.spad" 694660 694694 700159 700164) (-433 "FS2.spad" 694307 694323 694650 694655) (-432 "FS2EXPXP.spad" 693432 693455 694297 694302) (-431 "FRUTIL.spad" 692386 692396 693422 693427) (-430 "FR.spad" 686009 686019 691317 691386) (-429 "FRNAALG.spad" 681278 681288 685951 686004) (-428 "FRNAALG.spad" 676559 676571 681234 681239) (-427 "FRNAAF2.spad" 676015 676033 676549 676554) (-426 "FRMOD.spad" 675425 675455 675946 675951) (-425 "FRIDEAL.spad" 674650 674671 675405 675420) (-424 "FRIDEAL2.spad" 674254 674286 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"ATTREG.spad" 107285 107292 110314 110557) (-97 "ATTRBUT.spad" 103308 103315 107265 107280) (-96 "ATTRAST.spad" 103025 103032 103298 103303) (-95 "ATRIG.spad" 102495 102502 103015 103020) (-94 "ATRIG.spad" 101963 101972 102485 102490) (-93 "ASTCAT.spad" 101867 101874 101953 101958) (-92 "ASTCAT.spad" 101769 101778 101857 101862) (-91 "ASTACK.spad" 100991 101000 101259 101286) (-90 "ASSOCEQ.spad" 99817 99828 100947 100952) (-89 "ASP9.spad" 98898 98911 99807 99812) (-88 "ASP8.spad" 97941 97954 98888 98893) (-87 "ASP80.spad" 97263 97276 97931 97936) (-86 "ASP7.spad" 96423 96436 97253 97258) (-85 "ASP78.spad" 95874 95887 96413 96418) (-84 "ASP77.spad" 95243 95256 95864 95869) (-83 "ASP74.spad" 94335 94348 95233 95238) (-82 "ASP73.spad" 93606 93619 94325 94330) (-81 "ASP6.spad" 92473 92486 93596 93601) (-80 "ASP55.spad" 90982 90995 92463 92468) (-79 "ASP50.spad" 88799 88812 90972 90977) (-78 "ASP4.spad" 88094 88107 88789 88794) (-77 "ASP49.spad" 87093 87106 88084 88089) (-76 "ASP42.spad" 85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 47358 47371 47729 47734) (-52 "ANY.spad" 46217 46224 47348 47353) (-51 "ANY1.spad" 45288 45297 46207 46212) (-50 "ANTISYM.spad" 43733 43749 45268 45283) (-49 "ANON.spad" 43426 43433 43723 43728) (-48 "AN.spad" 41735 41742 43242 43335) (-47 "AMR.spad" 39920 39931 41633 41730) (-46 "AMR.spad" 37942 37955 39657 39662) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 "ALGSC.spad" 33977 34003 34714 34767) (-43 "ALGPKG.spad" 29760 29771 33933 33938) (-42 "ALGMFACT.spad" 28953 28967 29750 29755) (-41 "ALGMANIP.spad" 26427 26442 28786 28791) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index c82eb837..bf3538f3 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,5 +1,5 @@ -(203818 . 3486762012) +(203818 . 3486768668) (((|#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((#0=(-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) #0#) |has| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (-319 (-2 (|:| -4298 |#1|) (|:| -4437 |#2|))))) ((((-576)) . T) (($) -2755 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2755 (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-1057 (-419 (-576))))) ((|#1|) . T)) (((|#2| |#2|) . T)) @@ -75,7 +75,7 @@ ((((-576)) . T) (((-419 (-576))) -2755 (|has| |#2| (-38 (-419 (-576)))) (|has| |#2| (-1057 (-419 (-576))))) ((|#2|) . T) (($) -2755 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) (((-876 |#1|)) . T)) (-2755 (|has| |#1| (-374)) (|has| |#1| (-568))) (-2755 (|has| |#1| (-374)) (|has| |#1| (-568))) -((((-2 (|:| -3222 |#1|) (|:| -1567 |#2|))) . T)) +((((-2 (|:| -3222 |#1|) (|:| -3709 |#2|))) . T)) ((($) . T)) ((((-576)) . T) (((-419 (-576))) -2755 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1057 (-419 (-576))))) ((|#1|) . T) (($) -2755 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) (((-1195)) . T)) ((((-874)) -2755 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) @@ -309,11 +309,11 @@ ((((-548)) |has| |#2| (-626 (-548))) (((-905 (-390))) |has| |#2| (-626 (-905 (-390)))) (((-905 (-576))) |has| |#2| (-626 (-905 (-576))))) ((((-874)) . T)) (((|#1| |#2| |#3| |#4|) . T)) -((((-2 (|:| -3222 |#1|) (|:| -1567 |#2|))) . T) (((-874)) . T)) +((((-2 (|:| -3222 |#1|) (|:| -3709 |#2|))) . T) (((-874)) . T)) ((((-548)) |has| |#1| (-626 (-548))) (((-905 (-390))) |has| |#1| (-626 (-905 (-390)))) (((-905 (-576))) |has| |#1| (-626 (-905 (-576))))) (((|#4|) -2755 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1068)))) (((|#3|) -2755 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1068)))) -((((-2 (|:| -3222 |#1|) (|:| -1567 |#2|))) . T)) +((((-2 (|:| -3222 |#1|) (|:| -3709 |#2|))) . T)) ((((-874)) . T)) ((((-874)) . T)) ((((-548)) . T) (((-576)) . T) (((-905 (-576))) . T) (((-390)) . T) (((-227)) . T)) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index ea14f8ad..e5ffc653 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3486762003) +(30 . 3486768658) (4465 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -488,665 +488,670 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |f02aaf| |psolve| |difference| - |resultantEuclideannaif| |arg2| |alphabetic?| |s17dhf| |systemSizeIF| - |string| |qualifier| |balancedFactorisation| |insertRoot!| |stFuncN| - |curve?| |power| |swap| |shellSort| |recur| |say| |removeCosSq| - |generalizedEigenvectors| |factorOfDegree| |sts2stst| |BasicMethod| - |sechIfCan| |conditions| |tanh2coth| |ipow| |low| |commutative?| - |subscriptedVariables| |nextNormalPrimitivePoly| |c05nbf| |presub| - |pop!| |title| |match| |primlimintfrac| |s18acf| |bivariate?| |reset| - |f07adf| |ord| |internalDecompose| |writeLine!| |mix| |monomRDE| |sum| - |invertibleElseSplit?| |changeWeightLevel| |diagonal| |inc| - |zeroSquareMatrix| |groebnerIdeal| |trigs2explogs| - |degreeSubResultant| |symmetricTensors| |binary| |numberOfMonomials| - |companionBlocks| |write| |rewriteIdealWithQuasiMonicGenerators| - |clipPointsDefault| |gcdcofactprim| |getMatch| |moduloP| |roman| |e| - |lexTriangular| |setProperties| |save| |modularGcdPrimitive| |s17ajf| - |lp| |rightPower| |makeResult| |B1solve| |cyclicGroup| |unexpand| - |sign| |critBonD| |nothing| |rk4qc| |setVariableOrder| - |nextsousResultant2| |univariatePolynomials| |extractProperty| - |alphabetic| |splitSquarefree| |orbit| |createPrimitiveNormalPoly| - |leftRank| |extendedIntegrate| |numberOfHues| |divisorCascade| - |e04mbf| |noKaratsuba| |top| |polyRicDE| |symbol?| |f04faf| |mapDown!| - |d01ajf| |build| |factorPolynomial| |toseLastSubResultant| - |tanintegrate| |continue| |sinhcosh| |csch2sinh| |toseSquareFreePart| - |deleteRoutine!| |scalarMatrix| |updatF| |leastPower| |choosemon| - |maxIndex| |intChoose| |numerator| |unrankImproperPartitions0| - |d01gbf| |postfix| |expt| |diophantineSystem| |OMgetApp| |polygamma| - |RittWuCompare| ** |hash| |rename!| |null?| |generalizedInverse| - |stoseInvertibleSet| |viewDefaults| |totolex| |removeZero| |split!| - |sort!| |count| |createIrreduciblePoly| |testDim| |changeNameToObjf| - |environment| |palgextint| |cdr| |readInt16!| |child?| - |listConjugateBases| |ParCond| |stoseInvertibleSetsqfreg| |bumprow| - |sup| |head| |pushdterm| FG2F |tValues| |powerSum| |cyclotomic| - |constant| |c06fqf| |redpps| |pointSizeDefault| |positiveSolve| - |measure2Result| |imagi| |retractable?| |rootOf| |eulerPhi| - |strongGenerators| |laguerre| |mantissa| |iiabs| |elementary| - |coerceImages| |heap| |maxPoints| |makeop| |entry?| |adjoint| - |LazardQuotient2| |newLine| |mapSolve| |nary?| |oddintegers| - |stoseSquareFreePart| |overlabel| |insertMatch| |mainMonomial| - |clipSurface| |rotatex| |xn| |s18aef| |zeroSetSplit| |getCode| - |pointColorPalette| |f01mcf| |swapColumns!| |rarrow| |chiSquare1| - |getMultiplicationTable| |traceMatrix| |scale| |categoryFrame| - |semicolonSeparate| |setOrder| |basisOfRightAnnihilator| - |basisOfCenter| |directSum| |wholePart| |infinityNorm| |unknownEndian| - |omError| |orthonormalBasis| |iiasec| |integralRepresents| - |leftFactor| |cyclicParents| |edf2ef| |reduceByQuasiMonic| - |partialDenominators| |FormatRoman| |nullary| |outputAsTex| - |taylorRep| |initializeGroupForWordProblem| |mainVariable?| |unparse| - |dn| |rowEchLocal| |vspace| |components| |empty?| |lowerCase?| - |normalizedAssociate| |cycleElt| |computeCycleEntry| |nullary?| - |maxRowIndex| |pushucoef| |showScalarValues| |pquo| |iiacot| - |categories| |patternVariable| |stoseLastSubResultant| |newReduc| - |myDegree| |exponent| |numer| |sin?| |retractIfCan| |permutationGroup| - |repeating| |flexibleArray| |factorAndSplit| |expintegrate| - |iflist2Result| |nextPrimitiveNormalPoly| |algSplitSimple| |denom| - |binomial| |delete!| |partition| |digits| |zeroDimPrimary?| |leftMult| - |f04mbf| |zag| |llprop| |integrate| |inf| |mainExpression| - |inverseColeman| |f04adf| |mesh| |pdf2df| |nthRootIfCan| - |complexNormalize| |pi| |expintfldpoly| |supRittWu?| - |characteristicSet| |extractTop!| |subscript| |printingInfo?| - |goodPoint| |setEmpty!| |branchIfCan| |infinity| |partialFraction| - |physicalLength| |semiIndiceSubResultantEuclidean| |insertionSort!| - |concat| |step| |sparsityIF| |linearlyDependentOverZ?| |e02baf| - |e04fdf| |leftOne| |firstSubsetGray| |moebius| |extractPoint| - |solveLinear| |UnVectorise| |OMgetEndObject| |f01qcf| |acothIfCan| - |bombieriNorm| |integer?| |atanhIfCan| |child| |shiftRoots| - |thenBranch| |clearTheSymbolTable| |rootProduct| |complexRoots| - |kernel| |s19acf| |doubleFloatFormat| |alternating| - |monicRightFactorIfCan| |consnewpol| |formula| |eigenvalues| - |inputOutputBinaryFile| |closed?| |ffactor| |e04gcf| |list| |ptree| - |setPoly| |dictionary| |qPot| |mainContent| |lhs| |has?| |fullDisplay| - |recolor| |copy!| |draw| |subresultantVector| |f04asf| |clearCache| - |getOperands| |axesColorDefault| |rangeIsFinite| |rhs| |range| - |f01ref| |quadraticForm| |pseudoDivide| |readByte!| |upperCase| - |rootSimp| |surface| |f02axf| |primeFactor| |makeGraphImage| - |tubePlot| |meshFun2Var| |oddlambert| |singularAtInfinity?| - |ParCondList| |prepareDecompose| |lowerCase!| |currentEnv| |nrows| - |safetyMargin| |variationOfParameters| |rightUnits| |outputArgs| - |resultantReduit| |f02wef| |removeDuplicates| |indices| |f2df| |ncols| - |limit| |pseudoRemainder| |lyndon?| |seed| |makeObject| |acscIfCan| - |isList| |outputFixed| |members| |move| |pointLists| - |linearDependence| |setPosition| |rewriteIdealWithHeadRemainder| - |rotatez| |coef| |setColumn!| |mapExponents| |getRef| - |complexEigenvectors| |iiGamma| |traverse| |validExponential| |plot| - |linearAssociatedExp| |OMputAtp| |f02akf| |complexForm| |freeOf?| - |numFunEvals| |solveRetract| |iicoth| |besselJ| |exprex| |e02daf| - |reindex| |prindINFO| |saturate| |combineFeatureCompatibility| - |mapExpon| |numberOfIrreduciblePoly| |mapMatrixIfCan| |optpair| - |exportedOperators| |functionIsFracPolynomial?| - |leftCharacteristicPolynomial| |whatInfinity| |kind| |s13adf| - |getVariableOrder| |normInvertible?| |nullSpace| |stFunc1| |iiasin| - |bfEntry| |normalDenom| |dAndcExp| |op| |palglimint| |lquo| - |useNagFunctions| |revert| |getSyntaxFormsFromFile| |kernels| - |inverseLaplace| |UP2ifCan| |imagk| |makeTerm| |numericalOptimization| - |makeCrit| |certainlySubVariety?| |prinpolINFO| |characteristicSerie| - |leadingSupport| |s19abf| |operator| |evenlambert| |colorDef| |froot| - |goodnessOfFit| |element?| |jokerMode| |appendPoint| |hasoln| - |wordInStrongGenerators| SEGMENT |leftLcm| |expenseOfEvaluationIF| - |setValue!| |OMputSymbol| |OMUnknownSymbol?| |hasTopPredicate?| - |addiag| |generalSqFr| |f2st| |sort| |linearPart| |getOrder| - |removeDuplicates!| |univariate| |internalSubPolSet?| |normFactors| - |typeList| |derivative| |OMunhandledSymbol| |inverse| |dec| - |LyndonWordsList1| |leftExactQuotient| |yCoord| |mathieu24| - |showRegion| |outlineRender| |pointColor| |complement| - |makeFloatFunction| |positive?| |mkAnswer| |lazyIrreducibleFactors| - |crushedSet| |union| |overset?| |back| |factorGroebnerBasis| |f02xef| - |clearDenominator| |nativeModuleExtension| |factor| |deref| - |subTriSet?| |showTheFTable| |setLength!| |compound?| |iomode| - |OMputEndAttr| |OMgetInteger| |random| |convergents| |variable?| - |eof?| |sqrt| |collectQuasiMonic| |schwerpunkt| |weight| |isTimes| - |monicCompleteDecompose| |comp| |buildSyntax| |numberOfOperations| - |e02bcf| |real| |iterationVar| |divideIfCan| |var1Steps| - |tubePointsDefault| |asinIfCan| |radicalRoots| |SturmHabicht| |c06eaf| - |s17ahf| |imag| |rdHack1| |simpson| |super| |properties| |e02bef| - |setStatus| |factorials| |quasiRegular?| |OMwrite| |copy| - |directProduct| |fortranLinkerArgs| |mainSquareFreePart| - |extractSplittingLeaf| |d02bbf| |rootDirectory| |largest| |translate| - |euclideanSize| |linkToFortran| |direction| |ScanFloatIgnoreSpaces| - |iipow| |dflist| |transpose| |genericPosition| |OMgetEndBind| |depth| - |cylindrical| |d03edf| |secIfCan| |noLinearFactor?| |rootRadius| - |zeroDim?| |brace| |scanOneDimSubspaces| |mapUnivariate| |s18aff| - |reverseLex| |pair?| |select!| |inverseIntegralMatrixAtInfinity| - |lifting| |destruct| |OMclose| |simplify| |setPrologue!| - |initiallyReduce| |parabolic| |Is| |tan2trig| |processTemplate| - |multiplyCoefficients| |extensionDegree| |insertBottom!| |match?| - |anticoord| |symmetricProduct| |iisin| |acosIfCan| |autoCoerce| - |conditionP| |nextPrime| |create| |OMputFloat| |arguments| - |totalDifferential| |tanNa| |powmod| |OMReadError?| |iiatan| - |radicalEigenvector| |palgextint0| |computeBasis| - |generalInfiniteProduct| |getMultiplicationMatrix| |tanIfCan| - |implies| |expand| |createNormalPoly| |e02adf| |monomial| - |interpretString| |singular?| |rightFactorIfCan| |safeCeiling| - |headReduce| |baseRDEsys| |filterWhile| |iicos| |fillPascalTriangle| - |multivariate| |rightExactQuotient| |close| |decimal| - |createZechTable| F |root?| |dot| |filterUntil| |twoFactor| |iiasinh| - |genericRightDiscriminant| |variables| |specialTrigs| - |fortranDoubleComplex| |fixedPointExquo| |OMreadStr| |select| - |internalIntegrate| |cTanh| |mergeFactors| |display| |applyRules| - |rewriteSetWithReduction| |setRow!| |vertConcat| |fortranLiteral| - |d01apf| |LiePolyIfCan| |d03faf| |virtualDegree| |bumptab1| |rotatey| - |po| |factors| |minus!| |listRepresentation| |palgint0| - |palgintegrate| |rCoord| |tablePow| |perfectNthPower?| |totalfract| - |nthExpon| |predicate| |quartic| |tanAn| |palgRDE| |isImplies| - |unravel| |ldf2lst| |qqq| |debug| |taylor| |lineColorDefault| |reseed| - |position!| |s01eaf| |showTheRoutinesTable| |exactQuotient| |cn| - |setAdaptive| |copyInto!| |standardBasisOfCyclicSubmodule| D |laurent| - |input| |mappingAst| |simplifyPower| |addMatch| |prefixRagits| - |optional?| |expandTrigProducts| |ceiling| |iisinh| |roughSubIdeal?| - |puiseux| |library| |d02bhf| |rightAlternative?| - |stripCommentsAndBlanks| |endOfFile?| EQ |partialQuotients| - |mapUnivariateIfCan| |dimensionOfIrreducibleRepresentation| - |leftTrace| |car| |exponentialOrder| |removeRedundantFactorsInPols| - |bandedJacobian| |viewport3D| |max| |selectPDERoutines| |rotate| |inv| - |upperBound| |OMsupportsSymbol?| |bothWays| |derivationCoordinates| - |pr2dmp| |unrankImproperPartitions1| |fractionPart| |rationalPoints| - |f07fdf| |ground?| |discreteLog| |e02ahf| |antisymmetric?| - |integralBasis| |associatorDependence| |leftTraceMatrix| |rootsOf| - |compBound| |setelt!| |ground| |set| |radicalSimplify| |lyndon| - |f07fef| |mapdiv| |extractIfCan| |bipolarCylindrical| - |showArrayValues| |countRealRootsMultiple| |OMputEndObject| - |leadingMonomial| |paraboloidal| |nlde| |cycleLength| |graeffe| - |wronskianMatrix| |coerceL| |algebraicCoefficients?| |univariateSolve| - |refine| |leadingCoefficient| |parameters| |pile| |comparison| |Beta| - |inR?| |cross| |size| |problemPoints| |groebnerFactorize| |cyclicCopy| - |transcendentalDecompose| |primitiveMonomials| |setfirst!| - |numberOfNormalPoly| |semiResultantEuclidean2| |setFieldInfo| - |roughEqualIdeals?| |decrease| |irreducibleFactor| |cRationalPower| - |OMencodingUnknown| |print| |reductum| |rightNorm| |floor| |universe| - |substring?| |lSpaceBasis| |groebgen| |fortranReal| |list?| |compdegd| - |denominator| |resolve| |seriesToOutputForm| |interval| - |setAdaptive3D| |invertible?| |f02bjf| |createGenericMatrix| - |trivialIdeal?| |semiDegreeSubResultantEuclidean| |padicFraction| - |chiSquare| |groebSolve| |e04naf| |irreducibleRepresentation| - |suffix?| |newSubProgram| |infiniteProduct| |true| |setImagSteps| - |showFortranOutputStack| |eq?| |category| |printStats!| - |basisOfLeftNucloid| |mapmult| |rightGcd| |OMgetType| |domain| - |fortranTypeOf| |magnitude| |clikeUniv| |critT| |setDifference| - |accuracyIF| |optional| |maxrow| |f01qef| |OMserve| |df2ef| - |setClipValue| |numberOfDivisors| |e01sef| |prefix?| - |absolutelyIrreducible?| |zero?| |package| |innerEigenvectors| - |recoverAfterFail| |alphanumeric?| |df2mf| |extendedResultant| - |insert| |subResultantsChain| |s17def| |SturmHabichtMultiple| - |unitNormalize| |OMgetObject| |sumOfKthPowerDivisors| |changeMeasure| - |putProperty| |collect| |listBranches| |show| |increasePrecision| - |integralLastSubResultant| |clearTable!| |LiePoly| |curryLeft| - |d01bbf| |symFunc| |nextColeman| |hitherPlane| |rightOne| |search| - |logical?| |bitCoef| |graphs| |leadingIndex| |getPickedPoints| |lllp| - |node| |f01rcf| |binaryTree| |typeLists| |sin2csc| |trace| |e01sbf| - |createLowComplexityNormalBasis| |eisensteinIrreducible?| |lagrange| - |modifyPointData| |viewPhiDefault| |hMonic| |stirling1| - |approxNthRoot| |points| |branchPoint?| |rroot| |mightHaveRoots| - |charpol| |jacobian| |integers| |extractIndex| |d02gaf| |returnType!| - |multiEuclideanTree| |createNormalElement| |principal?| |ODESolve| - |infix?| |minset| |mindegTerm| |probablyZeroDim?| |balancedBinaryTree| - |rk4f| |closedCurve?| |critMTonD1| |leftMinimalPolynomial| |mask| - |f07aef| |internalAugment| |separateDegrees| |empty| - |OMencodingBinary| |minimize| |primitiveElement| |coth2trigh| - |nextIrreduciblePoly| |flatten| |taylorQuoByVar| |kroneckerDelta| - |d01akf| |fortranInteger| |symmetricDifference| |getGoodPrime| - |gensym| |sub| |ReduceOrder| |nextNormalPoly| |redPo| - |reducedContinuedFraction| |makeVariable| |notelem| |setMaxPoints| - |sequences| |rquo| |multiEuclidean| |subSet| |s15aef| |isQuotient| - |removeSuperfluousCases| |trapezoidal| |polyRDE| |nsqfree| |baseRDE| - |airyBi| |rubiksGroup| |degreeSubResultantEuclidean| |laurentRep| - |s18dcf| |contractSolve| |e02dff| |cotIfCan| |optAttributes| - |messagePrint| |createRandomElement| |point?| |startPolynomial| - |quadratic?| |resultantnaif| |separant| |round| |upDateBranches| - |more?| |monomial?| |e04jaf| |check| |cSinh| |coefChoose| |doubleRank| - |curve| |exprToXXP| |parametric?| |zeroDimensional?| |sturmSequence| - |directory| |htrigs| |createLowComplexityTable| |musserTrials| - |decompose| |removeRoughlyRedundantFactorsInContents| |size?| - |setCondition!| |toScale| |rationalIfCan| - |factorSquareFreeByRecursion| |shiftLeft| |drawToScale| |cAcot| - |frobenius| |OMgetVariable| |subQuasiComponent?| |height| |units| - |makeSketch| |log10| |s17adf| |leadingTerm| |explimitedint| |mapGen| - |slex| |merge| |equation| |monomRDEsys| |rootBound| |basis| |hexDigit| - |headAst| |bitand| |rst| |FormatArabic| |idealiser| |subNode?| - |csc2sin| |youngDiagram| |fortranLiteralLine| |cothIfCan| |fprindINFO| - |leaves| |skewSFunction| |outerProduct| |bitior| - |solveLinearPolynomialEquationByRecursion| |finite?| - |quasiAlgebraicSet| |fixedPoint| |linear| |transcendent?| - |particularSolution| |logIfCan| |interpolate| |iifact| - |useEisensteinCriterion| |disjunction| |csubst| |flexible?| |augment| - |att2Result| |c06ekf| |mainForm| |viewpoint| |macroExpand| - |irreducibleFactors| |mulmod| |green| |untab| |collectUnder| - |listYoungTableaus| |polynomial| |mainCoefficients| |hyperelliptic| - |dmpToP| |rotate!| |curveColor| |comment| |f01bsf| |divergence| - |rischDEsys| |coercePreimagesImages| |aQuadratic| |curryRight| - |center| |close!| |unprotectedRemoveRedundantFactors| |ode1| |hconcat| - |purelyAlgebraic?| |createPrimitivePoly| |controlPanel| |binding| - |lastSubResultantEuclidean| |minIndex| |iisqrt2| |squareTop| - |rightLcm| |cap| |extractBottom!| |figureUnits| - |conditionsForIdempotents| |numericIfCan| |merge!| |rule| |ridHack1| - |declare| |normalizedDivide| |s13acf| |rationalFunction| |coord| - |common| |slash| |OMsetEncoding| |regime| |s17akf| |primitivePart!| - |geometric| |pseudoQuotient| |evaluate| |powern| |listLoops| - |setright!| |blankSeparate| |decreasePrecision| |length| |OMgetBind| - |mirror| |lowerPolynomial| |escape| |scripted?| |sinh2csch| |legendre| - |lookup| |primintfldpoly| |scripts| |fixPredicate| |innerint| |solve| - |pascalTriangle| |socf2socdf| |nthRoot| |leftScalarTimes!| |s17dgf| - |iiacsc| |e02dcf| |laplacian| |algebraic?| |character?| |symmetric?| - |makeEq| |any?| |cycles| |replace| |characteristic| |matrix| - |selectsecond| |nextSubsetGray| |OMgetEndError| |monicModulo| - |iiacoth| |nilFactor| |zeroMatrix| |lazyIntegrate| |primeFrobenius| - |s20acf| |stoseInvertible?sqfreg| |ScanFloatIgnoreSpacesIfCan| - |iisqrt3| |primPartElseUnitCanonical!| |intersect| |sample| |mesh?| - |conjugate| |resetBadValues| |laurentIfCan| |setAttributeButtonStep| - |front| |irVar| |viewDeltaYDefault| |homogeneous?| |var2Steps| - |complexEigenvalues| Y |selectIntegrationRoutines| |cAtan| |se2rfi| - |bracket| |solid| |sdf2lst| |exprHasAlgebraicWeight| |complexSolve| - |label| |usingTable?| |fullPartialFraction| |checkForZero| |remainder| - |getGraph| |categoryMode| |neglist| |randomR| |PollardSmallFactor| - |intPatternMatch| |rk4| |Lazard2| |quickSort| |ricDsolve| |setlast!| - |cCot| |scan| |putProperties| |dmp2rfi| |e04dgf| |currentScope| - |partitions| |viewWriteAvailable| |cycleTail| |binaryFunction| - |setref| |result| |subtractIfCan| |lieAlgebra?| |bfKeys| |distribute| - |mainKernel| |in?| |expextendedint| |nonLinearPart| |elements| |block| - |call| |delay| |noValueMode| |zeroSetSplitIntoTriangularSystems| - |internalLastSubResultant| |isobaric?| |trueEqual| |prologue| - |pmintegrate| |numeric| |getProperty| |perspective| |d02gbf| - |updateStatus!| |extension| |radical| |s21baf| |expint| |cSin| - |showAllElements| |s17aef| |oddInfiniteProduct| |ef2edf| - |leftRegularRepresentation| |constructor| |times!| |matrixConcat3D| - |pointData| |setsubMatrix!| |OMgetString| |euclideanGroebner| |zoom| - |OMopenString| |internal?| |pole?| |bindings| |option| - |sortConstraints| |prem| |permutationRepresentation| |unary?| - |symbolTable| |showSummary| |cAsin| |tab1| |square?| |palglimint0| - |compactFraction| |prinshINFO| |subPolSet?| |overbar| |totalDegree| - |elliptic?| |mappingMode| |totalGroebner| |clipBoolean| |denomLODE| - |addPointLast| |henselFact| |internalInfRittWu?| - |pushFortranOutputStack| |integerIfCan| |showAttributes| |divide| - |tensorProduct| |autoReduced?| |duplicates?| |setTopPredicate| - |stiffnessAndStabilityFactor| |makeRecord| |selectAndPolynomials| - |simplifyLog| |popFortranOutputStack| |selectODEIVPRoutines| - |OMsupportsCD?| |biRank| |tanSum| |generic?| |extractClosed| |cAsinh| - |errorInfo| |outputAsFortran| |mainDefiningPolynomial| - |argumentListOf| |expPot| |linearAssociatedLog| |lepol| |name| - |parents| |ratDsolve| |charthRoot| |sinhIfCan| |lazyPquo| |imports| - |over| |uniform| |rightTrim| |reduction| |tanhIfCan| |body| - |selectOptimizationRoutines| |shape| |iteratedInitials| |HenselLift| - |hypergeometric0F1| |setnext!| |drawComplexVectorField| |leftTrim| - |cTan| |makeSUP| |null| |octon| |exp1| |readUInt16!| |isNot| - |hasSolution?| |stack| |solveInField| |isPlus| |setProperty| |c02agf| - |not| |monicDivide| |removeSinSq| |edf2df| |graphCurves| |maxint| BY - |intcompBasis| |e01bhf| |increase| |c06gcf| |and| |dimension| |frst| - |getProperties| |s20adf| |outputList| |wholeRadix| |zCoord| - |numberOfComponents| |redPol| |Vectorise| |principalAncestors| |or| - |rowEch| |structuralConstants| |cubic| |encodingDirectory| |writable?| - |lexico| |rur| |digit| |xor| |OMgetAtp| |leadingExponent| |makeUnit| - |antiAssociative?| |mainMonomials| |iidprod| |alternative?| - |quotientByP| |external?| |signature| |dim| |case| |open?| - |basisOfNucleus| |curry| |unitVector| |assert| |cardinality| - |semiSubResultantGcdEuclidean1| |port| |weighted| |upperCase!| - |d02ejf| |prime?| |pattern| |Zero| |create3Space| |computeCycleLength| - |repeating?| |ode2| |uncouplingMatrices| |factorial| |component| - |nonQsign| |trailingCoefficient| |listexp| |One| |printCode| - |primextendedint| |acschIfCan| |deepExpand| |internalIntegrate0| - |sncndn| |t| |parametersOf| |factorSquareFree| |exQuo| |setClosed| - |shift| |OMreadFile| NOT |basisOfLeftAnnihilator| |permutations| - |printStatement| |indicialEquation| |addmod| |output| |bytes| |paren| - |userOrdered?| |integerBound| |leftAlternative?| |smith| |reducedForm| - OR |leader| |vector| |genericLeftTrace| |lazyEvaluate| - |constantKernel| |e01bff| |intermediateResultsIF| - |removeRedundantFactors| |roughBasicSet| |rischDE| |message| - |prepareSubResAlgo| AND |initials| |differentiate| |leadingIdeal| - |children| |bezoutMatrix| |OMputApp| |rightRecip| |algDsolve| - |realElementary| |imagK| |solveid| |enterInCache| |capacity| |c06fpf| - |mdeg| |trigs| |wordInGenerators| |fortran| |atanh| |separateFactors| - |norm| |exactQuotient!| |tube| |OMputEndBind| |OMgetAttr| |elt| - |polygon| |basisOfCentroid| |approximants| |e01bgf| |OMcloseConn| - |acoth| |powerAssociative?| |overlap| |errorKind| |pastel| - |putColorInfo| |alternatingGroup| |chebyshevU| |localReal?| |fracPart| - |monomialIntegrate| |readLineIfCan!| |asech| |level| |conjunction| - |stopTable!| |tanQ| |mvar| |complex?| |radix| |padicallyExpand| - |belong?| |twist| |imagE| |supDimElseRittWu?| |genericRightNorm| - |e01sff| |bottom!| |setScreenResolution3D| |reciprocalPolynomial| - |conjugates| |bipolar| |coerceP| |split| |toseInvertibleSet| - |decomposeFunc| |multiple| |cons| |varselect| |atoms| |exponential1| - |selectSumOfSquaresRoutines| |equality| |pol| |weierstrass| - |raisePolynomial| |numberOfComposites| |discriminantEuclidean| |lex| - |applyQuote| |tubePoints| |patternMatch| |shallowCopy| |cond| - |diagonalProduct| |parseString| |quatern| |retract| |sumOfDivisors| - |exists?| |cAsech| |elRow2!| |taylorIfCan| |multinomial| |triangSolve| - |pack!| |rdregime| |numerators| |nextPartition| F2FG |isMult| - |compiledFunction| |yellow| |leftDivide| |ellipticCylindrical| |mat| - |relerror| |multisect| |prime| |crest| |scaleRoots| |second| * - |minrank| |idealiserMatrix| |laguerreL| |functorData| |concat!| - |ruleset| |rootPower| |bag| |mkcomm| |gcdprim| |returns| |asechIfCan| - |cAcoth| |third| |someBasis| |mergeDifference| |endSubProgram| - |lifting1| |arity| |stopMusserTrials| |compose| |interactiveEnv| - |updatD| |e01daf| |reduceLODE| |d02cjf| |index?| |failed?| |f01brf| - |f04axf| |source| |void| |unit?| |cAsec| |sizeLess?| |primintegrate| - |genus| |heapSort| |clearTheFTable| = |sorted?| |numberOfFactors| - |ramified?| |Ei| |suchThat| |swapRows!| |assign| |dualSignature| - |OMconnInDevice| |OMputAttr| |real?| |df2st| |fractRadix| - |exprToGenUPS| |var2StepsDefault| |maxrank| |script| |mapUp!| - |patternMatchTimes| |light| |polygon?| |push!| |divideExponents| - |polarCoordinates| < |d01anf| |f02awf| |badNum| |coordinates| - |plusInfinity| |fi2df| |factor1| |createNormalPrimitivePoly| |prinb| - |before?| |quasiComponent| |char| |normal?| > |littleEndian| |aCubic| - |outputAsScript| |algebraicDecompose| |systemCommand| |minusInfinity| - |multiplyExponents| |stFunc2| |infix| |imagI| |attributeData| - |generalTwoFactor| |Aleph| |multiset| <= |rightRankPolynomial| - |normal01| |complementaryBasis| |tex| |target| |differentialVariables| - |cosIfCan| |toroidal| |unit| |OMmakeConn| |OMgetEndAttr| |cup| >= - |pureLex| |digamma| |groebner| |linGenPos| |reify| |leftNorm| |order| - |nodes| |sec2cos| |primes| |interReduce| |expr| |principalIdeal| - |iicosh| |corrPoly| |reducedQPowers| |outputSpacing| |setleaves!| - |cCsch| |satisfy?| |quasiRegular| |phiCoord| |normal| - |brillhartIrreducible?| |triangulate| |s18adf| - |radicalOfLeftTraceForm| |hermiteH| |laplace| |resultant| |iiacos| - |sqfree| |ddFact| |numberOfImproperPartitions| |subResultantChain| - |stoseInternalLastSubResultant| + |makeViewport3D| |lfintegrate| - |OMgetBVar| |row| |changeThreshhold| |type| |identitySquareMatrix| - |cot2trig| |purelyTranscendental?| |stopTableGcd!| |getStream| - |OMputVariable| |complexIntegrate| |point| - |float| |d01amf| - |replaceKthElement| |addBadValue| |initiallyReduced?| |prevPrime| - |changeBase| |oneDimensionalArray| |gradient| |f02ajf| |variable| - |binomThmExpt| / |hcrf| |d01alf| |outputGeneral| - |univariatePolynomialsGcds| |representationType| |d02kef| - |fortranComplex| |determinant| |OMgetError| |iterators| |gethi| - |getZechTable| |s14aaf| |complexNumericIfCan| |stronglyReduced?| - |weights| |hue| |product| |rangePascalTriangle| |linearPolynomials| - |doubleResultant| |startTable!| |series| |outputMeasure| |linears| - |vedf2vef| |OMconnectTCP| |changeVar| |maxdeg| |PDESolve| - |toseInvertible?| |inspect| |univariate?| |highCommonTerms| - |eigenMatrix| |cAtanh| |definingInequation| |irForm| - |selectPolynomials| |leviCivitaSymbol| |invmod| |id| |c06gbf| - |normalizeIfCan| |squareMatrix| |idealSimplify| |atom?| |value| - |cosh2sech| |branchPointAtInfinity?| |makeSin| |f04qaf| |symbol| - |externalList| |lo| |subCase?| |cycleSplit!| |associatedSystem| - |checkRur| |numberOfComputedEntries| |powers| |primlimitedint| - |f02aff| |OMgetEndBVar| |expression| |separate| |sylvesterMatrix| - |ignore?| |min| |binaryTournament| |debug3D| |finiteBound| - |commonDenominator| |parabolicCylindrical| |denomRicDE| |minPoints3D| - |integer| |ode| |gcdcofact| |column| |indicialEquationAtInfinity| GE - |drawComplex| |nthFractionalTerm| |qfactor| |lazy?| - |rightRegularRepresentation| |minRowIndex| |OMputInteger| - |stoseIntegralLastSubResultant| |realRoots| |minGbasis| |iprint| GT - |e02gaf| |integral| |cAcosh| |dimensions| |f04jgf| |indicialEquations| - |changeName| |constantIfCan| |OMencodingSGML| |selectOrPolynomials| LE - |f02fjf| |routines| |completeHensel| |symmetricSquare| |OMputBind| - |factorSquareFreePolynomial| |squareFreePolynomial| - |primPartElseUnitCanonical| |nextSublist| |equiv| LT - |exteriorDifferential| |stoseInvertibleSetreg| |makeYoungTableau| - |birth| |basisOfMiddleNucleus| |realEigenvalues| |rationalPoint?| - |c06gqf| |createMultiplicationTable| |extract!| |resetNew| |polar| - |remove!| |sumSquares| |hasHi| |nthCoef| |approxSqrt| |c02aff| - |inconsistent?| |normalize| |moebiusMu| |definingPolynomial| - |isAbsolutelyIrreducible?| |putGraph| |key?| |measure| |iiperm| - |listOfMonoms| |realSolve| |jordanAlgebra?| |keys| |content| |s14abf| - |spherical| |module| |critM| |squareFreeLexTriangular| |reflect| - |relativeApprox| |useSingleFactorBound?| |leftRecip| |shufflein| - |pomopo!| |headRemainder| |color| |trim| |option?| - |commutativeEquality| |oblateSpheroidal| |palginfieldint| - |genericLeftMinimalPolynomial| |index| |genericLeftTraceForm| - |lexGroebner| |expIfCan| |numberOfChildren| |extendIfCan| |f02aef| - |shade| |shanksDiscLogAlgorithm| |showTheSymbolTable| |s17acf| |iicsc| - |identity| |rightFactorCandidate| |OMputBVar| |monic?| |acotIfCan| - |findBinding| |adaptive?| |boundOfCauchy| |wordsForStrongGenerators| - |clipParametric| |complexExpand| |c05adf| |f01maf| |removeCoshSq| - |zerosOf| |exponential| |pair| |numberOfVariables| |setMaxPoints3D| - |tree| |open| |LagrangeInterpolation| |lowerCase| |ip4Address| - |pushNewContour| |getConstant| |s17dlf| |bright| |e02bdf| |odd?| - |bivariateSLPEBR| |closed| |gramschmidt| |stoseInvertible?| - |setButtonValue| |property| |inRadical?| |setOfMinN| |double?| - |mapBivariate| |s19adf| |var1StepsDefault| |cyclotomicDecomposition| - |mathieu11| |genericRightTraceForm| |contains?| |rightMult| - |isConnected?| |eval| |fortranDouble| |unmakeSUP| |infLex?| - |monicRightDivide| |hdmpToP| |viewWriteDefault| |pleskenSplit| - |completeEchelonBasis| |explicitEntries?| |f04atf| |splitNodeOf!| - |operations| |OMgetEndApp| |isAtom| |lowerBound| |cCos| |intensity| - |elRow1!| |lazyPremWithDefault| |factorByRecursion| |float?| |janko2| - |setchildren!| |monomialIntPoly| |drawStyle| |inputBinaryFile| - |interpret| |OMlistCDs| |error| |factorsOfCyclicGroupSize| - |bubbleSort!| |coordinate| |deepestTail| |constant?| |composite| - |number?| |meatAxe| |numberOfPrimitivePoly| |associative?| |palgRDE0| - |thetaCoord| |nthFactor| |iicot| |ratPoly| |removeConstantTerm| |kmax| - |atanIfCan| |optimize| |reopen!| |minordet| |inHallBasis?| |every?| - |precision| |complete| |function| |OMputEndBVar| |OMgetSymbol| - |removeRedundantFactorsInContents| |chvar| |bringDown| |ranges| - |wholeRagits| |rootPoly| |f02agf| |LazardQuotient| |OMsend| - |critpOrder| |dmpToHdmp| |top!| |lprop| |sizePascalTriangle| - |composites| |pdf2ef| |LyndonWordsList| |width| |symbolTableOf| - |fixedDivisor| |represents| |middle| |exprToUPS| |ratpart| - |numFunEvals3D| |leastMonomial| |rules| |double| |meshPar2Var| - |selectFiniteRoutines| |lookupFunction| |aQuartic| - |leadingCoefficientRicDE| |mainValue| |expandPower| |squareFree| - |iiatanh| |pushup| |meshPar1Var| |sinIfCan| |resetAttributeButtons| - |basicSet| |completeEval| |algintegrate| |df2fi| |lazyVariations| - |iibinom| |e01bef| |semiResultantReduitEuclidean| |ratDenom| - |subMatrix| |s14baf| |selectMultiDimensionalRoutines| |removeSinhSq| - |finiteBasis| |dual| |perfectNthRoot| |fglmIfCan| |youngGroup| - |constantRight| |createThreeSpace| |setleft!| |s17dcf| - |checkPrecision| |mr| |quotient| |OMbindTCP| |const| |redmat| - |iFTable| |ocf2ocdf| |splitLinear| |setScreenResolution| - |semiSubResultantGcdEuclidean2| |inGroundField?| |cAcsc| |quasiMonic?| - |deleteProperty!| |connectTo| |generalizedContinuumHypothesisAssumed?| - |SFunction| |bezoutDiscriminant| |mainCharacterization| |complexZeros| - |LyndonBasis| |subst| |rem| |vconcat| |rewriteIdealWithRemainder| - |doubleDisc| |node?| |outputBinaryFile| |hclf| |constantOpIfCan| - |zeroDimPrime?| |componentUpperBound| |lllip| |outputFloating| |quo| - |quotedOperators| |latex| |s18def| |withPredicates| |declare!| - |varList| |factorsOfDegree| |generalizedEigenvector| - |nextLatticePermutation| |iiexp| |sequence| |generic| |s15adf| - |symbolIfCan| |besselI| |primextintfrac| |lcm| |irDef| |swap!| - |triangularSystems| |setTex!| |readIfCan!| |delete| |div| - |constDsolve| |subspace| |OMParseError?| |firstDenom| |enterPointData| - |write!| |quoted?| |discriminant| |cyclic| |dequeue| |exquo| - |superscript| |dominantTerm| |setvalue!| |shiftRight| |simpsono| |any| - |arrayStack| |fintegrate| |increment| |append| |backOldPos| - |gcdPolynomial| ~= |linearAssociatedOrder| |tan2cot| |limitedint| - |aromberg| |tRange| |preprocess| |euclideanNormalForm| |d03eef| - |halfExtendedResultant1| |gcd| |goto| |plotPolar| |objects| |#| - |infieldIntegrate| |bsolve| |whileLoop| |setUnion| |yCoordinates| - |eigenvector| |generateIrredPoly| |lazyGintegrate| |eulerE| |false| - |computePowers| |normalise| |base| ~ |euler| |extendedSubResultantGcd| - |zeroVector| |randomLC| |genericRightMinimalPolynomial| |algebraicOf| - |signAround| |numberOfCycles| |central?| |continuedFraction| |ravel| - |leftDiscriminant| |setEpilogue!| |normalizeAtInfinity| |cCosh| - |dfRange| |segment| |part?| |symmetricPower| |d01gaf| - |exprHasLogarithmicWeights| |addPoint| |init| |rightRank| |terms| - |adaptive3D?| |queue| |reshape| |roughBase?| |logGamma| |extendedint| - |high| |divideIfCan!| |e04ucf| |/\\| |find| |elaborateFile| - |unitNormal| |subResultantGcdEuclidean| |lastSubResultantElseSplit| - GF2FG |elaborate| |cyclicSubmodule| |nand| |mindeg| |\\/| |Si| - |leftExtendedGcd| |bitTruth| |less?| |unitsColorDefault| |apply| - |coerce| |minimalPolynomial| |readInt8!| |besselY| |c06ecf| - |atrapezoidal| |sizeMultiplication| UTS2UP |setIntersection| - |argscript| |c06gsf| |first| |construct| |presuper| |physicalLength!| - |region| |doublyTransitive?| |xCoord| |showTheIFTable| - |purelyAlgebraicLeadingMonomial?| |limitedIntegrate| |reverse!| - |symmetricGroup| |rest| |repSq| |removeRoughlyRedundantFactorsInPols| - |airyAi| |generalPosition| |logpart| |plus| |stoseInvertible?reg| - |Gamma| |OMconnOutDevice| |OMopenFile| |qroot| |update| - |rootNormalize| |insertTop!| |shallowExpand| |ptFunc| |enqueue!| - |jordanAdmissible?| |symmetricRemainder| |GospersMethod| - |sylvesterSequence| |numberOfFractionalTerms| |realEigenvectors| - |linearMatrix| |screenResolution3D| |midpoints| |coefficients| - |divisors| |asecIfCan| |cAcsch| |hdmpToDmp| |semiResultantEuclidean1| - |rational| |karatsubaDivide| |squareFreePart| |bitLength| |resize| - |nor| |just| |divisor| |extend| |localIntegralBasis| |times| - |viewport2D| |rightQuotient| |completeHermite| |lfunc| |pToHdmp| - |previous| |delta| |lazyPseudoQuotient| |closeComponent| - |cyclePartition| |halfExtendedSubResultantGcd2| |OMputEndAtp| - |typeForm| |startStats!| |characteristicPolynomial| |rational?| - |iiasech| |makingStats?| |conjug| |quoByVar| |box| |reorder| - |stopTableInvSet!| |position| |infRittWu?| |basisOfRightNucleus| - |palgLODE| |pointColorDefault| |argument| |e02ddf| |fibonacci| - |e01baf| |setPredicates| |stosePrepareSubResAlgo| |reduced?| - |datalist| |lift| |ListOfTerms| |isOr| |getlo| |e02ajf| - |integralAtInfinity?| |f01qdf| |makeMulti| |c05pbf| - |expenseOfEvaluation| |sqfrFactor| |bat| |monom| |reduce| |dark| - |indiceSubResultantEuclidean| |digit?| |writeByte!| |localUnquote| - |totalLex| |f02bbf| |coHeight| |perfectSqrt| |Lazard| |weakBiRank| - |loadNativeModule| |stirling2| |subResultantGcd| - |inverseIntegralMatrix| |factorset| |iCompose| |mpsode| - |tryFunctionalDecomposition?| |vark| |antiCommutator| |rightDivide| - |root| |polCase| |lazyPseudoRemainder| |cscIfCan| |gbasis| |cSec| - |upperCase?| |primitive?| |badValues| |imaginary| |makeFR| - |genericLeftDiscriminant| |vectorise| |irreducible?| - |showIntensityFunctions| |associatedEquations| |maximumExponent| - |diag| |opeval| |lambda| |wrregime| |bernoulli| |seriesSolve| |c06fuf| - |ldf2vmf| |rank| |stiffnessAndStabilityOfODEIF| |pdct| |lambert| - |rightScalarTimes!| |truncate| |e04ycf| |f04maf| |npcoef| |isOpen?| - |addPoint2| |log| |mainVariable| |parent| |removeZeroes| - |partialNumerators| |expandLog| |iiacsch| |s17agf| |fortranLogical| - 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|jacobiIdentity?| |Ci| |fixedPoints| |bounds| |zero| |d01asf| - |getBadValues| |domainTemplate| |reverse| |inrootof| |normalized?| - |graphImage| |red| |permutation| |currentSubProgram| |imagj| - |enumerate| |one?| |writeUInt8!| |fortranCharacter| |elColumn2!| |li| - |pow| LODO2FUN |viewZoomDefault| |nthExponent| |OMputError| - |monicDecomposeIfCan| |shrinkable| |And| |s21bcf| |constantOperator| - |OMputObject| |pointPlot| |read!| |unknown| |dilog| - |fractionFreeGauss!| |deriv| |UpTriBddDenomInv| |sincos| |Or| - |moreAlgebraic?| |ScanRoman| |linearDependenceOverZ| - |solveLinearPolynomialEquationByFractions| |complexElementary| - |minPol| |lyndonIfCan| |sin| |ramifiedAtInfinity?| |relationsIdeal| - |BumInSepFFE| |modulus| |Not| RF2UTS - |removeSuperfluousQuasiComponents| |iitan| |power!| - |radicalEigenvectors| |gderiv| |cos| - |generalizedContinuumHypothesisAssumed| |tableau| |flagFactor| - |nextsubResultant2| |packageCall| |int| |makeViewport2D| - |removeIrreducibleRedundantFactors| |eyeDistance| |computeInt| - |infieldint| |tan| |host| |linear?| |e02akf| |calcRanges| |clip| - |makeCos| |elseBranch| |distFact| |cot| |normalForm| - |chineseRemainder| |lighting| |subNodeOf?| |triangular?| - |rightMinimalPolynomial| |jacobi| |extendedEuclidean| |nthFlag| |sec| - |functionIsContinuousAtEndPoints| |sumOfSquares| |coth2tanh| |algint| - |palgLODE0| |localAbs| |mainVariables| |rightRemainder| |coefficient| - |csc| |leftReducedSystem| |rischNormalize| |infinite?| |cLog| - |multMonom| |leadingBasisTerm| |newTypeLists| |asin| |asimpson| |test| - |status| |hostByteOrder| |operation| |hostPlatform| |s21bdf| |remove| - |beauzamyBound| |getOperator| |rightDiscriminant| |tubeRadiusDefault| - |acos| |setrest!| |safeFloor| |indiceSubResultant| |OMencodingXML| - |curveColorPalette| |Nul| |pushdown| |arbitrary| |e01saf| |atan| - |splitConstant| |sn| |makeSeries| |graphState| |OMread| |parts| - |credPol| |last| |identityMatrix| |sech2cosh| |scopes| |nthr| |acot| - |iicsch| |plus!| |assoc| |roughUnitIdeal?| |normalDeriv| - |subresultantSequence| |quote| |diagonal?| |asec| |degreePartition| - |explicitlyEmpty?| |qinterval| |condition| |tower| |testModulus| - |elem?| |contract| |reducedSystem| |noncommutativeJordanAlgebra?| - |genericRightTrace| |acsc| |restorePrecision| |singularitiesOf| - |startTableGcd!| |axes| |imagJ| |fill!| |substitute| |prefix| - |semiLastSubResultantEuclidean| |fmecg| |sinh| |leftQuotient| - |readBytes!| |e02zaf| |entries| |unitCanonical| - |rewriteSetByReducingWithParticularGenerators| |besselK| |cosh| - |useSingleFactorBound| |solveLinearPolynomialEquation| - |definingEquations| |setMinPoints| |solve1| |An| - |firstUncouplingMatrix| |basisOfLeftNucleus| |f04mcf| |obj| |tanh| - |palgint| |eq| |fortranCarriageReturn| |polyred| |minPoints| - |leftFactorIfCan| |LyndonCoordinates| |cschIfCan| |elliptic| - |leftUnit| |cache| |coth| |clearFortranOutputStack| |iter| |transform| - |commutator| |complexNumeric| |viewThetaDefault| - |rationalApproximation| |fTable| |rightTraceMatrix| |d01aqf| - |complexLimit| |torsionIfCan| |sech| |monicLeftDivide| - |basisOfCommutingElements| |dimensionsOf| |style| |modTree| - |OMputEndApp| |s13aaf| |mainPrimitivePart| |fortranCompilerName| - |startTableInvSet!| |csch| |bit?| |maxPoints3D| |schema| - |pmComplexintegrate| |makeprod| |unvectorise| |cot2tan| |outputForm| - |printTypes| |asinh| |setErrorBound| |constantToUnaryFunction| - |simplifyExp| |perfectSquare?| |superHeight| - |setLegalFortranSourceExtensions| |tryFunctionalDecomposition| - |leftRemainder| |semiDiscriminantEuclidean| |exponents| |KrullNumber| - |acosh| |multiple?| |voidMode| |torsion?| |SturmHabichtCoefficients| - |minimumDegree| |loopPoints| |minColIndex| |sh| |d02raf| - |coerceListOfPairs| |elaboration| |ksec| |f02adf| |innerSolve| - |normDeriv2| |commaSeparate| |graphStates| |explicitlyFinite?| - |transcendenceDegree| |invmultisect| |exp| |rightZero| |topPredicate| - |lintgcd| |modularFactor| |tableForDiscreteLogarithm| |deepCopy| - |readInt32!| |lastSubResultant| |factorFraction| |scalarTypeOf| - |exptMod| |cos2sec| |map| |rowEchelonLocal| |solid?| - |antiCommutative?| |createPrimitiveElement| |lazyResidueClass| - |trace2PowMod| |cosSinInfo| |chainSubResultants| |bat1| UP2UTS |table| - |generator| |mkPrim| |anfactor| |factorSFBRlcUnit| |cSech| |cAcos| - |nil| |leastAffineMultiple| |cCoth| |dioSolve| |RemainderList| - |alphanumeric| |new| |wreath| |member?| |cycleEntry| |charClass| - |maxColIndex| |compile| |resultantReduitEuclidean| |bandedHessian| - |trapezoidalo| |resultantEuclidean| |rationalPower| |clearTheIFTable| - |algebraicVariables| |nonSingularModel| |viewSizeDefault| - |plenaryPower| |normalElement| |radicalSolve| |completeSmith| - |uniform01| |acoshIfCan| |allRootsOf| |unaryFunction| |abs| - |approximate| |stop| |isAnd| |modularGcd| |returnTypeOf| |droot| - |convert| |possiblyInfinite?| |padecf| |isEquiv| |prolateSpheroidal| - |tanh2trigh| |complex| |insert!| |d01fcf| |coshIfCan| |writeInt8!| - |getCurve| |hex| |possiblyNewVariety?| |findConstructor| |critMonD1| - |iroot| |useEisensteinCriterion?| |showClipRegion| - |integralCoordinates| |rombergo| |rightExtendedGcd| |contours| |ideal| - |c06frf| |failed| |asinhIfCan| |identification| |hspace| |cExp| - |reducedDiscriminant| |iisech| |splitDenominator| |bernoulliB| - |mathieu23| |distdfact| |even?| |leaf?| |areEquivalent?| - |karatsubaOnce| |topFortranOutputStack| |ScanArabic| |setRealSteps| - |lfextendedint| |OMgetEndAtp| |incrementKthElement| |initTable!| - |readable?| |incr| |bezoutResultant| |callForm?| |setMinPoints3D| - |leftUnits| |univcase| |associates?| |nil?| |drawCurves| |copies| |hi| - |selectNonFiniteRoutines| |conical| |readUInt8!| |getIdentifier| - |generators| |rk4a| |log2| |quadraticNorm| |gcdPrimitive| |left| - |cCsc| |f02abf| |invertibleSet| |supersub| |univariatePolynomial| - |romberg| |addMatchRestricted| |dihedralGroup| |chebyshevT| |right| - |setStatus!| |mapCoef| |integralMatrix| |lieAdmissible?| |OMreceive| - |integralBasisAtInfinity| |countable?| |abelianGroup| |OMlistSymbols| - |generalLambert| |removeRoughlyRedundantFactorsInPol| |modifyPoint| - |countRealRoots| |medialSet| |internalSubQuasiComponent?| - |getButtonValue| |dihedral| |quadratic| |morphism| |setFormula!| - |singleFactorBound| |groebner?| |matrixGcd| |qelt| |zeroOf| |iilog| - |HermiteIntegrate| |expressIdealMember| |qsetelt| |deepestInitial| - |space| |antisymmetricTensors| |cPower| |subset?| |initial| - |rowEchelon| |LowTriBddDenomInv| |diagonals| |OMputEndError| - |leftZero| |cfirst| |harmonic| |pade| |xRange| |midpoint| |rootSplit| - |next| |leftPower| |isPower| |currentCategoryFrame| |key| |btwFact| - |critB| |cycle| |signatureAst| |yRange| |bivariatePolynomials| |push| - |irCtor| |recip| |positiveRemainder| |tracePowMod| |OMgetFloat| - |edf2efi| |explogs2trigs| |zRange| |poisson| |summation| |bigEndian| - |viewDeltaXDefault| |minimumExponent| |filename| |sPol| |findCycle| - |map!| |diagonalMatrix| |printInfo!| |solveLinearlyOverQ| |lazyPrem| - |setprevious!| |firstNumer| |simpleBounds?| |clipWithRanges| - |constantCoefficientRicDE| |qsetelt!| |realZeros| |linearlyDependent?| - |closedCurve| |repeatUntilLoop| |polynomialZeros| |permanent| - |forLoop| |parse| |mathieu22| |rspace| |support| |getMeasure| |tab| - |functionIsOscillatory| |regularRepresentation| |code| |Frobenius| - |minPoly| |generate| |primitivePart| |rightTrace| - |SturmHabichtSequence| |sayLength| |rootOfIrreduciblePoly| |bumptab| - |knownInfBasis| |setLabelValue| |randnum| |primaryDecomp| |linSolve| - |listOfLists| |factorList| |hessian| |s19aaf| |f04arf| |s21bbf| - |algebraicSort| |incrementBy| |connect| |iidsum| |squareFreeFactors| - |horizConcat| |aspFilename| |numericalIntegration| |edf2fi| - |negative?| |fractRagits| |collectUpper| |legendreP| |dequeue!| - |cycleRagits| |ref| |acsch| |iitanh| |rootKerSimp| |distance| |rename| - |rightCharacteristicPolynomial| |mathieu12| |lfinfieldint| |printInfo| - |readUInt32!| |halfExtendedSubResultantGcd1| |e02agf| |moduleSum| - |squareFreePrim| |writeBytes!| |getExplanations| |associator| |trunc| - |matrixDimensions| |hasPredicate?| |nullity| |evenInfiniteProduct| - |stronglyReduce| |doubleComplex?| |string?| |tubeRadius| - |cyclicEntries| |invertIfCan| |Hausdorff| |eigenvectors| |e02bbf| - |operators| |options| |colorFunction| |denominators| |headReduced?| - |iisec| |bits| |tail| |hermite| |dom| |duplicates| |genericLeftNorm| - |orbits| |pToDmp| |integralDerivationMatrix| - |exprHasWeightCosWXorSinWX| |sturmVariationsOf| |radPoly| |polyPart| - |arg1| |createMultiplicationMatrix| |entry| |brillhartTrials| - |hexDigit?| |resetVariableOrder| |binarySearchTree| - |integralMatrixAtInfinity| |nil| |infinite| |arbitraryExponent| - |approximate| |complex| |shallowMutable| |canonical| |noetherian| - |central| |partiallyOrderedSet| |arbitraryPrecision| - |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| - |additiveValuation| |unitsKnown| |canonicalUnitNormal| - |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| - |commutative|)
\ No newline at end of file + |Record| |Union| |commutative?| |numberOfDivisors| |ScanRoman| + |OMputEndBind| |arg2| |nilFactor| |compound?| |string| |mindeg| + |c06frf| |subscriptedVariables| |complexExpand| |e01sef| |OMgetAttr| + |linearDependenceOverZ| |iomode| |Si| |zeroMatrix| |say| |asinhIfCan| + |absolutelyIrreducible?| |nextNormalPrimitivePoly| |c05adf| + |solveLinearPolynomialEquationByFractions| |polygon| |conditions| + |OMputEndAttr| |leftExtendedGcd| |lazyIntegrate| |identification| + |basisOfCentroid| |f01maf| |zero?| |c05nbf| |complexElementary| + |title| |match| |primeFrobenius| |OMgetInteger| |bitTruth| |reset| + |hspace| |approximants| |innerEigenvectors| |removeCoshSq| |minPol| + |presub| |sum| |s20acf| |less?| |cExp| |inc| |zerosOf| |lyndonIfCan| + |recoverAfterFail| |e01bgf| |pop!| |rewriteIdealWithHeadRemainder| + |stoseInvertible?sqfreg| |write| |unitsColorDefault| + |reducedDiscriminant| |alphanumeric?| |ramifiedAtInfinity?| + |exponential| |primlimintfrac| |OMcloseConn| |e| |rotatez| |save| + |minimalPolynomial| |ScanFloatIgnoreSpacesIfCan| |iisech| |lp| |df2mf| + |powerAssociative?| |numberOfVariables| |relationsIdeal| |s18acf| + |setColumn!| |iisqrt3| |readInt8!| |nothing| |splitDenominator| + |overlap| |bivariate?| |BumInSepFFE| |mapExponents| + |primPartElseUnitCanonical!| |besselY| |bernoulliB| |exponentialOrder| + |gcdcofact| |f07adf| |errorKind| |modulus| |getRef| |top| |c06ecf| + |intersect| |mathieu23| |removeRedundantFactorsInPols| |column| |ord| + |pastel| RF2UTS |complexEigenvectors| |continue| |atrapezoidal| + |sample| |distdfact| |bandedJacobian| |indicialEquationAtInfinity| + |putColorInfo| |removeSuperfluousQuasiComponents| |internalDecompose| + |iiGamma| |even?| |drawComplex| |viewport3D| |iitan| + |alternatingGroup| |writeLine!| |traverse| |outputFloating| + |transcendent?| |leaf?| ** |hash| |nthFractionalTerm| |max| |power!| + |mix| |chebyshevU| |validExponential| |quotedOperators| + |particularSolution| |areEquivalent?| |count| |qfactor| + |selectPDERoutines| |localReal?| |monomRDE| |radicalEigenvectors| + |plot| |logIfCan| |latex| |karatsubaOnce| |lazy?| |rotate| + |linearAssociatedExp| |s18def| |interpolate| |topFortranOutputStack| + |rightRegularRepresentation| |upperBound| |getProperties| + |lflimitedint| |constant| |OMputAtp| |iifact| |withPredicates| + |ScanArabic| |OMsupportsSymbol?| |minRowIndex| |s20adf| |coleman| + |f02akf| |useEisensteinCriterion| |factorsOfDegree| |mantissa| + |setRealSteps| |bothWays| |OMputInteger| |wholeRadix| |karatsuba| + |complexForm| |generalizedEigenvector| |disjunction| |setProperties| + |derivationCoordinates| |stoseIntegralLastSubResultant| |byteBuffer| + |zCoord| |freeOf?| |nextLatticePermutation| |csubst| |sh| + |modularGcdPrimitive| |realRoots| |pr2dmp| |OMputString| + |numberOfComponents| |numFunEvals| |iiexp| |flexible?| |d02raf| + |minGbasis| |unrankImproperPartitions1| |redPol| |whitePoint| + |solveRetract| |sequence| |augment| |coerceListOfPairs| |iprint| + |fractionPart| |Vectorise| |subHeight| |iicoth| |att2Result| |generic| + |elaboration| |rationalPoints| |e02gaf| |principalAncestors| + |cartesian| |associator| |besselJ| |c06ekf| |s15adf| |ksec| |f07fdf| + |integral| |rowEch| |radicalEigenvalues| |trunc| |exprex| + |symbolIfCan| |mainForm| |f02adf| |s17ajf| |discreteLog| |cAcosh| + |ran| |structuralConstants| |matrixDimensions| |e02daf| |besselI| + |viewpoint| |innerSolve| |rightPower| |categories| |e02ahf| + |dimensions| |s17aff| |cubic| |hasPredicate?| |numer| |reindex| + |retractIfCan| |primextintfrac| |irreducibleFactors| |normDeriv2| + |f04jgf| |antisymmetric?| |encodingDirectory| |is?| |nullity| |denom| + |prindINFO| |mulmod| |irDef| |commaSeparate| |indicialEquations| + |integralBasis| |writable?| |removeSquaresIfCan| |evenInfiniteProduct| + |saturate| |swap!| |green| |graphStates| |changeName| + |associatorDependence| |singRicDE| |lexico| |stronglyReduce| |pi| + |combineFeatureCompatibility| |triangularSystems| |untab| + |explicitlyFinite?| |leftTraceMatrix| |constantIfCan| |predicates| + |rur| |doubleComplex?| |infinity| |mapExpon| |collectUnder| |setTex!| + |transcendenceDegree| |concat| |step| |rootsOf| |OMencodingSGML| + |digit| |c06ebf| |string?| |numberOfIrreduciblePoly| + |listYoungTableaus| |readIfCan!| |invmultisect| |compBound| + |selectOrPolynomials| |OMgetAtp| |nodeOf?| |tubeRadius| + |mapMatrixIfCan| |constDsolve| |mainCoefficients| |rightZero| + |setelt!| |f02fjf| |leadingExponent| |kovacic| |kernel| + |cyclicEntries| |optpair| |hyperelliptic| |subspace| |topPredicate| + |formula| |makeUnit| |radicalSimplify| |routines| |invertIfCan| + |degree| |list| |ptree| |exportedOperators| |OMParseError?| |dmpToP| + |lintgcd| |lhs| |completeHensel| |lyndon| |antiAssociative?| + |halfExtendedResultant2| |draw| |Hausdorff| + |functionIsFracPolynomial?| |firstDenom| |rotate!| |clearCache| + |modularFactor| |rhs| |symmetricSquare| |f07fef| + |quasiMonicPolynomials| |mainMonomials| |eigenvectors| + |leftCharacteristicPolynomial| |curveColor| |enterPointData| + |tableForDiscreteLogarithm| |OMputBind| |mapdiv| |iidprod| |isExpt| + |e02bbf| |whatInfinity| |write!| |f01bsf| |deepCopy| |currentEnv| + |nrows| |factorSquareFreePolynomial| |extractIfCan| |alternative?| + |readLine!| |operators| |s13adf| |divergence| |quoted?| |readInt32!| + |ncols| |bipolarCylindrical| |squareFreePolynomial| |quotientByP| + |blue| |makeObject| |colorFunction| |getVariableOrder| |rischDEsys| + |discriminant| |lastSubResultant| |showArrayValues| + |primPartElseUnitCanonical| |external?| |pushuconst| |denominators| + |coef| |normInvertible?| |cyclic| |coercePreimagesImages| + |factorFraction| |nextSublist| |countRealRootsMultiple| |isOp| |open?| + |headReduced?| |nullSpace| |dequeue| |aQuadratic| |scalarTypeOf| + |OMputEndObject| |equiv| |basisOfNucleus| |monomials| |iisec| + |stFunc1| |curryRight| |superscript| |exptMod| |paraboloidal| + |exteriorDifferential| |reduceBasisAtInfinity| |curry| |bits| |iiasin| + |close!| |dominantTerm| |cos2sec| |kind| |stoseInvertibleSetreg| + |nlde| |prod| |unitVector| |hermite| |bfEntry| + |unprotectedRemoveRedundantFactors| |setvalue!| |rowEchelonLocal| |op| + |makeYoungTableau| |cycleLength| |cardinality| |iExquo| |duplicates| + |kernels| |normalDenom| |shiftRight| |ode1| |solid?| |makeResult| + |graeffe| |birth| |semiSubResultantGcdEuclidean1| |argumentList!| + |genericLeftNorm| |dAndcExp| |operator| |simpsono| |hconcat| + |antiCommutative?| |B1solve| |basisOfMiddleNucleus| |wronskianMatrix| + |iiacosh| |weighted| |orbits| SEGMENT |palglimint| |arrayStack| + |purelyAlgebraic?| |createPrimitiveElement| |coerceL| + |realEigenvalues| |leftGcd| |upperCase!| |pToDmp| |sort| + |createPrimitivePoly| |lquo| |univariate| |fintegrate| + |lazyResidueClass| |rationalPoint?| |algebraicCoefficients?| |submod| + |d02ejf| |integralDerivationMatrix| |useNagFunctions| |dec| + |increment| |controlPanel| |trace2PowMod| 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|e02dff| |leastMonomial| |groebnerIdeal| |fmecg| + |fortranDoubleComplex| |determinant| |writeByte!| |totalDegree| + |bigEndian| |primintegrate| |consnewpol| |meshPar2Var| |cotIfCan| + |trigs2explogs| |leftQuotient| |localUnquote| |OMgetError| + |fixedPointExquo| |elliptic?| |keys| |viewDeltaXDefault| |eigenvalues| + |optAttributes| |selectFiniteRoutines| |genus| |readBytes!| |gethi| + |OMreadStr| |mappingMode| |totalLex| |minimumExponent| + |lookupFunction| |messagePrint| |heapSort| |e02zaf| |getZechTable| + |internalIntegrate| |f02bbf| |totalGroebner| |sPol| |index| + |semicolonSeparate| |createRandomElement| |aQuartic| |clearTheFTable| + |entries| |cTanh| |s14aaf| |clipBoolean| |coHeight| |findCycle| + |setOrder| |leadingCoefficientRicDE| |point?| |sorted?| + |unitCanonical| |mergeFactors| |complexNumericIfCan| |perfectSqrt| + |denomLODE| |diagonalMatrix| |basisOfRightAnnihilator| + |startPolynomial| |mainValue| |numberOfFactors| + |rewriteSetByReducingWithParticularGenerators| |Lazard| |addPointLast| + |pair| |printInfo!| |basisOfCenter| |tree| |open| |quadratic?| + |expandPower| |ramified?| |besselK| |convergents| |exprToGenUPS| + |bright| |weakBiRank| |henselFact| |solveLinearlyOverQ| |directSum| + |resultantnaif| |squareFree| |useSingleFactorBound| |Ei| |variable?| + |var2StepsDefault| |stirling2| |internalInfRittWu?| |lazyPrem| + |wholePart| |separant| |iiatanh| |swapRows!| + |solveLinearPolynomialEquation| |eof?| |eval| |maxrank| |integerIfCan| + |subResultantGcd| |setprevious!| |infinityNorm| |assign| + |definingEquations| |mapUp!| |collectQuasiMonic| + |inverseIntegralMatrix| |divide| |firstNumer| |unknownEndian| + |operations| |extendedResultant| |setMaxPoints3D| |dualSignature| + |setMinPoints| |schwerpunkt| |patternMatchTimes| |factorset| + |tensorProduct| |simpleBounds?| |omError| |subResultantsChain| + |LagrangeInterpolation| |solve1| |interpret| |OMconnInDevice| |weight| + |error| |light| |iCompose| |autoReduced?| |clipWithRanges| + |orthonormalBasis| |s17def| |lowerCase| |An| |OMputAttr| |isTimes| + |polygon?| |constantCoefficientRicDE| |iiasec| |ip4Address| + |SturmHabichtMultiple| |firstUncouplingMatrix| |real?| |optimize| + |push!| |monicCompleteDecompose| |sizeMultiplication| |mesh?| + |integralRepresents| |realZeros| |unitNormalize| |precision| + |function| |pushNewContour| |basisOfLeftNucleus| |df2st| |buildSyntax| + |divideExponents| |conjugate| UTS2UP |linearlyDependent?| |leftFactor| + |getConstant| |OMgetObject| |f04mcf| |fractRadix| |polarCoordinates| + |numberOfOperations| |setIntersection| |resetBadValues| |width| + |closedCurve| |cyclicParents| |sumOfKthPowerDivisors| |s17dlf| + |d01anf| |e02bcf| |rules| |argscript| |laurentIfCan| |double| + |repeatUntilLoop| |edf2ef| |e02bdf| |changeMeasure| |fracPart| + |gderiv| |f02awf| |iterationVar| |setAttributeButtonStep| |c06gsf| + |polynomialZeros| |reduceByQuasiMonic| |putProperty| |odd?| + |generalizedContinuumHypothesisAssumed| |monomialIntegrate| |badNum| + |divideIfCan| |presuper| |front| |permanent| |partialDenominators| + |bivariateSLPEBR| |collect| |tableau| |readLineIfCan!| |var1Steps| + |coordinates| |physicalLength!| |irVar| |FormatRoman| |closed| + |listBranches| |flagFactor| |conjunction| |checkPrecision| |mr| + |fi2df| |tubePointsDefault| |region| |viewDeltaYDefault| + |lfextendedint| |nullary| |increasePrecision| |gramschmidt| + |nextsubResultant2| |stopTable!| |factor1| |asinIfCan| + |doublyTransitive?| |homogeneous?| |OMgetEndAtp| |outputAsTex| + |integralLastSubResultant| |stoseInvertible?| |tanQ| |packageCall| + |subst| |rem| |createNormalPrimitivePoly| |radicalRoots| |var2Steps| + |xCoord| |incrementKthElement| |taylorRep| |setButtonValue| + |clearTable!| |mvar| |makeViewport2D| |prinb| |quo| + |complexEigenvalues| |SturmHabicht| |initTable!| |showTheIFTable| + |declare!| |varList| |initializeGroupForWordProblem| |LiePoly| + |property| |complex?| |removeIrreducibleRedundantFactors| |c06eaf| + |before?| |selectIntegrationRoutines| + |purelyAlgebraicLeadingMonomial?| |readable?| |lcm| |mainVariable?| + |inRadical?| |curryLeft| |radix| |eyeDistance| |delete| |div| |s17ahf| + |quasiComponent| |limitedIntegrate| |cAtan| |bezoutResultant| + |unparse| |d01bbf| |setOfMinN| |computeInt| |padicallyExpand| |exquo| + |normal?| |rdHack1| |reverse!| |se2rfi| |callForm?| |any| |dn| + |double?| |append| |symFunc| |infieldint| |belong?| ~= |littleEndian| + |simpson| |bracket| |symmetricGroup| |setMinPoints3D| |alphabetic| + |mapBivariate| |rowEchLocal| |gcd| |nextColeman| |host| |twist| + |objects| |#| |e02bef| |aCubic| |solid| |repSq| |leftUnits| + |splitSquarefree| |s19adf| |vspace| |false| |hitherPlane| |imagE| + |linear?| |base| ~ |setStatus| |outputAsScript| |sdf2lst| + |removeRoughlyRedundantFactorsInPols| |univcase| |components| + |rightOne| |var1StepsDefault| |e02akf| |supDimElseRittWu?| |ravel| + |factorials| |algebraicDecompose| |exprHasAlgebraicWeight| |airyAi| + |associates?| |segment| |empty?| |cyclotomicDecomposition| |logical?| + |genericRightNorm| |calcRanges| |init| |multiplyExponents| + |quasiRegular?| |complexSolve| |generalPosition| |reshape| |nil?| + |lowerCase?| |bitCoef| |mathieu11| |clip| |e01sff| |/\\| |OMwrite| + |stFunc2| |logpart| |usingTable?| |drawCurves| |normalizedAssociate| + |genericRightTraceForm| |graphs| |bottom!| |makeCos| |\\/| + |fortranLinkerArgs| |infix| |fullPartialFraction| + |stoseInvertible?reg| |copies| |apply| |coerce| |cycleElt| + |leadingIndex| |contains?| |elseBranch| |setScreenResolution3D| + |imagI| |mainSquareFreePart| |checkForZero| |Gamma| + |selectNonFiniteRoutines| |first| |construct| |computeCycleEntry| + |rightMult| |getPickedPoints| |reciprocalPolynomial| |distFact| + |attributeData| |extractSplittingLeaf| |OMconnOutDevice| |remainder| + |conical| |rest| |nullary?| |isConnected?| |lllp| |conjugates| + |normalForm| |readUInt8!| |d02bbf| |generalTwoFactor| |OMopenFile| + |getGraph| |plus| |update| |maxRowIndex| |fortranDouble| |f01rcf| + |bipolar| |chineseRemainder| |Aleph| |rootDirectory| |categoryMode| + |qroot| |getIdentifier| |pushucoef| |binaryTree| |unmakeSUP| |coerceP| + |lighting| |multiset| |largest| |rootNormalize| |neglist| |generators| + |showScalarValues| |infLex?| |typeLists| |subNodeOf?| |split| + |euclideanSize| |rightRankPolynomial| |insertTop!| |randomR| |rk4a| + |times| |pquo| |monicRightDivide| |sin2csc| |triangular?| + |toseInvertibleSet| |previous| |delta| |linkToFortran| |normal01| + |shallowExpand| |PollardSmallFactor| |log2| |iiacot| |typeForm| + |e01sbf| |hdmpToP| |rightMinimalPolynomial| |decomposeFunc| + |complementaryBasis| |direction| |box| |intPatternMatch| |ptFunc| + |quadraticNorm| |position| |patternVariable| + |createLowComplexityNormalBasis| |viewWriteDefault| |jacobi| + |varselect| |differentialVariables| |ScanFloatIgnoreSpaces| |rk4| + |enqueue!| |gcdPrimitive| |datalist| |lift| |leftRank| + |stoseLastSubResultant| |pleskenSplit| |eisensteinIrreducible?| + |extendedEuclidean| |atoms| |iipow| |cosIfCan| |jordanAdmissible?| + |Lazard2| |cCsc| |monom| |reduce| |newReduc| |extendedIntegrate| + |completeEchelonBasis| |lagrange| |nthFlag| |exponential1| |toroidal| + |dflist| |quickSort| |symmetricRemainder| |f02abf| |loadNativeModule| + |numberOfHues| |myDegree| |explicitEntries?| |modifyPointData| + |functionIsContinuousAtEndPoints| |selectSumOfSquaresRoutines| + |cyclicGroup| |unit| |transpose| |GospersMethod| |ricDsolve| + |invertibleSet| |divisorCascade| |exponent| |f04atf| |viewPhiDefault| + |equality| |sumOfSquares| |unexpand| |genericPosition| |OMmakeConn| + |sylvesterSequence| |setlast!| |supersub| |sin?| |hMonic| + |splitNodeOf!| |pol| |coth2tanh| |lambda| |OMgetEndAttr| + |OMgetEndBind| |cCot| |numberOfFractionalTerms| |univariatePolynomial| + |rank| |permutationGroup| |stirling1| |OMgetEndApp| |algint| + |weierstrass| |cylindrical| |cup| |realEigenvectors| |scan| |romberg| + |log| |repeating| |approxNthRoot| |isAtom| |raisePolynomial| + |palgLODE0| |d03edf| |pureLex| |linearMatrix| |putProperties| + |addMatchRestricted| |setelt| |flexibleArray| |lowerBound| |points| + |localAbs| |numberOfComposites| |secIfCan| |digamma| |dmp2rfi| + |screenResolution3D| |dihedralGroup| |zeroSquareMatrix| + |factorAndSplit| |branchPoint?| |cCos| |discriminantEuclidean| + |mainVariables| |noLinearFactor?| |groebner| |e04dgf| |midpoints| + |chebyshevT| |expintegrate| |rroot| |intensity| |rightRemainder| |lex| + |rootRadius| |linGenPos| |currentScope| |coefficients| |setStatus!| + |iflist2Result| |elRow1!| |mightHaveRoots| |tubePoints| |coefficient| + |reify| |zeroDim?| |divisors| |partitions| |mapCoef| + |nextPrimitiveNormalPoly| |binary| |charpol| |lazyPremWithDefault| + |leftReducedSystem| |patternMatch| |leftNorm| |scanOneDimSubspaces| + |asecIfCan| |viewWriteAvailable| |integralMatrix| |byte| |lists| + |algSplitSimple| |numberOfMonomials| |jacobian| |factorByRecursion| + |rischNormalize| |shallowCopy| |mapUnivariate| |order| |cAcsch| + |cycleTail| |lieAdmissible?| |binomial| |float?| |integers| + |infinite?| |diagonalProduct| |erf| |binaryFunction| |s18aff| |nodes| + |hdmpToDmp| |zero| |OMreceive| |getMatch| |delete!| |reverse| |janko2| + |extractIndex| |parseString| |cLog| |reverseLex| |sec2cos| + |semiResultantEuclidean1| |setref| |integralBasisAtInfinity| |moduloP| + |multMonom| |partition| |d02gaf| |setchildren!| |li| |quatern| + |subtractIfCan| |primes| |pair?| |rational| |And| |countable?| + |leadingBasisTerm| |monomialIntPoly| |returnType!| |sumOfDivisors| + |unknown| |dilog| |select!| |lieAlgebra?| |interReduce| + |karatsubaDivide| |Or| |abelianGroup| |readInt16!| |diagonal| + |multiEuclideanTree| |drawStyle| |exists?| |newTypeLists| |sin| + |bfKeys| |inverseIntegralMatrixAtInfinity| |principalIdeal| + |squareFreePart| |Not| |OMlistSymbols| |child?| |createNormalElement| + |inputBinaryFile| |cAsech| |asimpson| |cos| |iicosh| |lifting| + |distribute| |bitLength| |generalLambert| |listConjugateBases| |int| + |principal?| |OMlistCDs| |elRow2!| |status| |tan| |mainKernel| + |resize| |removeRoughlyRedundantFactorsInPol| |ParCond| + |factorsOfCyclicGroupSize| |ODESolve| |hostByteOrder| |taylorIfCan| + |cot| |leadingSupport| |nor| |in?| |modifyPoint| + |stoseInvertibleSetsqfreg| |minset| |bubbleSort!| |multinomial| + |hostPlatform| |sec| |s19abf| |expextendedint| |just| |countRealRoots| + |bumprow| |coordinate| |mindegTerm| |s21bdf| |triangSolve| |csc| + |evenlambert| |nonLinearPart| |divisor| |medialSet| |sup| + |beauzamyBound| |pack!| |asin| |colorDef| |test| |elements| |extend| + |operation| |internalSubQuasiComponent?| |remove| |head| + |roughEqualIdeals?| |isAbsolutelyIrreducible?| |rdregime| + |getOperator| |acos| |froot| |block| |localIntegralBasis| + |getButtonValue| |pushdterm| |decrease| |putGraph| |numerators| + |rightDiscriminant| |atan| |goodnessOfFit| |sn| |call| |viewport2D| + |dihedral| |parts| FG2F |last| |irreducibleFactor| |key?| + |nextPartition| |tubeRadiusDefault| |acot| |element?| |quadratic| + |assoc| |tValues| |cRationalPower| |measure| F2FG |setrest!| |asec| + |eigenvector| |jokerMode| |OMsetEncoding| |condition| |morphism| + |tower| |powerSum| |iiperm| |OMencodingUnknown| |isMult| |safeFloor| + |acsc| |appendPoint| |generateIrredPoly| |regime| |setFormula!| + |cyclotomic| |rightNorm| |listOfMonoms| |compiledFunction| |prefix| + |indiceSubResultant| |sinh| |hasoln| |s17akf| |lazyGintegrate| + |singleFactorBound| |c06fqf| |floor| |realSolve| |cosh| + |wordInStrongGenerators| |eulerE| |primitivePart!| |groebner?| + |redpps| |jordanAlgebra?| |universe| |basisOfLeftAnnihilator| + |selectfirst| |obj| |tanh| |leftLcm| |eq| |computePowers| |geometric| + |matrixGcd| |pointSizeDefault| |lSpaceBasis| |content| |adaptive| + |permutations| |cache| |coth| |expenseOfEvaluationIF| |iter| + |normalise| |pseudoQuotient| |zeroOf| |complexNumeric| |ipow| + |positiveSolve| |groebgen| |s14abf| |printStatement| |limitPlus| + |sech| |setValue!| |evaluate| |euler| |nextsousResultant2| |spherical| + |measure2Result| |fortranReal| |e02aef| |indicialEquation| |low| + |csch| |OMputSymbol| |extendedSubResultantGcd| |powern| + |algebraicVariables| |imagi| |module| |list?| |addmod| + |viewPosDefault| |asinh| |OMUnknownSymbol?| |zeroVector| |listLoops| + |nonSingularModel| |univariatePolynomials| |critM| |retractable?| + |compdegd| |orbit| |jacobiIdentity?| |bytes| |acosh| + |hasTopPredicate?| |setright!| |randomLC| |viewSizeDefault| + |extractProperty| |rootOf| |squareFreeLexTriangular| |denominator| + |Ci| |paren| |addiag| |genericRightMinimalPolynomial| |blankSeparate| + |plenaryPower| |eulerPhi| |reflect| |seriesToOutputForm| |fixedPoints| + |userOrdered?| |generalSqFr| |exp| |decreasePrecision| |algebraicOf| + |normalElement| |strongGenerators| |interval| |relativeApprox| + |integerBound| |bounds| |f2st| |signAround| |OMgetBind| |radicalSolve| + |map| |laguerre| |useSingleFactorBound?| |setAdaptive3D| + |leftAlternative?| |d01asf| |linearPart| |companionBlocks| + |numberOfCycles| |mirror| |completeSmith| |table| |generator| |iiabs| + |leftRecip| |invertible?| |getBadValues| |smith| |nil| |getOrder| + |rewriteIdealWithQuasiMonicGenerators| |central?| |lowerPolynomial| + |uniform01| |new| |elementary| |f02bjf| |shufflein| |reducedForm| + |domainTemplate| |escape| |removeDuplicates!| |compile| + |continuedFraction| |acoshIfCan| |coerceImages| |pomopo!| + |createGenericMatrix| |inrootof| |genericLeftTrace| + |internalSubPolSet?| |leftDiscriminant| |scripted?| |allRootsOf| + |heap| |headRemainder| |trivialIdeal?| |lazyEvaluate| |normalized?| + |approximate| |stop| |normFactors| |setEpilogue!| |sinh2csch| + |unaryFunction| |convert| |maxPoints| + |semiDegreeSubResultantEuclidean| |color| |graphImage| + |constantKernel| |complex| |typeList| |normalizeAtInfinity| |legendre| + |abs| |makeop| |padicFraction| |trim| |e01bff| |red| |derivative| + |lookup| |cCosh| |isAnd| |entry?| |option?| |chiSquare| |permutation| + |intermediateResultsIF| |failed| |OMunhandledSymbol| |dfRange| + |primintfldpoly| |modularGcd| |adjoint| |groebSolve| + |commutativeEquality| |removeRedundantFactors| |currentSubProgram| + |inverse| |fixPredicate| |part?| |returnTypeOf| |LazardQuotient2| + |oblateSpheroidal| |e04naf| |imagj| |roughBasicSet| |LyndonWordsList1| + |innerint| |symmetricPower| |droot| |incr| |newLine| |palginfieldint| + |irreducibleRepresentation| |rischDE| |enumerate| |leftExactQuotient| + |d01gaf| |solve| |possiblyInfinite?| |hi| |mapSolve| + |genericLeftMinimalPolynomial| |newSubProgram| |one?| + |prepareSubResAlgo| |yCoord| |exprHasLogarithmicWeights| + |pascalTriangle| |padecf| |left| |nary?| |genericLeftTraceForm| + |infiniteProduct| |writeUInt8!| |initials| |mathieu24| |socf2socdf| + |addPoint| |isEquiv| |right| |oddintegers| |setImagSteps| + |lexGroebner| |fortranCharacter| |leadingIdeal| |showRegion| + |rightRank| |nthRoot| |prolateSpheroidal| |stoseSquareFreePart| + |showFortranOutputStack| |expIfCan| |elColumn2!| |children| + |outlineRender| |leftScalarTimes!| |terms| |tanh2trigh| |eq?| + |overlabel| |bezoutMatrix| |numberOfChildren| |pow| |qelt| + |pointColor| |s17dgf| |adaptive3D?| |insert!| |qsetelt| |insertMatch| + |printStats!| |extendIfCan| |OMputApp| LODO2FUN |initial| |complement| + |iiacsc| |queue| |d01fcf| |basisOfLeftNucloid| |mainMonomial| + |rightRecip| |f02aef| |xRange| |viewZoomDefault| |next| + |makeFloatFunction| |e02dcf| |roughBase?| |coshIfCan| |key| + |nthExponent| |clipSurface| |shade| |mapmult| |algDsolve| |yRange| + |positive?| |logGamma| |laplacian| |writeInt8!| |rotatex| + |shanksDiscLogAlgorithm| |realElementary| |rightGcd| |OMputError| + |zRange| |mkAnswer| |extendedint| |algebraic?| |getCurve| |filename| + |map!| |xn| |OMgetType| |showTheSymbolTable| |imagK| + |monicDecomposeIfCan| |lazyIrreducibleFactors| |character?| |high| + |hex| |qsetelt!| |s18aef| |s17acf| |fortranTypeOf| |solveid| + |shrinkable| |crushedSet| |divideIfCan!| |symmetric?| + |possiblyNewVariety?| |parse| |zeroSetSplit| |iicsc| |magnitude| + |s21bcf| |enterInCache| |code| |overset?| |makeEq| |e04ucf| + |findConstructor| |generate| |getCode| |identity| |clikeUniv| + |constantOperator| |capacity| |back| |find| |any?| |critMonD1| + |pointColorPalette| |critT| |rightFactorCandidate| |c06fpf| + |OMputObject| |factorGroebnerBasis| |elaborateFile| |cycles| |iroot| + |incrementBy| |f01mcf| |setDifference| |OMputBVar| |pointPlot| |mdeg| + |f02xef| |unitNormal| |replace| |useEisensteinCriterion?| |accuracyIF| + |swapColumns!| |read!| |monic?| |acsch| |trigs| |clearDenominator| + |subResultantGcdEuclidean| |characteristic| |showClipRegion| + |acotIfCan| |rarrow| |printInfo| |maxrow| |fractionFreeGauss!| + |wordInGenerators| |nativeModuleExtension| |selectsecond| + |lastSubResultantElseSplit| |integralCoordinates| |chiSquare1| + |f01qef| |findBinding| |separateFactors| |deriv| |deref| + |nextSubsetGray| GF2FG |rombergo| |getMultiplicationTable| |OMserve| + |adaptive?| |norm| |UpTriBddDenomInv| |elaborate| |subTriSet?| + |OMgetEndError| |options| |rightExtendedGcd| |df2ef| |traceMatrix| + |boundOfCauchy| |tail| |exactQuotient!| |sincos| |dom| |showTheFTable| + |cyclicSubmodule| |monicModulo| |contours| |scale| |setClipValue| + |wordsForStrongGenerators| |moreAlgebraic?| |tube| |arg1| |setLength!| + |entry| |nand| |iiacoth| |ideal| |clipParametric| |categoryFrame| + |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) ((-234 $) -2755 (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1068)))) ((-232 |#2|) |has| |#2| (-1068)) ((-238) -12 (|has| |#2| (-238)) (|has| |#2| (-1068))) ((-237) -2755 (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1068)))) ((-272 |#2|) |has| |#2| (-1068)) ((-296 #1=(-576) |#2|) . T) ((-298 #1# |#2|) . T) ((-319 |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((-379) |has| |#2| (-379)) ((-388 |#2|) |has| |#2| (-1068)) ((-423 |#2|) |has| |#2| (-1119)) ((-501 |#2|) . T) ((-616 #1# |#2|) . 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T) ((-937) |has| |#1| (-568)) ((-1057 (-419 (-576))) -2755 (|has| |#1| (-1057 (-419 (-576)))) (-12 (|has| |#1| (-568)) (|has| |#1| (-1057 (-576))))) ((-1057 #1#) |has| |#1| (-568)) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 #2#) . T) ((-1057 #3#) |has| |#1| (-1068)) ((-1057 #4#) . T) ((-1057 |#1|) . T) ((-1070 #0#) |has| |#1| (-568)) ((-1070 |#1|) |has| |#1| (-174)) ((-1070 $) |has| |#1| (-568)) ((-1075 #0#) |has| |#1| (-568)) ((-1075 |#1|) |has| |#1| (-174)) ((-1075 $) |has| |#1| (-568)) ((-1068) -2755 (|has| |#1| (-1068)) (|has| |#1| (-568)) (|has| |#1| (-174)) (|has| |#1| (-148)) (|has| |#1| (-146))) ((-1077) -2755 (|has| |#1| (-1068)) (|has| |#1| (-568)) (|has| |#1| (-174)) (|has| |#1| (-148)) (|has| |#1| (-146))) ((-1131) -2755 (|has| |#1| (-1131)) (|has| |#1| (-1068)) (|has| |#1| (-568)) (|has| |#1| (-485)) (|has| |#1| (-174)) (|has| |#1| (-148)) (|has| |#1| (-146))) ((-1119) . T) ((-1236) . 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T) ((-23) . T) ((-47 |#1| #0=(-576)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-374)) ((-38 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-374)) ((-111 $ $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-628 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1195)) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-1195)))) ((-628 |#1|) |has| |#1| (-174)) ((-628 |#2|) . T) ((-628 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-625 (-874)) . T) ((-174) -2755 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-227)) -12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((-626 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((-626 (-548)) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-548)))) ((-626 (-905 (-390))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-905 (-390))))) ((-626 (-905 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-905 (-576))))) ((-234 $) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-232 |#2|) |has| |#1| (-374)) ((-238) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-237) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-272 |#2|) |has| |#1| (-374)) ((-248) |has| |#1| (-374)) ((-294) |has| |#1| (-38 (-419 (-576)))) ((-296 #0# |#1|) . T) ((-296 |#2| $) -12 (|has| |#1| (-374)) (|has| |#2| (-296 |#2| |#2|))) ((-296 $ $) |has| (-576) (-1131)) ((-300) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-374) |has| |#1| (-374)) ((-349 |#2|) |has| |#1| (-374)) ((-388 |#2|) |has| |#1| (-374)) ((-412 |#2|) |has| |#1| (-374)) ((-464) |has| |#1| (-374)) ((-505) |has| |#1| (-38 (-419 (-576)))) ((-526 (-1195) |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-526 (-1195) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-568) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-658 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 |#2|) |has| |#1| (-374)) ((-658 $) . T) ((-660 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-660 #3=(-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-660 |#1|) . T) ((-660 |#2|) |has| |#1| (-374)) ((-660 $) . T) ((-652 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 |#2|) |has| |#1| (-374)) ((-652 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-651 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-651 |#2|) |has| |#1| (-374)) ((-729 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 |#2|) |has| |#1| (-374)) ((-729 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-738) . T) ((-803) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-804) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-806) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-807) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-832) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-860) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-862) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-862))) (-12 (|has| |#1| (-374)) (|has| |#2| (-832)))) ((-909 $ #4=(-1195)) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1195)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195))))) ((-915 (-1195)) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195))))) ((-917 #4#) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1195)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195))))) ((-899 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-899 (-390)))) ((-899 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-899 (-576)))) ((-897 |#2|) |has| |#1| (-374)) ((-926) -12 (|has| |#1| (-374)) (|has| |#2| (-926))) ((-992 |#1| #0# (-1101)) . T) ((-937) |has| |#1| (-374)) ((-1011 |#2|) |has| |#1| (-374)) ((-1021) |has| |#1| (-38 (-419 (-576)))) ((-1041) -12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((-1057 (-419 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-576)))) ((-1057 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-576)))) ((-1057 #2#) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-1195)))) ((-1057 |#2|) . T) ((-1070 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1070 |#1|) . T) ((-1070 |#2|) |has| |#1| (-374)) ((-1070 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1075 |#1|) . T) ((-1075 |#2|) |has| |#1| (-374)) ((-1075 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) -12 (|has| |#1| (-374)) (|has| |#2| (-1171))) ((-1221) |has| |#1| (-38 (-419 (-576)))) ((-1224) |has| |#1| (-38 (-419 (-576)))) ((-1236) . T) ((-1240) |has| |#1| (-374)) ((-1246 |#1|) . T) ((-1264 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-783)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #1#) -2755 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1101)) . T) ((-628 |#1|) . T) ((-628 $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-625 (-874)) . T) ((-174) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-548)) -12 (|has| (-1101) (-626 (-548))) (|has| |#1| (-626 (-548)))) ((-626 (-905 (-390))) -12 (|has| (-1101) (-626 (-905 (-390)))) (|has| |#1| (-626 (-905 (-390))))) ((-626 (-905 (-576))) -12 (|has| (-1101) (-626 (-905 (-576)))) (|has| |#1| (-626 (-905 (-576))))) ((-234 $) . T) ((-232 |#1|) . T) ((-238) . T) ((-237) . T) ((-272 |#1|) . T) ((-296 (-419 $) (-419 $)) |has| |#1| (-568)) ((-296 |#1| |#1|) . T) ((-296 $ $) . T) ((-300) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 $) . T) ((-336 |#1| #0#) . T) ((-388 |#1|) . T) ((-423 |#1|) . T) ((-464) -2755 (|has| |#1| (-926)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-526 #2# |#1|) . T) ((-526 #2# $) . T) ((-526 $ $) . T) ((-568) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-658 #1#) |has| |#1| (-38 (-419 (-576)))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #1#) |has| |#1| (-38 (-419 (-576)))) ((-660 #3=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #1#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-651 #3#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #1#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-738) . T) ((-909 $ #2#) . T) ((-909 $ #4=(-1195)) -2755 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-915 #2#) . T) ((-915 (-1195)) |has| |#1| (-915 (-1195))) ((-917 #2#) . T) ((-917 #4#) -2755 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-899 (-390)) -12 (|has| (-1101) (-899 (-390))) (|has| |#1| (-899 (-390)))) ((-899 (-576)) -12 (|has| (-1101) (-899 (-576))) (|has| |#1| (-899 (-576)))) ((-966 |#1| #0# #2#) . T) ((-926) |has| |#1| (-926)) ((-937) |has| |#1| (-374)) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 #2#) . T) ((-1057 |#1|) . T) ((-1070 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1070 |#1|) . T) ((-1070 $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1075 |#1|) . T) ((-1075 $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) |has| |#1| (-1171)) ((-1236) . 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(-12 (-4 *1 (-1229 *3 *4 *5 *6)) (-4 *3 (-568)) (-4 *4 (-805)) + (-4 *5 (-862)) (-4 *6 (-1084 *3 *4 *5)) (-5 *2 (-656 *5))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-1176 *4)) (-4 *4 (-38 *3)) (-4 *4 (-1068)) + (-5 *3 (-419 (-576))) (-5 *1 (-1179 *4))))) +(((*1 *2 *1 *1) + (-12 + (-5 *2 + (-2 (|:| -3495 (-794 *3)) (|:| |coef1| (-794 *3)) + (|:| |coef2| (-794 *3)))) + (-5 *1 (-794 *3)) (-4 *3 (-568)) (-4 *3 (-1068)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-568)) (-4 *3 (-1068)) (-4 *4 (-805)) (-4 *5 (-862)) + (-5 *2 (-2 (|:| -3495 *1) (|:| |coef1| *1) (|:| |coef2| *1))) + (-4 *1 (-1084 *3 *4 *5))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-1177)) (-5 *2 (-1291)) (-5 *1 (-834))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -2166,43 +2378,59 @@ ((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3))))) -(((*1 *2 *3 *3 *3) - (-12 (-5 *3 (-1177)) (-4 *4 (-464)) (-4 *5 (-805)) (-4 *6 (-862)) - (-4 *7 (-1084 *4 *5 *6)) (-5 *2 (-1291)) - (-5 *1 (-1091 *4 *5 *6 *7 *8)) (-4 *8 (-1090 *4 *5 *6 *7)))) - ((*1 *2 *3 *3 *3) - (-12 (-5 *3 (-1177)) (-4 *4 (-464)) (-4 *5 (-805)) (-4 *6 (-862)) - (-4 *7 (-1084 *4 *5 *6)) (-5 *2 (-1291)) - (-5 *1 (-1127 *4 *5 *6 *7 *8)) (-4 *8 (-1090 *4 *5 *6 *7))))) -(((*1 *2) (-12 (-5 *2 (-1177)) (-5 *1 (-771))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1084 *2 *3 *4)) (-4 *2 (-1068)) (-4 *3 (-805)) - (-4 *4 (-862)) (-4 *2 (-464))))) +(((*1 *2 *1) (-12 (-4 *1 (-1112 *2)) (-4 *2 (-1236))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-576)) (-5 *2 (-1054)) (-5 *1 (-770))))) -(((*1 *2 *1) (-12 (-5 *2 (-1291)) (-5 *1 (-834))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-656 *3)) (-4 *3 (-317)) (-5 *1 (-181 *3))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-1177)) (-5 *3 (-656 (-270))) (-5 *1 (-268)))) - ((*1 *1 *2) (-12 (-5 *2 (-1177)) (-5 *1 (-270))))) -(((*1 *2 *1) (-12 (-5 *2 (-656 (-969 (-576)))) (-5 *1 (-449)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-1195)) (-5 *4 (-701 (-227))) (-5 *2 (-1123)) - (-5 *1 (-771)))) + (-12 (-4 *2 (-1262 *4)) (-5 *1 (-819 *4 *2 *3 *5)) + (-4 *4 (-13 (-374) (-148) (-1057 (-419 (-576))))) (-4 *3 (-668 *2)) + (-4 *5 (-668 (-419 *2))))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1195)) (-5 *4 (-701 (-576))) (-5 *2 (-1123)) - (-5 *1 (-771))))) -(((*1 *2) - (-12 (-4 *3 (-568)) (-5 *2 (-656 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-429 *3))))) -(((*1 *2 *1 *1) - (-12 (-4 *3 (-568)) (-4 *3 (-1068)) - (-5 *2 (-2 (|:| -3405 *1) (|:| -2503 *1))) (-4 *1 (-864 *3)))) - ((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-99 *5)) (-4 *5 (-568)) (-4 *5 (-1068)) - (-5 *2 (-2 (|:| -3405 *3) (|:| -2503 *3))) (-5 *1 (-865 *5 *3)) - (-4 *3 (-864 *5))))) + (-12 (-4 *2 (-1262 *4)) (-5 *1 (-819 *4 *2 *5 *3)) + (-4 *4 (-13 (-374) (-148) (-1057 (-419 (-576))))) (-4 *5 (-668 *2)) + (-4 *3 (-668 (-419 *2)))))) +(((*1 *2 *3 *4 *5 *3) + (-12 (-5 *3 (-576)) (-5 *4 (-701 (-227))) (-5 *5 (-227)) + (-5 *2 (-1054)) (-5 *1 (-764))))) +(((*1 *1) (-5 *1 (-449)))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| -3977 (-390)) (|:| -2624 (-1177)) + (|:| |explanations| (-656 (-1177))))) + (-5 *2 (-1054)) (-5 *1 (-315)))) + ((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| -3977 (-390)) (|:| -2624 (-1177)) + (|:| |explanations| (-656 (-1177))) (|:| |extra| (-1054)))) + (-5 *2 (-1054)) (-5 *1 (-315))))) +(((*1 *2 *2) + (-12 (-5 *2 (-960 *3)) (-4 *3 (-13 (-374) (-1221) (-1021))) + (-5 *1 (-178 *3))))) +(((*1 *2 *2 *2 *2 *3) + (-12 (-4 *3 (-568)) (-5 *1 (-988 *3 *2)) (-4 *2 (-1262 *3))))) +(((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-573)))) + ((*1 *2 *3) + (-12 (-5 *2 (-1191 (-419 (-576)))) (-5 *1 (-959)) (-5 *3 (-576))))) +(((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-115)) (-5 *4 (-656 *2)) (-5 *1 (-114 *2)) + (-4 *2 (-1119)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-115)) (-5 *3 (-1 *4 (-656 *4))) (-4 *4 (-1119)) + (-5 *1 (-114 *4)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-115)) (-5 *3 (-1 *4 *4)) (-4 *4 (-1119)) + (-5 *1 (-114 *4)))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-115)) (-5 *2 (-1 *4 (-656 *4))) + (-5 *1 (-114 *4)) (-4 *4 (-1119)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-660 *3)) (-4 *3 (-1068)) + (-5 *1 (-726 *3 *4)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1068)) (-5 *1 (-848 *3))))) +(((*1 *1 *1 *2) + (-12 (-5 *1 (-1159 *2 *3)) (-4 *2 (-13 (-1119) (-34))) + (-4 *3 (-13 (-1119) (-34)))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -2219,85 +2447,46 @@ ((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3))))) -(((*1 *2 *3) - (|partial| -12 (-5 *3 (-347 *5 *6 *7 *8)) (-4 *5 (-442 *4)) - (-4 *6 (-1262 *5)) (-4 *7 (-1262 (-419 *6))) - (-4 *8 (-353 *5 *6 *7)) (-4 *4 (-13 (-568) (-1057 (-576)))) - (-5 *2 (-2 (|:| -2996 (-783)) (|:| -3337 *8))) - (-5 *1 (-928 *4 *5 *6 *7 *8)))) - ((*1 *2 *3) - (|partial| -12 (-5 *3 (-347 (-419 (-576)) *4 *5 *6)) - (-4 *4 (-1262 (-419 (-576)))) (-4 *5 (-1262 (-419 *4))) - (-4 *6 (-353 (-419 (-576)) *4 *5)) - (-5 *2 (-2 (|:| -2996 (-783)) (|:| -3337 *6))) - (-5 *1 (-929 *4 *5 *6))))) +(((*1 *2 *1) + (|partial| -12 (-4 *3 (-13 (-1057 (-576)) (-651 (-576)) (-464))) + (-5 *2 (-855 *4)) (-5 *1 (-323 *3 *4 *5 *6)) + (-4 *4 (-13 (-27) (-1221) (-442 *3))) (-14 *5 (-1195)) + (-14 *6 *4))) + ((*1 *2 *1) + (|partial| -12 (-4 *3 (-13 (-1057 (-576)) (-651 (-576)) (-464))) + (-5 *2 (-855 *4)) (-5 *1 (-1272 *3 *4 *5 *6)) + (-4 *4 (-13 (-27) (-1221) (-442 *3))) (-14 *5 (-1195)) + (-14 *6 *4)))) +(((*1 *1 *2) (-12 (-5 *2 (-656 (-874))) (-5 *1 (-340))))) (((*1 *2 *3 *4) - (|partial| -12 (-5 *4 (-304 (-845 *3))) - (-4 *5 (-13 (-464) (-1057 (-576)) (-651 (-576)))) - (-5 *2 (-845 *3)) (-5 *1 (-648 *5 *3)) - (-4 *3 (-13 (-27) (-1221) (-442 *5))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-304 (-845 (-969 *5)))) (-4 *5 (-464)) - (-5 *2 (-845 (-419 (-969 *5)))) (-5 *1 (-649 *5)) - (-5 *3 (-419 (-969 *5))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-304 (-419 (-969 *5)))) (-5 *3 (-419 (-969 *5))) - (-4 *5 (-464)) (-5 *2 (-845 *3)) (-5 *1 (-649 *5))))) -(((*1 *2 *3 *3 *3 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-227)) (-5 *4 (-576)) - (-5 *5 (-3 (|:| |fn| (-400)) (|:| |fp| (-64 G)))) (-5 *2 (-1054)) - (-5 *1 (-760))))) + (-12 (-5 *3 (-227)) (-5 *4 (-576)) (-5 *2 (-1054)) (-5 *1 (-770))))) (((*1 *2 *3) - (-12 (-5 *3 (-1286 *1)) (-4 *1 (-378 *4)) (-4 *4 (-174)) - (-5 *2 (-701 *4)))) - ((*1 *2) - (-12 (-4 *4 (-174)) (-5 *2 (-701 *4)) (-5 *1 (-428 *3 *4)) - (-4 *3 (-429 *4)))) - ((*1 *2) (-12 (-4 *1 (-429 *3)) (-4 *3 (-174)) (-5 *2 (-701 *3))))) -(((*1 *1 *2) - (-12 + (-12 (-14 *4 (-656 (-1195))) (-4 *5 (-464)) (-5 *2 - (-656 - (-2 - (|:| -4298 - (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) - (|:| -1668 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) - (|:| |relerr| (-227)))) - (|:| -4437 - (-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| (-1176 (-227))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -1668 - (-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 (-571))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-783)) (-5 *2 (-419 (-576))) (-5 *1 (-227)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-783)) (-5 *2 (-419 (-576))) (-5 *1 (-227)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-783)) (-5 *2 (-419 (-576))) (-5 *1 (-390)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-783)) (-5 *2 (-419 (-576))) (-5 *1 (-390))))) -(((*1 *2 *2) (-12 (-5 *2 (-390)) (-5 *1 (-1288)))) - ((*1 *2) (-12 (-5 *2 (-390)) (-5 *1 (-1288))))) + (-2 (|:| |glbase| (-656 (-253 *4 *5))) (|:| |glval| (-656 (-576))))) + (-5 *1 (-643 *4 *5)) (-5 *3 (-656 (-253 *4 *5)))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1065 *4 *5)) (-4 *4 (-13 (-860) (-317) (-148) (-1041))) + (-14 *5 (-656 (-1195))) (-5 *2 (-656 (-656 (-1043 (-419 *4))))) + (-5 *1 (-1313 *4 *5 *6)) (-14 *6 (-656 (-1195))))) + ((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-656 (-969 *5))) (-5 *4 (-112)) + (-4 *5 (-13 (-860) (-317) (-148) (-1041))) + (-5 *2 (-656 (-656 (-1043 (-419 *5))))) (-5 *1 (-1313 *5 *6 *7)) + (-14 *6 (-656 (-1195))) (-14 *7 (-656 (-1195))))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-656 (-969 *5))) (-5 *4 (-112)) + (-4 *5 (-13 (-860) (-317) (-148) (-1041))) + (-5 *2 (-656 (-656 (-1043 (-419 *5))))) (-5 *1 (-1313 *5 *6 *7)) + (-14 *6 (-656 (-1195))) (-14 *7 (-656 (-1195))))) + ((*1 *2 *3) + (-12 (-5 *3 (-656 (-969 *4))) + (-4 *4 (-13 (-860) (-317) (-148) (-1041))) + (-5 *2 (-656 (-656 (-1043 (-419 *4))))) (-5 *1 (-1313 *4 *5 *6)) + (-14 *5 (-656 (-1195))) (-14 *6 (-656 (-1195)))))) +(((*1 *2 *3) + (-12 (-5 *3 (-656 *2)) (-4 *2 (-442 *4)) (-5 *1 (-159 *4 *2)) + (-4 *4 (-568))))) (((*1 *2 *3) (-12 (-5 *2 (-171 (-390))) (-5 *1 (-797 *3)) (-4 *3 (-626 (-390))))) ((*1 *2 *3 *4) @@ -2346,14 +2535,25 @@ (-12 (-5 *3 (-326 (-171 *5))) (-5 *4 (-938)) (-4 *5 (-568)) (-4 *5 (-862)) (-4 *5 (-626 (-390))) (-5 *2 (-171 (-390))) (-5 *1 (-797 *5))))) -(((*1 *1 *1 *1) (-4 *1 (-485))) ((*1 *1 *1 *1) (-4 *1 (-773)))) -(((*1 *2 *3) - (-12 (-5 *3 (-253 *4 *5)) (-14 *4 (-656 (-1195))) (-4 *5 (-464)) - (-5 *2 (-493 *4 *5)) (-5 *1 (-643 *4 *5))))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-1191 *1)) (-5 *3 (-1195)) (-4 *1 (-27)))) + ((*1 *1 *2) (-12 (-5 *2 (-1191 *1)) (-4 *1 (-27)))) + ((*1 *1 *2) (-12 (-5 *2 (-969 *1)) (-4 *1 (-27)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-1195)) (-4 *1 (-29 *3)) (-4 *3 (-568)))) + ((*1 *1 *1) (-12 (-4 *1 (-29 *2)) (-4 *2 (-568))))) +(((*1 *1 *1 *1) + (-12 (-4 *1 (-1262 *2)) (-4 *2 (-1068)) (-4 *2 (-568))))) +(((*1 *2 *2) (-12 (-5 *2 (-701 (-326 (-576)))) (-5 *1 (-1050))))) (((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *2)) (-5 *4 (-783)) (-4 *2 (-1119)) (-5 *1 (-690 *2))))) -(((*1 *2) (-12 (-5 *2 (-1166 (-1177))) (-5 *1 (-403))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) + (|:| |fn| (-1286 (-326 (-227)))) (|:| |yinit| (-656 (-227))) + (|:| |intvals| (-656 (-227))) (|:| |g| (-326 (-227))) + (|:| |abserr| (-227)) (|:| |relerr| (-227)))) + (-5 *2 (-390)) (-5 *1 (-207))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -2371,41 +2571,45 @@ (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3))))) (((*1 *2) (-12 (-5 *2 (-656 *3)) (-5 *1 (-1103 *3)) (-4 *3 (-133))))) -(((*1 *1) - (|partial| -12 (-4 *1 (-378 *2)) (-4 *2 (-568)) (-4 *2 (-174))))) (((*1 *2 *3) - (-12 (-5 *2 (-1 (-960 *3) (-960 *3))) (-5 *1 (-178 *3)) - (-4 *3 (-13 (-374) (-1221) (-1021))))) - ((*1 *2) - (|partial| -12 (-4 *4 (-1240)) (-4 *5 (-1262 (-419 *2))) - (-4 *2 (-1262 *4)) (-5 *1 (-352 *3 *4 *2 *5)) - (-4 *3 (-353 *4 *2 *5)))) - ((*1 *2) - (|partial| -12 (-4 *1 (-353 *3 *2 *4)) (-4 *3 (-1240)) - (-4 *4 (-1262 (-419 *2))) (-4 *2 (-1262 *3))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1002 *2)) (-4 *2 (-1221))))) + (-12 (-5 *2 (-1176 (-656 (-576)))) (-5 *1 (-896)) (-5 *3 (-576))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-112)) (-5 *3 (-656 (-270))) (-5 *1 (-268)))) + ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-270)))) + ((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-479)))) + ((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-479))))) (((*1 *2 *1) - (-12 (-5 *2 (-656 (-2 (|:| |k| (-684 *3)) (|:| |c| *4)))) - (-5 *1 (-639 *3 *4 *5)) (-4 *3 (-862)) - (-4 *4 (-13 (-174) (-729 (-419 (-576))))) (-14 *5 (-938))))) -(((*1 *2 *2 *2) - (|partial| -12 (-4 *3 (-13 (-568) (-148))) (-5 *1 (-1256 *3 *2)) - (-4 *2 (-1262 *3))))) -(((*1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-479)))) - ((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-479)))) - ((*1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-944))))) -(((*1 *2 *2) - (-12 (-4 *3 (-1262 (-419 (-576)))) (-5 *1 (-930 *3 *2)) - (-4 *2 (-1262 (-419 *3)))))) -(((*1 *2) (-12 (-5 *2 (-1291)) (-5 *1 (-448))))) + (-12 (-4 *1 (-336 *2 *3)) (-4 *3 (-804)) (-4 *2 (-1068)) + (-4 *2 (-464)))) + ((*1 *2 *3) + (-12 (-5 *3 (-656 *4)) (-4 *4 (-1262 (-576))) (-5 *2 (-656 (-576))) + (-5 *1 (-498 *4)))) + ((*1 *2 *1) (-12 (-4 *1 (-864 *2)) (-4 *2 (-1068)) (-4 *2 (-464)))) + ((*1 *1 *1 *2) + (-12 (-4 *1 (-966 *3 *4 *2)) (-4 *3 (-1068)) (-4 *4 (-805)) + (-4 *2 (-862)) (-4 *3 (-464))))) +(((*1 *2 *1) + (-12 (-4 *3 (-374)) (-4 *4 (-1262 *3)) (-4 *5 (-1262 (-419 *4))) + (-5 *2 (-1286 *6)) (-5 *1 (-347 *3 *4 *5 *6)) + (-4 *6 (-353 *3 *4 *5))))) +(((*1 *2) (-12 (-5 *2 (-938)) (-5 *1 (-1289)))) + ((*1 *2 *2) (-12 (-5 *2 (-938)) (-5 *1 (-1289))))) +(((*1 *2 *3 *2 *4) + (-12 (-5 *3 (-701 *2)) (-5 *4 (-783)) + (-4 *2 (-13 (-317) (-10 -8 (-15 -3267 ((-430 $) $))))) + (-4 *5 (-1262 *2)) (-5 *1 (-511 *2 *5 *6)) (-4 *6 (-421 *2 *5))))) +(((*1 *2 *3) + (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-576))) (-5 *1 (-1066))))) +(((*1 *2) + (-12 (-4 *3 (-1068)) (-5 *2 (-975 (-724 *3 *4))) (-5 *1 (-724 *3 *4)) + (-4 *4 (-1262 *3))))) (((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1093)))) ((*1 *2 *1 *1) (-12 (-4 *1 (-1122 *3 *4 *5 *6 *7)) (-4 *3 (-1119)) (-4 *4 (-1119)) (-4 *5 (-1119)) (-4 *6 (-1119)) (-4 *7 (-1119)) (-5 *2 (-112))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-624 *3)) (-4 *3 (-13 (-442 *5) (-27) (-1221))) - (-4 *5 (-13 (-464) (-1057 (-576)) (-148) (-651 (-576)))) - (-5 *2 (-598 *3)) (-5 *1 (-578 *5 *3 *6)) (-4 *6 (-1119))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-374)) (-5 *1 (-778 *2 *3)) (-4 *2 (-720 *3)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-864 *2)) (-4 *2 (-1068)) (-4 *2 (-374))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -2426,39 +2630,36 @@ (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3))))) (((*1 *2 *1) (-12 (-5 *2 (-786)) (-5 *1 (-52))))) -(((*1 *2 *3 *4 *3 *4 *5 *3 *4 *3 *3 *3 *3) - (-12 (-5 *4 (-701 (-227))) (-5 *5 (-701 (-576))) (-5 *3 (-576)) - (-5 *2 (-1054)) (-5 *1 (-768))))) -(((*1 *2) - (-12 (-4 *3 (-568)) (-5 *2 (-656 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-429 *3))))) -(((*1 *2 *3 *4) - (|partial| -12 (-5 *4 (-938)) (-4 *5 (-568)) (-5 *2 (-701 *5)) - (-5 *1 (-973 *5 *3)) (-4 *3 (-668 *5))))) -(((*1 *2 *1) - (-12 (-4 *3 (-1068)) (-5 *2 (-1286 *3)) (-5 *1 (-724 *3 *4)) - (-4 *4 (-1262 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1191 *5)) (-4 *5 (-374)) (-5 *2 (-656 *6)) - (-5 *1 (-544 *5 *6 *4)) (-4 *6 (-374)) (-4 *4 (-13 (-374) (-860)))))) -(((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-944))))) (((*1 *2 *1) - (-12 (-4 *3 (-464)) (-4 *4 (-862)) (-4 *5 (-805)) (-5 *2 (-656 *6)) - (-5 *1 (-1006 *3 *4 *5 *6)) (-4 *6 (-966 *3 *5 *4))))) + (-12 (-4 *2 (-1119)) (-5 *1 (-981 *2 *3)) (-4 *3 (-1119))))) +(((*1 *2 *3) + (-12 (-4 *4 (-568)) (-5 *2 (-656 *3)) (-5 *1 (-43 *4 *3)) + (-4 *3 (-429 *4))))) +(((*1 *1) (-12 (-4 *1 (-437 *2)) (-4 *2 (-379)) (-4 *2 (-1119))))) +(((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-377 *3 *4)) + (-4 *3 (-378 *4)))) + ((*1 *2) (-12 (-4 *1 (-378 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) (((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-656 (-1191 *5))) (-5 *3 (-1191 *5)) - (-4 *5 (-167 *4)) (-4 *4 (-557)) (-5 *1 (-150 *4 *5)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-656 *3)) (-4 *3 (-1262 *5)) - (-4 *5 (-1262 *4)) (-4 *4 (-360)) (-5 *1 (-369 *4 *5 *3)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-656 (-1191 (-576)))) (-5 *3 (-1191 (-576))) - (-5 *1 (-584)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-656 (-1191 *1))) (-5 *3 (-1191 *1)) - (-4 *1 (-926))))) -(((*1 *2 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-454 *3)) (-4 *3 (-1262 (-576)))))) + (-12 + (-5 *2 + (-2 (|:| |partsol| (-1286 (-419 (-969 *4)))) + (|:| -2437 (-656 (-1286 (-419 (-969 *4))))))) + (-5 *3 (-656 *7)) (-4 *4 (-13 (-317) (-148))) + (-4 *7 (-966 *4 *6 *5)) (-4 *5 (-13 (-862) (-626 (-1195)))) + (-4 *6 (-805)) (-5 *1 (-941 *4 *5 *6 *7))))) +(((*1 *2 *1) + (-12 (-4 *3 (-374)) (-4 *4 (-805)) (-4 *5 (-862)) (-5 *2 (-112)) + (-5 *1 (-516 *3 *4 *5 *6)) (-4 *6 (-966 *3 *4 *5))))) +(((*1 *1 *1) + (-12 (-4 *1 (-1084 *2 *3 *4)) (-4 *2 (-1068)) (-4 *3 (-805)) + (-4 *4 (-862)) (-4 *2 (-464))))) +(((*1 *2 *3 *2) + (-12 (-5 *3 (-783)) (-5 *1 (-795 *2)) (-4 *2 (-38 (-419 (-576)))) + (-4 *2 (-174))))) +(((*1 *2 *3 *1) + (-12 (-5 *3 (-922 *4)) (-4 *4 (-1119)) (-5 *2 (-656 (-783))) + (-5 *1 (-921 *4))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -2478,61 +2679,57 @@ ((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-227)) (-5 *1 (-228)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-171 (-227))) (-5 *1 (-228)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-568)) (-5 *1 (-443 *3 *2)) (-4 *2 (-442 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1158)))) -(((*1 *2 *2 *3 *4 *5) - (-12 (-5 *2 (-656 *9)) (-5 *3 (-1 (-112) *9)) - (-5 *4 (-1 (-112) *9 *9)) (-5 *5 (-1 *9 *9 *9)) - (-4 *9 (-1084 *6 *7 *8)) (-4 *6 (-568)) (-4 *7 (-805)) - (-4 *8 (-862)) (-5 *1 (-996 *6 *7 *8 *9))))) -(((*1 *1 *1) (-4 *1 (-568)))) -(((*1 *2 *1) - (-12 +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-656 (-969 (-576)))) (-5 *4 (-656 (-1195))) + (-5 *2 (-656 (-656 (-390)))) (-5 *1 (-1042)) (-5 *5 (-390)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1065 *4 *5)) (-4 *4 (-13 (-860) (-317) (-148) (-1041))) + (-14 *5 (-656 (-1195))) (-5 *2 (-656 (-656 (-1043 (-419 *4))))) + (-5 *1 (-1313 *4 *5 *6)) (-14 *6 (-656 (-1195))))) + ((*1 *2 *3 *4 *4 *4) + (-12 (-5 *3 (-656 (-969 *5))) (-5 *4 (-112)) + (-4 *5 (-13 (-860) (-317) (-148) (-1041))) + (-5 *2 (-656 (-656 (-1043 (-419 *5))))) (-5 *1 (-1313 *5 *6 *7)) + (-14 *6 (-656 (-1195))) (-14 *7 (-656 (-1195))))) + ((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-656 (-969 *5))) (-5 *4 (-112)) + (-4 *5 (-13 (-860) (-317) (-148) (-1041))) + (-5 *2 (-656 (-656 (-1043 (-419 *5))))) (-5 *1 (-1313 *5 *6 *7)) + (-14 *6 (-656 (-1195))) (-14 *7 (-656 (-1195))))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-656 (-969 *5))) (-5 *4 (-112)) + (-4 *5 (-13 (-860) (-317) (-148) (-1041))) + (-5 *2 (-656 (-656 (-1043 (-419 *5))))) (-5 *1 (-1313 *5 *6 *7)) + (-14 *6 (-656 (-1195))) (-14 *7 (-656 (-1195))))) + ((*1 *2 *3) + (-12 (-5 *3 (-656 (-969 *4))) + (-4 *4 (-13 (-860) (-317) (-148) (-1041))) + (-5 *2 (-656 (-656 (-1043 (-419 *4))))) (-5 *1 (-1313 *4 *5 *6)) + (-14 *5 (-656 (-1195))) (-14 *6 (-656 (-1195)))))) +(((*1 *2 *1) (-12 (-4 *1 (-1011 *2)) (-4 *2 (-568)) (-4 *2 (-557)))) + ((*1 *1 *1) (-4 *1 (-1079)))) +(((*1 *2 *3 *3 *4 *5 *5 *3) + (-12 (-5 *3 (-576)) (-5 *4 (-1177)) (-5 *5 (-701 (-227))) + (-5 *2 (-1054)) (-5 *1 (-759))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-783)) (-4 *5 (-1068)) (-5 *2 (-576)) + (-5 *1 (-455 *5 *3 *6)) (-4 *3 (-1262 *5)) + (-4 *6 (-13 (-416) (-1057 *5) (-374) (-1221) (-294))))) + ((*1 *2 *3) + (-12 (-4 *4 (-1068)) (-5 *2 (-576)) (-5 *1 (-455 *4 *3 *5)) + (-4 *3 (-1262 *4)) + (-4 *5 (-13 (-416) (-1057 *4) (-374) (-1221) (-294)))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-1 *4 (-576))) (-5 *5 (-1 (-1176 *4))) (-4 *4 (-374)) + (-4 *4 (-1068)) (-5 *2 (-1176 *4)) (-5 *1 (-1179 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-227)) (-5 *4 (-576)) (-5 *2 (-1054)) (-5 *1 (-770))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-13 (-317) (-148))) (-4 *5 (-13 (-862) (-626 (-1195)))) + (-4 *6 (-805)) (-4 *7 (-966 *4 *6 *5)) (-5 *2 - (-656 - (-2 - (|:| -4298 - (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) - (|:| -1668 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) - (|:| |relerr| (-227)))) - (|:| -4437 - (-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| (-1176 (-227))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -1668 - (-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 (-571)))) - ((*1 *2 *1) - (-12 (-4 *1 (-616 *3 *4)) (-4 *3 (-1119)) (-4 *4 (-1236)) - (-5 *2 (-656 *4))))) -(((*1 *2 *3 *3 *4 *4 *3 *4 *4 *3 *3 *3) - (-12 (-5 *3 (-576)) (-5 *4 (-701 (-227))) (-5 *2 (-1054)) - (-5 *1 (-764))))) -(((*1 *2 *1 *3) (-12 (-4 *1 (-539)) (-5 *3 (-129)) (-5 *2 (-783))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-374)) (-5 *1 (-778 *2 *3)) (-4 *2 (-720 *3)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-864 *2)) (-4 *2 (-1068)) (-4 *2 (-374))))) + (-2 (|:| |sysok| (-112)) (|:| |z0| (-656 *7)) (|:| |n0| (-656 *7)))) + (-5 *1 (-941 *4 *5 *6 *7)) (-5 *3 (-656 *7))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -2552,60 +2749,48 @@ ((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3))))) -(((*1 *1 *1 *2 *3 *1) - (-12 (-5 *2 (-783)) (-5 *1 (-794 *3)) (-4 *3 (-1068)))) - ((*1 *1 *1 *2 *3 *1) - (-12 (-5 *1 (-980 *3 *2)) (-4 *2 (-132)) (-4 *3 (-568)) - (-4 *3 (-1068)) (-4 *2 (-804)))) - ((*1 *1 *1 *2 *3 *1) - (-12 (-5 *2 (-783)) (-5 *1 (-1191 *3)) (-4 *3 (-1068)))) - ((*1 *1 *1 *2 *3 *1) - (-12 (-5 *2 (-990)) (-4 *2 (-132)) (-5 *1 (-1197 *3)) (-4 *3 (-568)) - (-4 *3 (-1068)))) - ((*1 *1 *1 *2 *3 *1) - (-12 (-5 *2 (-783)) (-5 *1 (-1259 *4 *3)) (-14 *4 (-1195)) - (-4 *3 (-1068))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-568)) - (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) - (-5 *1 (-988 *4 *3)) (-4 *3 (-1262 *4))))) +(((*1 *2 *2 *2 *3) + (-12 (-5 *3 (-783)) (-4 *4 (-568)) (-5 *1 (-988 *4 *2)) + (-4 *2 (-1262 *4))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-656 (-874))) (-5 *1 (-874))))) -(((*1 *1 *2 *2 *1) (-12 (-5 *1 (-659 *2)) (-4 *2 (-1119))))) -(((*1 *1 *1 *2) - (-12 (-4 *1 (-57 *2 *3 *4)) (-4 *2 (-1236)) (-4 *3 (-384 *2)) - (-4 *4 (-384 *2)))) - ((*1 *1 *1 *2) - (-12 (|has| *1 (-6 -4463)) (-4 *1 (-616 *3 *2)) (-4 *3 (-1119)) - (-4 *2 (-1236))))) -(((*1 *2 *1) (-12 (-4 *1 (-809 *2)) (-4 *2 (-174)))) - ((*1 *2 *1) (-12 (-4 *1 (-1016 *2)) (-4 *2 (-174))))) -(((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-938)) (-5 *4 (-886)) (-5 *2 (-1291)) (-5 *1 (-1287)))) - ((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-938)) (-5 *4 (-1177)) (-5 *2 (-1291)) (-5 *1 (-1287)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (-1177)) (-5 *2 (-1291)) (-5 *1 (-1288))))) -(((*1 *2 *3 *3 *3) - (-12 (-5 *3 (-1177)) (-4 *4 (-464)) (-4 *5 (-805)) (-4 *6 (-862)) - (-4 *7 (-1084 *4 *5 *6)) (-5 *2 (-1291)) - (-5 *1 (-1091 *4 *5 *6 *7 *8)) (-4 *8 (-1090 *4 *5 *6 *7)))) - ((*1 *2 *3 *3 *3) - (-12 (-5 *3 (-1177)) (-4 *4 (-464)) (-4 *5 (-805)) (-4 *6 (-862)) - (-4 *7 (-1084 *4 *5 *6)) (-5 *2 (-1291)) - (-5 *1 (-1127 *4 *5 *6 *7 *8)) (-4 *8 (-1090 *4 *5 *6 *7))))) +(((*1 *2 *3 *4 *4) + (-12 (-5 *4 (-1195)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-714 *3 *5 *6 *7)) + (-4 *3 (-626 (-548))) (-4 *5 (-1236)) (-4 *6 (-1236)) + (-4 *7 (-1236)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-1195)) (-5 *2 (-1 *6 *5)) (-5 *1 (-718 *3 *5 *6)) + (-4 *3 (-626 (-548))) (-4 *5 (-1236)) (-4 *6 (-1236))))) +(((*1 *2 *1) + (-12 (-5 *2 (-656 (-2 (|:| |gen| *3) (|:| -4101 *4)))) + (-5 *1 (-661 *3 *4 *5)) (-4 *3 (-1119)) (-4 *4 (-23)) (-14 *5 *4)))) +(((*1 *2 *1) (-12 (-4 *1 (-378 *2)) (-4 *2 (-174))))) (((*1 *2 *3) + (-12 (-5 *2 (-1191 (-576))) (-5 *1 (-193)) (-5 *3 (-576)))) + ((*1 *2 *3 *2) (-12 (-5 *3 (-783)) (-5 *1 (-795 *2)) (-4 *2 (-174)))) + ((*1 *2 *3) + (-12 (-5 *2 (-1191 (-576))) (-5 *1 (-959)) (-5 *3 (-576))))) +(((*1 *2 *1 *2) (-12 (-5 *2 (-656 (-1177))) (-5 *1 (-406))))) +(((*1 *2 *3 *4 *5 *6 *7 *7 *8) (-12 (-5 *3 - (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) - (|:| -1668 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) - (|:| |relerr| (-227)))) - (-5 *2 (-1176 (-227))) (-5 *1 (-194)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-326 (-227))) (-5 *4 (-656 (-1195))) - (-5 *5 (-1113 (-855 (-227)))) (-5 *2 (-1176 (-227))) (-5 *1 (-310)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1286 (-326 (-227)))) (-5 *4 (-656 (-1195))) - (-5 *5 (-1113 (-855 (-227)))) (-5 *2 (-1176 (-227))) (-5 *1 (-310))))) -(((*1 *2) (-12 (-5 *2 (-1291)) (-5 *1 (-771))))) + (-2 (|:| |det| *12) (|:| |rows| (-656 (-576))) + (|:| |cols| (-656 (-576))))) + (-5 *4 (-701 *12)) (-5 *5 (-656 (-419 (-969 *9)))) + (-5 *6 (-656 (-656 *12))) (-5 *7 (-783)) (-5 *8 (-576)) + (-4 *9 (-13 (-317) (-148))) (-4 *12 (-966 *9 *11 *10)) + (-4 *10 (-13 (-862) (-626 (-1195)))) (-4 *11 (-805)) + (-5 *2 + (-2 (|:| |eqzro| (-656 *12)) (|:| |neqzro| (-656 *12)) + (|:| |wcond| (-656 (-969 *9))) + (|:| |bsoln| + (-2 (|:| |partsol| (-1286 (-419 (-969 *9)))) + (|:| -2437 (-656 (-1286 (-419 (-969 *9))))))))) + (-5 *1 (-941 *9 *10 *11 *12))))) +(((*1 *2 *3) + (-12 (-5 *3 (-938)) (-5 *2 (-1191 *4)) (-5 *1 (-600 *4)) + (-4 *4 (-360))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-960 (-227))) (-5 *2 (-1291)) (-5 *1 (-480))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) @@ -2622,52 +2807,35 @@ ((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3))))) +(((*1 *2 *3) + (-12 (-5 *2 (-576)) (-5 *1 (-457 *3)) (-4 *3 (-416)) (-4 *3 (-1068))))) (((*1 *2 *1) - (-12 (-5 *2 (-419 (-969 *3))) (-5 *1 (-465 *3 *4 *5 *6)) - (-4 *3 (-568)) (-4 *3 (-174)) (-14 *4 (-938)) - (-14 *5 (-656 (-1195))) (-14 *6 (-1286 (-701 *3)))))) -(((*1 *2) - (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-377 *3 *4)) - (-4 *3 (-378 *4)))) - ((*1 *2) (-12 (-4 *1 (-378 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-701 *1)) (-5 *4 (-1286 *1)) (-4 *1 (-651 *5)) - (-4 *5 (-1068)) - (-5 *2 (-2 (|:| -2875 (-701 *5)) (|:| |vec| (-1286 *5)))))) - ((*1 *2 *3) - (-12 (-5 *3 (-701 *1)) (-4 *1 (-651 *4)) (-4 *4 (-1068)) - (-5 *2 (-701 *4))))) -(((*1 *1 *1 *2 *2) - (-12 (-5 *2 (-576)) (-5 *1 (-137 *3 *4 *5)) (-14 *3 *2) - (-14 *4 (-783)) (-4 *5 (-174)))) - ((*1 *1 *1 *2 *1 *2) - (-12 (-5 *2 (-576)) (-5 *1 (-137 *3 *4 *5)) (-14 *3 *2) - (-14 *4 (-783)) (-4 *5 (-174)))) - ((*1 *2 *2 *3) - (-12 - (-5 *2 - (-516 (-419 (-576)) (-245 *5 (-783)) (-876 *4) - (-253 *4 (-419 (-576))))) - (-5 *3 (-656 (-876 *4))) (-14 *4 (-656 (-1195))) (-14 *5 (-783)) - (-5 *1 (-517 *4 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-598 *3)) (-4 *3 (-374))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-656 *5)) (-4 *5 (-1262 *3)) (-4 *3 (-317)) - (-5 *2 (-112)) (-5 *1 (-467 *3 *5))))) + (|partial| -12 (-4 *3 (-25)) (-4 *3 (-1119)) + (-5 *2 (-2 (|:| -1713 (-576)) (|:| |var| (-624 *1)))) + (-4 *1 (-442 *3))))) +(((*1 *1) (-5 *1 (-835)))) +(((*1 *2 *3) + (-12 (-5 *3 (-656 *2)) (-4 *2 (-442 *4)) (-5 *1 (-159 *4 *2)) + (-4 *4 (-568))))) +(((*1 *2 *3) + (-12 (-5 *3 (-938)) (-5 *2 (-1197 (-419 (-576)))) (-5 *1 (-192))))) (((*1 *2 *1) (-12 (-5 *2 (-656 (-624 *1))) (-4 *1 (-312))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1 *3 *3 (-576))) (-4 *3 (-1068)) (-5 *1 (-99 *3)))) + ((*1 *1 *2 *2) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1068)) (-5 *1 (-99 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1068)) (-5 *1 (-99 *3))))) (((*1 *2 *1) (-12 (-5 *2 (-1154)) (-5 *1 (-529)))) ((*1 *2 *1) (-12 (-4 *2 (-13 (-1119) (-34))) (-5 *1 (-1159 *3 *2)) (-4 *3 (-13 (-1119) (-34))))) ((*1 *2 *1) (-12 (-5 *2 (-1154)) (-5 *1 (-1297))))) -(((*1 *1 *2 *2) (-12 (-4 *1 (-566 *2)) (-4 *2 (-13 (-416) (-1221)))))) -(((*1 *2 *1) (-12 (-4 *1 (-686 *3)) (-4 *3 (-1236)) (-5 *2 (-112))))) -(((*1 *2 *3) - (-12 (-5 *3 (-656 (-2 (|:| -1825 *4) (|:| -3779 (-576))))) - (-4 *4 (-1262 (-576))) (-5 *2 (-749 (-783))) (-5 *1 (-454 *4)))) - ((*1 *2 *3) - (-12 (-5 *3 (-430 *5)) (-4 *5 (-1262 *4)) (-4 *4 (-1068)) - (-5 *2 (-749 (-783))) (-5 *1 (-456 *4 *5))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-835)) (-5 *2 (-1291)) (-5 *1 (-834))))) +(((*1 *1) (-5 *1 (-609)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-3 (-419 (-969 *5)) (-1184 (-1195) (-969 *5)))) + (-4 *5 (-464)) (-5 *2 (-656 (-701 (-419 (-969 *5))))) + (-5 *1 (-302 *5)) (-5 *4 (-701 (-419 (-969 *5))))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) @@ -2684,32 +2852,127 @@ ((*1 *2 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(-390)) (-5 *2 (-227)) (-5 *1 (-1289)))) + ((*1 *2) (-12 (-5 *2 (-227)) (-5 *1 (-1289))))) +(((*1 *2 *2 *2 *3) + (-12 (-5 *2 (-1286 (-576))) (-5 *3 (-576)) (-5 *1 (-1129)))) + ((*1 *2 *3 *2 *4) + (-12 (-5 *2 (-1286 (-576))) (-5 *3 (-656 (-576))) (-5 *4 (-576)) + (-5 *1 (-1129))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-622 *3 *4)) (-4 *3 (-1119)) (-4 *4 (-1119)) + (-5 *2 (-112))))) +(((*1 *1 *2 *3) (-12 (-5 *3 (-576)) (-5 *1 (-430 *2)) (-4 *2 (-568))))) (((*1 *2 *1) (-12 (-4 *1 (-249 *2)) (-4 *2 (-1236)))) ((*1 *2 *1) (-12 (-5 *2 (-1154)) (-5 *1 (-1115)))) ((*1 *2 *1) @@ -2750,9 +3008,10 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-783)) (-4 *1 (-1274 *3)) (-4 *3 (-1236)))) ((*1 *2 *1) (-12 (-4 *1 (-1274 *2)) (-4 *2 (-1236))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-656 *2)) (-4 *2 (-966 *4 *5 *6)) (-4 *4 (-464)) - (-4 *5 (-805)) (-4 *6 (-862)) (-5 *1 (-461 *4 *5 *6 *2))))) +(((*1 *2 *3) + (-12 (-4 *4 (-568)) (-4 *2 (-13 (-442 *4) (-1021) (-1221))) + (-5 *1 (-612 *4 *2 *3)) + (-4 *3 (-13 (-442 (-171 *4)) 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(-12 (-5 *3 (-390)) (-5 *2 (-227)) (-5 *1 (-1289)))) - ((*1 *2) (-12 (-5 *2 (-227)) (-5 *1 (-1289))))) -(((*1 *2 *3) (-12 (-5 *3 (-1286 *1)) (-4 *1 (-378 *2)) (-4 *2 (-174)))) - ((*1 *2) (-12 (-4 *2 (-174)) (-5 *1 (-428 *3 *2)) (-4 *3 (-429 *2)))) - ((*1 *2) (-12 (-4 *1 (-429 *2)) (-4 *2 (-174))))) (((*1 *2 *1) (|partial| -12 (-5 *2 (-518)) (-5 *1 (-289)))) ((*1 *2 *1) (-12 (-5 *2 (-3 (-576) (-227) (-518) (-1177) (-1200))) (-5 *1 (-1200))))) (((*1 *2 *3) - (-12 (-4 *4 (-1068)) (-5 *2 (-576)) (-5 *1 (-455 *4 *3 *5)) - (-4 *3 (-1262 *4)) - (-4 *5 (-13 (-416) (-1057 *4) (-374) (-1221) (-294)))))) + (-12 (-5 *3 (-1177)) (-4 *4 (-13 (-317) (-148))) + (-4 *5 (-13 (-862) (-626 (-1195)))) (-4 *6 (-805)) + (-5 *2 + (-656 + (-2 (|:| |eqzro| (-656 *7)) (|:| |neqzro| (-656 *7)) + (|:| |wcond| (-656 (-969 *4))) + (|:| |bsoln| + (-2 (|:| |partsol| (-1286 (-419 (-969 *4)))) + (|:| -2437 (-656 (-1286 (-419 (-969 *4)))))))))) + (-5 *1 (-941 *4 *5 *6 *7)) (-4 *7 (-966 *4 *6 *5))))) +(((*1 *2 *3 *4) + 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*2 (-1177)) (-5 *1 (-1205))))) +(((*1 *2 *3 *3) + (|partial| -12 (-4 *4 (-464)) (-4 *5 (-805)) (-4 *6 (-862)) + (-4 *7 (-1084 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-1007 *4 *5 *6 *7 *3)) (-4 *3 (-1090 *4 *5 *6 *7)))) + ((*1 *2 *3 *3) + (|partial| -12 (-4 *4 (-464)) (-4 *5 (-805)) (-4 *6 (-862)) + (-4 *7 (-1084 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-1126 *4 *5 *6 *7 *3)) (-4 *3 (-1090 *4 *5 *6 *7))))) (((*1 *2 *1) (-12 (-5 *2 @@ -2894,21 +3183,41 @@ (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print"))) (-5 *1 (-340))))) -(((*1 *2) (-12 (-5 *2 (-131)) (-5 *1 (-1205))))) -(((*1 *2 *1) - (|partial| -12 (-4 *3 (-464)) (-4 *4 (-862)) (-4 *5 (-805)) - (-5 *2 (-112)) (-5 *1 (-1006 *3 *4 *5 *6)) - (-4 *6 (-966 *3 *5 *4)))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-176 *3)) (-4 *3 (-317)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-576)) (-4 *1 (-686 *3)) (-4 *3 (-1236)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-783)) (-4 *1 (-752 *3 *4)) 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*2 *1) (-12 (-5 *2 (-656 (-1154))) (-5 *1 (-683)))) ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1159 *3 *4)) (-4 *3 (-13 (-1119) (-34))) - (-4 *4 (-13 (-1119) (-34)))))) + (-12 (-5 *2 (-656 (-938))) (-5 *1 (-1120 *3 *4)) (-14 *3 (-938)) + (-14 *4 (-938))))) (((*1 *1 *1) (-5 *1 (-112)))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) - (-12 (-5 *3 (-1 (-390) (-390))) (-5 *4 (-390)) - (-5 *2 - (-2 (|:| -3102 *4) (|:| -3311 *4) (|:| |totalpts| (-576)) - (|:| |success| (-112)))) - (-5 *1 (-801)) (-5 *5 (-576))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-158)) (-5 *2 (-1291)) (-5 *1 (-1288))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) @@ -2928,37 +3237,45 @@ ((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-1123)) (-5 *1 (-1199))))) -(((*1 *1 *1) - (-12 (-5 *1 (-50 *2 *3)) (-4 *2 (-1068)) (-14 *3 (-656 (-1195))))) +(((*1 *1 *1) (-12 (-5 *1 (-620 *2)) (-4 *2 (-1119)))) + ((*1 *1 *1) (-5 *1 (-644)))) +(((*1 *2 *3) + (-12 (-4 *4 (-1068)) (-5 *2 (-576)) (-5 *1 (-455 *4 *3 *5)) + (-4 *3 (-1262 *4)) + (-4 *5 (-13 (-416) (-1057 *4) (-374) (-1221) (-294)))))) +(((*1 *2 *1) (-12 (-4 *1 (-566 *2)) (-4 *2 (-13 (-416) (-1221))))) + ((*1 *1 *1 *1) (-4 *1 (-805)))) +(((*1 *1 *2) + (|partial| -12 (-5 *2 (-656 *6)) (-4 *6 (-1084 *3 *4 *5)) + (-4 *3 (-568)) (-4 *4 (-805)) (-4 *5 (-862)) + (-5 *1 (-1299 *3 *4 *5 *6)))) + ((*1 *1 *2 *3 *4) + (|partial| -12 (-5 *2 (-656 *8)) (-5 *3 (-1 (-112) *8 *8)) + (-5 *4 (-1 *8 *8 *8)) (-4 *8 (-1084 *5 *6 *7)) (-4 *5 (-568)) + (-4 *6 (-805)) (-4 *7 (-862)) (-5 *1 (-1299 *5 *6 *7 *8))))) +(((*1 *1 *2 *3 *3 *3 *4) + (-12 (-4 *4 (-374)) (-4 *3 (-1262 *4)) (-4 *5 (-1262 (-419 *3))) + (-4 *1 (-346 *4 *3 *5 *2)) (-4 *2 (-353 *4 *3 *5)))) + ((*1 *1 *2 *2 *3) + (-12 (-5 *3 (-576)) (-4 *2 (-374)) (-4 *4 (-1262 *2)) + (-4 *5 (-1262 (-419 *4))) (-4 *1 (-346 *2 *4 *5 *6)) + (-4 *6 (-353 *2 *4 *5)))) + ((*1 *1 *2 *2) + (-12 (-4 *2 (-374)) (-4 *3 (-1262 *2)) (-4 *4 (-1262 (-419 *3))) + (-4 *1 (-346 *2 *3 *4 *5)) (-4 *5 (-353 *2 *3 *4)))) + ((*1 *1 *2) + (-12 (-4 *3 (-374)) (-4 *4 (-1262 *3)) (-4 *5 (-1262 (-419 *4))) + (-4 *1 (-346 *3 *4 *5 *2)) (-4 *2 (-353 *3 *4 *5)))) + ((*1 *1 *2) + (-12 (-5 *2 (-425 *4 (-419 *4) *5 *6)) (-4 *4 (-1262 *3)) + (-4 *5 (-1262 (-419 *4))) (-4 *6 (-353 *3 *4 *5)) (-4 *3 (-374)) + (-4 *1 (-346 *3 *4 *5 *6))))) +(((*1 *2 *2) (-12 (-5 *2 (-656 (-326 (-227)))) (-5 *1 (-276))))) +(((*1 *2 *2) + (-12 (-5 *2 (-1176 *3)) (-4 *3 (-1068)) (-5 *1 (-1179 *3)))) ((*1 *1 *1) - (-12 (-5 *1 (-225 *2 *3)) (-4 *2 (-13 (-1068) (-862))) - (-14 *3 (-656 (-1195)))))) -(((*1 *1 *2 *3 *1) - (-12 (-14 *4 (-656 (-1195))) (-4 *2 (-174)) - (-4 *3 (-243 (-3500 *4) (-783))) - (-14 *6 - (-1 (-112) (-2 (|:| -3222 *5) (|:| -1567 *3)) - (-2 (|:| -3222 *5) (|:| -1567 *3)))) - (-5 *1 (-473 *4 *2 *5 *3 *6 *7)) (-4 *5 (-862)) - (-4 *7 (-966 *2 *3 (-876 *4)))))) -(((*1 *1 *1) - (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1068))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-845 *3)) (-4 *3 (-1119)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-855 *3)) (-4 *3 (-1119))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1195)) - (-4 *5 (-13 (-568) (-1057 (-576)) (-651 (-576)))) - (-5 *2 - (-2 (|:| |func| *3) (|:| |kers| (-656 (-624 *3))) - (|:| |vals| (-656 *3)))) - (-5 *1 (-286 *5 *3)) (-4 *3 (-13 (-27) (-1221) (-442 *5)))))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-1286 *1)) (-4 *1 (-651 *4)) (-4 *4 (-1068)) - (-5 *2 (-2 (|:| -2875 (-701 *4)) (|:| |vec| (-1286 *4)))))) - ((*1 *2 *3) - (-12 (-5 *3 (-1286 *1)) (-4 *1 (-651 *4)) (-4 *4 (-1068)) - (-5 *2 (-701 *4))))) + (-12 (-5 *1 (-1278 *2 *3 *4)) (-4 *2 (-1068)) (-14 *3 (-1195)) + (-14 *4 *2)))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -2975,99 +3292,49 @@ (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3)))) ((*1 *1 *1) (-4 *1 (-1224)))) -(((*1 *2 *1 *3) - (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-804)) (-4 *2 (-1068)))) - ((*1 *2 *1 *1) - (-12 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(-1068)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-656 *6)) (-5 *3 (-656 (-783))) (-4 *1 (-966 *4 *5 *6)) - (-4 *4 (-1068)) (-4 *5 (-805)) (-4 *6 (-862)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *3 (-783)) (-4 *1 (-966 *4 *5 *2)) (-4 *4 (-1068)) - (-4 *5 (-805)) (-4 *2 (-862)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-783)) (-4 *2 (-966 *4 (-543 *5) *5)) - (-5 *1 (-1145 *4 *5 *2)) (-4 *4 (-1068)) (-4 *5 (-862)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-783)) (-5 *2 (-969 *4)) (-5 *1 (-1230 *4)) - (-4 *4 (-1068))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-864 *2)) (-4 *2 (-1068)) (-4 *2 (-374))))) +(((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-656 (-969 *5))) (-5 *4 (-112)) + (-4 *5 (-13 (-860) (-317) (-148) (-1041))) + (-5 *2 (-656 (-1065 *5 *6))) (-5 *1 (-1313 *5 *6 *7)) + (-14 *6 (-656 (-1195))) (-14 *7 (-656 (-1195))))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-656 (-969 *5))) (-5 *4 (-112)) + (-4 *5 (-13 (-860) (-317) (-148) (-1041))) + (-5 *2 (-656 (-1065 *5 *6))) (-5 *1 (-1313 *5 *6 *7)) + (-14 *6 (-656 (-1195))) (-14 *7 (-656 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(-5 *6 (-1191 *4)) - (-4 *4 (-13 (-442 *7) (-27) (-1221))) - (-4 *7 (-13 (-464) (-1057 (-576)) (-148) (-651 (-576)))) - (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2335 (-656 *4)))) - (-5 *1 (-572 *7 *4 *3)) (-4 *3 (-668 *4)) (-4 *3 (-1119)))) - ((*1 *2 *3 *4 *5 *5 *5 *4 *6) - (-12 (-5 *5 (-624 *4)) (-5 *6 (-419 (-1191 *4))) - (-4 *4 (-13 (-442 *7) (-27) (-1221))) - (-4 *7 (-13 (-464) (-1057 (-576)) (-148) (-651 (-576)))) - (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2335 (-656 *4)))) - (-5 *1 (-572 *7 *4 *3)) (-4 *3 (-668 *4)) (-4 *3 (-1119))))) -(((*1 *2 *3 *4 *4 *5) - (-12 (-5 *4 (-624 *3)) (-5 *5 (-1 (-1191 *3) (-1191 *3))) - (-4 *3 (-13 (-27) (-442 *6))) (-4 *6 (-568)) (-5 *2 (-598 *3)) - (-5 *1 (-563 *6 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-464)) (-5 *1 (-1227 *3 *2)) - (-4 *2 (-13 (-442 *3) (-1221)))))) -(((*1 *2 *2) (|partial| -12 (-5 *2 (-326 (-227))) (-5 *1 (-276))))) + (-12 (-4 *1 (-1303 *3 *4)) (-4 *3 (-862)) (-4 *4 (-1068)) + (-5 *2 (-2 (|:| |k| (-831 *3)) (|:| |c| *4)))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-783)) (-5 *1 (-890 *2)) (-4 *2 (-1236)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-783)) (-5 *1 (-892 *2)) (-4 *2 (-1236)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-783)) (-5 *1 (-895 *2)) (-4 *2 (-1236))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-1 (-112) *6 *6)) (-4 *6 (-862)) (-5 *4 (-656 *6)) + (-5 *2 (-2 (|:| |fs| (-112)) (|:| |sd| *4) (|:| |td| (-656 *4)))) + (-5 *1 (-1206 *6)) (-5 *5 (-656 *4))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) - (|:| -1668 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) - (|:| |relerr| (-227)))) + (-12 (-5 *3 (-1259 *5 *4)) (-4 *4 (-832)) (-14 *5 (-1195)) + (-5 *2 (-576)) (-5 *1 (-1133 *4 *5))))) +(((*1 *1 *2) (-12 (-5 *1 (-703 *2)) (-4 *2 (-625 (-874)))))) +(((*1 *2 *3 *4 *5 *3) + (-12 (-5 *4 (-1 *7 *7)) + (-5 *5 + (-1 (-2 (|:| |ans| *6) (|:| -4247 *6) (|:| |sol?| (-112))) (-576) + *6)) + (-4 *6 (-374)) (-4 *7 (-1262 *6)) (-5 *2 - (-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"))) - (-5 *1 (-194))))) + (-3 (-2 (|:| |answer| (-419 *7)) (|:| |a0| *6)) + (-2 (|:| -3160 (-419 *7)) (|:| |coeff| (-419 *7))) "failed")) + (-5 *1 (-586 *6 *7)) (-5 *3 (-419 *7))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-227)) (-5 *4 (-576)) (-5 *2 (-1054)) (-5 *1 (-770))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -3084,55 +3351,43 @@ (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3)))) ((*1 *1 *1) (-4 *1 (-1224)))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-576)) (-5 *2 (-3 "nil" "sqfr" "irred" "prime")) - (-5 *1 (-430 *4)) (-4 *4 (-568))))) -(((*1 *2 *1 *1 *1) - (|partial| -12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1))) - (-4 *1 (-317)))) - ((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -4126 *1))) - (-4 *1 (-317))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-573))))) -(((*1 *2 *1) - (-12 (-4 *1 (-378 *3)) (-4 *3 (-174)) (-4 *3 (-568)) - (-5 *2 (-1191 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-995 *3 *4 *5 *6)) (-4 *3 (-1068)) (-4 *4 (-805)) - (-4 *5 (-862)) (-4 *6 (-1084 *3 *4 *5)) (-4 *3 (-568)) - (-5 *2 (-112))))) -(((*1 *2 *3 *1 *4) - (-12 (-5 *3 (-1159 *5 *6)) (-5 *4 (-1 (-112) *6 *6)) - (-4 *5 (-13 (-1119) (-34))) (-4 *6 (-13 (-1119) (-34))) - (-5 *2 (-112)) (-5 *1 (-1160 *5 *6))))) -(((*1 *2 *1 *3 *3 *3) - (-12 (-5 *3 (-390)) (-5 *2 (-1291)) (-5 *1 (-1288))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-656 *2)) (-5 *1 (-181 *2)) (-4 *2 (-317)))) - ((*1 *2 *3 *2) - (-12 (-5 *3 (-656 (-656 *4))) (-5 *2 (-656 *4)) (-4 *4 (-317)) - (-5 *1 (-181 *4)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-656 *8)) - (-5 *4 - (-656 - (-2 (|:| -2335 (-701 *7)) (|:| |basisDen| *7) - (|:| |basisInv| (-701 *7))))) - (-5 *5 (-783)) (-4 *8 (-1262 *7)) (-4 *7 (-1262 *6)) (-4 *6 (-360)) - (-5 *2 - (-2 (|:| -2335 (-701 *7)) (|:| |basisDen| *7) - (|:| |basisInv| (-701 *7)))) - (-5 *1 (-510 *6 *7 *8)))) - ((*1 *2 *2 *2 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-573))))) +(((*1 *2) (-12 (-5 *2 (-1177)) (-5 *1 (-1205))))) (((*1 *2 *2 *3) - (-12 (-5 *3 (-656 *2)) (-4 *2 (-966 *4 *5 *6)) (-4 *4 (-374)) - (-4 *4 (-464)) (-4 *5 (-805)) (-4 *6 (-862)) - (-5 *1 (-462 *4 *5 *6 *2)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-99 *6)) (-5 *5 (-1 *6 *6)) (-4 *6 (-374)) - (-5 *2 - (-2 (|:| R (-701 *6)) (|:| A (-701 *6)) (|:| |Ainv| (-701 *6)))) - (-5 *1 (-997 *6)) (-5 *3 (-701 *6))))) + (-12 (-5 *3 (-656 *2)) (-4 *2 (-557)) (-5 *1 (-160 *2))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1236)) (-5 *1 (-1151 *4 *2)) + (-4 *2 (-13 (-616 (-576) *4) (-10 -7 (-6 -4462) (-6 -4463)))))) + ((*1 *2 *2) + (-12 (-4 *3 (-862)) (-4 *3 (-1236)) (-5 *1 (-1151 *3 *2)) + (-4 *2 (-13 (-616 (-576) *3) (-10 -7 (-6 -4462) (-6 -4463))))))) +(((*1 *2 *2) + (-12 (-5 *2 (-656 (-656 *6))) (-4 *6 (-966 *3 *5 *4)) + (-4 *3 (-13 (-317) (-148))) (-4 *4 (-13 (-862) (-626 (-1195)))) + (-4 *5 (-805)) (-5 *1 (-941 *3 *4 *5 *6))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-464)) (-4 *6 (-805)) (-4 *7 (-862)) + (-4 *3 (-1084 *5 *6 *7)) (-5 *2 (-656 *4)) + (-5 *1 (-1127 *5 *6 *7 *3 *4)) (-4 *4 (-1090 *5 *6 *7 *3))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-783)) (-5 *3 (-960 *5)) (-4 *5 (-1068)) + (-5 *1 (-1183 *4 *5)) (-14 *4 (-938)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-656 (-783))) (-5 *3 (-783)) (-5 *1 (-1183 *4 *5)) + (-14 *4 (-938)) (-4 *5 (-1068)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-656 (-783))) (-5 *3 (-960 *5)) (-4 *5 (-1068)) + (-5 *1 (-1183 *4 *5)) (-14 *4 (-938))))) +(((*1 *2 *3) + (-12 (-5 *3 (-227)) (-5 *2 (-112)) (-5 *1 (-309 *4 *5)) (-14 *4 *3) + (-14 *5 *3))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-1113 (-855 (-227)))) (-5 *3 (-227)) (-5 *2 (-112)) + (-5 *1 (-315)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-374)) (-4 *4 (-805)) (-4 *5 (-862)) (-5 *2 (-112)) + (-5 *1 (-516 *3 *4 *5 *6)) (-4 *6 (-966 *3 *4 *5))))) +(((*1 *1 *1 *1) (-5 *1 (-112))) ((*1 *1 *1 *1) (-4 *1 (-124)))) +(((*1 *2 *1) (-12 (-4 *1 (-521 *3 *2)) (-4 *3 (-1119)) (-4 *2 (-862))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -3149,60 +3404,38 @@ (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3)))) ((*1 *1 *1) (-4 *1 (-1224)))) -(((*1 *2 *3 *4 *5 *6 *7 *6) - (|partial| -12 - (-5 *5 - (-2 (|:| |contp| *3) - (|:| -1984 (-656 (-2 (|:| |irr| *10) (|:| -3847 (-576))))))) - (-5 *6 (-656 *3)) (-5 *7 (-656 *8)) (-4 *8 (-862)) (-4 *3 (-317)) - (-4 *10 (-966 *3 *9 *8)) (-4 *9 (-805)) - (-5 *2 - (-2 (|:| |polfac| (-656 *10)) (|:| |correct| *3) - (|:| |corrfact| (-656 (-1191 *3))))) - (-5 *1 (-637 *8 *9 *3 *10)) (-5 *4 (-656 (-1191 *3)))))) -(((*1 *2 *1) (-12 (-5 *2 (-1154)) (-5 *1 (-529))))) -(((*1 *1 *2 *3) - (-12 (-5 *1 (-439 *3 *2)) (-4 *3 (-13 (-174) (-38 (-419 (-576))))) - (-4 *2 (-13 (-862) (-21)))))) +(((*1 *2 *1) + (|partial| -12 (-4 *1 (-1248 *3 *2)) (-4 *3 (-1068)) + (-4 *2 (-1277 *3))))) +(((*1 *2) (-12 (-5 *2 (-131)) (-5 *1 (-1205))))) (((*1 *2 *3) - (-12 (-5 *3 (-944)) - (-5 *2 - (-2 (|:| |brans| (-656 (-656 (-960 (-227))))) - (|:| |xValues| (-1113 (-227))) (|:| |yValues| (-1113 (-227))))) - (-5 *1 (-154)))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-944)) (-5 *4 (-419 (-576))) - (-5 *2 - (-2 (|:| |brans| (-656 (-656 (-960 (-227))))) - (|:| |xValues| (-1113 (-227))) (|:| |yValues| (-1113 (-227))))) - (-5 *1 (-154)))) - ((*1 *2 *3) - (-12 - (-5 *2 - (-2 (|:| |brans| (-656 (-656 (-960 (-227))))) - (|:| |xValues| (-1113 (-227))) (|:| |yValues| (-1113 (-227))))) - (-5 *1 (-154)) (-5 *3 (-656 (-960 (-227)))))) - ((*1 *2 *3) - (-12 + (-12 (-4 *1 (-812)) + (-5 *3 + (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) + (|:| |fn| (-1286 (-326 (-227)))) (|:| |yinit| (-656 (-227))) + (|:| |intvals| (-656 (-227))) (|:| |g| (-326 (-227))) + (|:| |abserr| (-227)) (|:| |relerr| (-227)))) + (-5 *2 (-1054))))) +(((*1 *2) + (-12 (-4 *1 (-360)) + (-5 *2 (-656 (-2 (|:| -1825 (-576)) (|:| -3709 (-576)))))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-701 *8)) (-5 *4 (-783)) (-4 *8 (-966 *5 *7 *6)) + (-4 *5 (-13 (-317) (-148))) (-4 *6 (-13 (-862) (-626 (-1195)))) + (-4 *7 (-805)) (-5 *2 - (-2 (|:| |brans| (-656 (-656 (-960 (-227))))) - (|:| |xValues| (-1113 (-227))) (|:| |yValues| (-1113 (-227))))) - (-5 *1 (-154)) (-5 *3 (-656 (-656 (-960 (-227))))))) - ((*1 *1 *2) (-12 (-5 *2 (-656 (-1113 (-390)))) (-5 *1 (-270)))) - ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-270))))) -(((*1 *2 *3) - (-12 (-5 *3 (-656 (-656 (-960 (-227))))) - (-5 *2 (-656 (-1113 (-227)))) (-5 *1 (-945))))) -(((*1 *2 *3 *4 *4 *5 *3 *3 *4 *3) - (-12 (-5 *3 (-576)) (-5 *5 (-701 (-227))) (-5 *4 (-227)) - (-5 *2 (-1054)) (-5 *1 (-764))))) -(((*1 *2 *3) - (-12 (-5 *3 (-656 (-326 (-227)))) (-5 *2 (-112)) (-5 *1 (-276)))) - ((*1 *2 *3) (-12 (-5 *3 (-326 (-227))) (-5 *2 (-112)) (-5 *1 (-276)))) - ((*1 *2 *3) - (-12 (-4 *4 (-568)) (-4 *5 (-805)) (-4 *6 (-862)) (-5 *2 (-112)) - (-5 *1 (-996 *4 *5 *6 *3)) (-4 *3 (-1084 *4 *5 *6))))) -(((*1 *1 *2) (-12 (-5 *2 (-1177)) (-5 *1 (-503))))) + (-656 + (-2 (|:| |det| *8) (|:| |rows| (-656 (-576))) + (|:| |cols| (-656 (-576)))))) + (-5 *1 (-941 *5 *6 *7 *8))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-656 *2)) (-4 *2 (-1084 *4 *5 *6)) (-4 *4 (-568)) + (-4 *5 (-805)) (-4 *6 (-862)) (-5 *1 (-996 *4 *5 *6 *2))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-938)) (-5 *2 (-1291)) (-5 *1 (-1287)))) + ((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-938)) (-5 *2 (-1291)) (-5 *1 (-1288))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-624 *1)) (-4 *1 (-312))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -3222,22 +3455,21 @@ (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3)))) ((*1 *1 *1) (-4 *1 (-1224)))) -(((*1 *2 *2) - (|partial| -12 (-5 *2 (-419 *4)) (-4 *4 (-1262 *3)) - (-4 *3 (-13 (-374) (-148) (-1057 (-576)))) (-5 *1 (-580 *3 *4))))) -(((*1 *2 *3 *4 *2 *2 *5) - 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*1 (-841))))) +(((*1 *2 *1) + (-12 (-4 *1 (-346 *3 *4 *5 *6)) (-4 *3 (-374)) (-4 *4 (-1262 *3)) + (-4 *5 (-1262 (-419 *4))) (-4 *6 (-353 *3 *4 *5)) (-5 *2 (-112))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-1195)) (-4 *4 (-13 (-317) (-1057 (-576)) (-651 (-576)) (-148))) @@ -3246,18 +3478,34 @@ ((*1 *1 *1) (-5 *1 (-874))) ((*1 *2 *3) (-12 (-5 *2 (-1176 *3)) (-5 *1 (-1179 *3)) (-4 *3 (-1068))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1195)) (-5 *2 (-548)) (-5 *1 (-547 *4)) - (-4 *4 (-1236))))) -(((*1 *1 *1 *1 *1 *1) - (-12 (-4 *1 (-1084 *2 *3 *4)) (-4 *2 (-1068)) (-4 *3 (-805)) - (-4 *4 (-862)) (-4 *2 (-568))))) -(((*1 *1 *2 *3 *4) - (-12 (-5 *3 (-576)) (-5 *4 (-3 "nil" "sqfr" "irred" "prime")) - (-5 *1 (-430 *2)) (-4 *2 (-568))))) -(((*1 *1 *2) - (-12 (-5 *2 (-656 (-656 *3))) (-4 *3 (-1119)) (-5 *1 (-1207 *3))))) -(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-135))))) +(((*1 *2 *3 *4 *4) + (-12 (-5 *4 (-783)) (-4 *5 (-360)) (-4 *6 (-1262 *5)) + (-5 *2 + (-656 + (-2 (|:| -2437 (-701 *6)) (|:| |basisDen| *6) + (|:| |basisInv| (-701 *6))))) + (-5 *1 (-510 *5 *6 *7)) + (-5 *3 + (-2 (|:| -2437 (-701 *6)) (|:| |basisDen| *6) + (|:| |basisInv| (-701 *6)))) + (-4 *7 (-1262 *6))))) +(((*1 *2 *2 *3 *3) + (-12 (-5 *2 (-1176 *4)) (-5 *3 (-576)) (-4 *4 (-1068)) + (-5 *1 (-1179 *4)))) + ((*1 *1 *1 *2 *2) + (-12 (-5 *2 (-576)) (-5 *1 (-1278 *3 *4 *5)) (-4 *3 (-1068)) + (-14 *4 (-1195)) (-14 *5 *3)))) +(((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-565))))) +(((*1 *1 *1 *1) (-4 *1 (-312))) ((*1 *1 *1) (-4 *1 (-312)))) +(((*1 *2 *3 *4 *5 *6 *7 *8 *9) + (|partial| -12 (-5 *4 (-656 *11)) (-5 *5 (-656 (-1191 *9))) + (-5 *6 (-656 *9)) (-5 *7 (-656 *12)) (-5 *8 (-656 (-783))) + (-4 *11 (-862)) (-4 *9 (-317)) (-4 *12 (-966 *9 *10 *11)) + (-4 *10 (-805)) (-5 *2 (-656 (-1191 *12))) + (-5 *1 (-719 *10 *11 *9 *12)) (-5 *3 (-1191 *12))))) +(((*1 *2 *2) + (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) + (-4 *2 (-13 (-442 *3) (-1021)))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -3278,67 +3526,43 @@ (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3)))) ((*1 *1 *1) (-4 *1 (-1224)))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-1176 *4)) (-5 *3 (-1 *4 (-576))) (-4 *4 (-1068)) - (-5 *1 (-1179 *4))))) -(((*1 *2 *3) - (-12 (-5 *3 (-701 (-419 (-969 (-576))))) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) + (-12 (-5 *3 (-1 (-390) (-390))) (-5 *4 (-390)) (-5 *2 - (-656 - (-2 (|:| |radval| (-326 (-576))) (|:| |radmult| (-576)) - (|:| |radvect| (-656 (-701 (-326 (-576)))))))) - (-5 *1 (-1050))))) -(((*1 *2 *2 *2 *2 *2 *3) - (-12 (-5 *2 (-701 *4)) (-5 *3 (-783)) (-4 *4 (-1068)) - (-5 *1 (-702 *4))))) -(((*1 *2 *2) - (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) - (-4 *2 (-13 (-442 *3) (-1021)))))) -(((*1 *2 *2) - (-12 (-5 *2 (-656 *7)) (-4 *7 (-1090 *3 *4 *5 *6)) (-4 *3 (-464)) - (-4 *4 (-805)) (-4 *5 (-862)) (-4 *6 (-1084 *3 *4 *5)) - (-5 *1 (-1007 *3 *4 *5 *6 *7)))) - ((*1 *2 *2) - (-12 (-5 *2 (-656 *7)) (-4 *7 (-1090 *3 *4 *5 *6)) (-4 *3 (-464)) - (-4 *4 (-805)) (-4 *5 (-862)) (-4 *6 (-1084 *3 *4 *5)) - (-5 *1 (-1126 *3 *4 *5 *6 *7))))) + (-2 (|:| -3103 *4) (|:| -3312 *4) (|:| |totalpts| (-576)) + (|:| |success| (-112)))) + (-5 *1 (-801)) (-5 *5 (-576))))) +(((*1 *1 *1) + (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1068))))) +(((*1 *1 *2) (-12 (-5 *2 (-1177)) (-5 *1 (-541)))) + ((*1 *1 *2) (-12 (-5 *2 (-400)) (-5 *1 (-541))))) +(((*1 *1) (-12 (-4 *1 (-339 *2)) (-4 *2 (-379)) (-4 *2 (-374))))) +(((*1 *2 *1 *1) + (-12 (-4 *1 (-1029 *3)) (-4 *3 (-1236)) (-4 *3 (-1119)) + (-5 *2 (-112))))) (((*1 *2 *3) - (-12 (-5 *3 (-419 *5)) (-4 *5 (-1262 *4)) (-4 *4 (-568)) - (-4 *4 (-1068)) (-4 *2 (-1277 *4)) (-5 *1 (-1280 *4 *5 *6 *2)) - (-4 *6 (-668 *5))))) + (-12 (-5 *2 (-656 (-1177))) (-5 *1 (-841)) (-5 *3 (-1177))))) (((*1 *1 *1) (-12 (-5 *1 (-512 *2)) (-14 *2 (-576)))) ((*1 *1 *1) (-5 *1 (-1139)))) -(((*1 *2 *1) - (-12 (-4 *3 (-174)) (-4 *2 (-23)) (-5 *1 (-299 *3 *4 *2 *5 *6 *7)) - (-4 *4 (-1262 *3)) (-14 *5 (-1 *4 *4 *2)) - (-14 *6 (-1 (-3 *2 "failed") *2 *2)) - (-14 *7 (-1 (-3 *4 "failed") *4 *4 *2)))) - ((*1 *2 *1) - (-12 (-4 *2 (-23)) (-5 *1 (-723 *3 *2 *4 *5 *6)) (-4 *3 (-174)) - (-14 *4 (-1 *3 *3 *2)) (-14 *5 (-1 (-3 *2 "failed") *2 *2)) - (-14 *6 (-1 (-3 *3 "failed") *3 *3 *2)))) - ((*1 *2) - (-12 (-4 *2 (-1262 *3)) (-5 *1 (-724 *3 *2)) (-4 *3 (-1068)))) - ((*1 *2 *1) - (-12 (-4 *2 (-23)) (-5 *1 (-727 *3 *2 *4 *5 *6)) (-4 *3 (-174)) - (-14 *4 (-1 *3 *3 *2)) (-14 *5 (-1 (-3 *2 "failed") *2 *2)) - (-14 *6 (-1 (-3 *3 "failed") *3 *3 *2)))) - ((*1 *2) (-12 (-4 *1 (-881 *3)) (-5 *2 (-576))))) -(((*1 *2 *2) - (-12 - (-5 *2 - (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) - (|:| |xpnt| (-576)))) - (-4 *4 (-13 (-1262 *3) (-568) (-10 -8 (-15 -3496 ($ $ $))))) - (-4 *3 (-568)) (-5 *1 (-1265 *3 *4))))) +(((*1 *1 *1) + (-12 (-4 *1 (-966 *2 *3 *4)) (-4 *2 (-1068)) (-4 *3 (-805)) + (-4 *4 (-862)) (-4 *2 (-464)))) + ((*1 *2 *3 *1) + (-12 (-4 *4 (-464)) (-4 *5 (-805)) (-4 *6 (-862)) + (-4 *3 (-1084 *4 *5 *6)) + (-5 *2 (-656 (-2 (|:| |val| *3) (|:| -3986 *1)))) + (-4 *1 (-1090 *4 *5 *6 *3)))) + ((*1 *1 *1) (-4 *1 (-1240))) + ((*1 *2 *2) + (-12 (-4 *3 (-568)) (-5 *1 (-1265 *3 *2)) + (-4 *2 (-13 (-1262 *3) (-568) (-10 -8 (-15 -3495 ($ $ $)))))))) (((*1 *2 *3) - (-12 (-5 *3 (-656 *7)) (-4 *7 (-966 *4 *5 *6)) (-4 *6 (-626 (-1195))) - (-4 *4 (-374)) (-4 *5 (-805)) (-4 *6 (-862)) - (-5 *2 (-1184 (-656 (-969 *4)) (-656 (-304 (-969 *4))))) - (-5 *1 (-516 *4 *5 *6 *7))))) + (-12 (-4 *1 (-937)) (-5 *2 (-2 (|:| -1713 (-656 *1)) (|:| -4126 *1))) + (-5 *3 (-656 *1))))) (((*1 *2) (-12 (-4 *1 (-353 *3 *4 *5)) (-4 *3 (-1240)) (-4 *4 (-1262 *3)) - (-4 *5 (-1262 (-419 *4))) (-5 *2 (-112))))) + (-4 *5 (-1262 (-419 *4))) (-5 *2 (-701 (-419 *4)))))) +(((*1 *2) (-12 (-5 *2 (-656 (-1195))) (-5 *1 (-105))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -3359,530 +3583,600 @@ (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3)))) ((*1 *1 *1) (-4 *1 (-1224)))) -(((*1 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(-227))) (-5 *4 (-227)) - (-5 *2 (-1054)) (-5 *1 (-767))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-1286 *5)) (-4 *5 (-804)) (-5 *2 (-112)) - (-5 *1 (-857 *4 *5)) (-14 *4 (-783))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-656 (-1195))) (-4 *4 (-1119)) - (-4 *5 (-13 (-1068) (-899 *4) (-626 (-905 *4)))) - (-5 *1 (-54 *4 *5 *2)) - (-4 *2 (-13 (-442 *5) (-899 *4) (-626 (-905 *4))))))) -(((*1 *2 *1 *3) - (-12 (-4 *1 (-872)) (-5 *2 (-703 (-130))) (-5 *3 (-130))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-145))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-783)) (-4 *5 (-568)) - (-5 *2 - (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3))) - (-5 *1 (-988 *5 *3)) (-4 *3 (-1262 *5))))) -(((*1 *1 *2) (-12 (-5 *2 (-158)) (-5 *1 (-886))))) + (-12 (-4 *3 (-13 (-568) (-1057 (-576)))) (-5 *2 (-1291)) + (-5 *1 (-445 *3 *4)) (-4 *4 (-442 *3))))) (((*1 *1 *1) (-5 *1 (-48))) ((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-59 *5)) (-4 *5 (-1236)) @@ -4286,7 +4585,7 @@ (-4 *2 (-1236)))) ((*1 *2 *3) (-12 (-4 *4 (-1068)) - (-5 *2 (-2 (|:| -2843 (-1191 *4)) (|:| |deg| (-938)))) + (-5 *2 (-2 (|:| -3723 (-1191 *4)) (|:| |deg| (-938)))) (-5 *1 (-223 *4 *5)) (-5 *3 (-1191 *4)) (-4 *5 (-568)))) ((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) @@ -4361,51 +4660,47 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-831 *4)) (-4 *4 (-862)) (-4 *1 (-1303 *4 *3)) (-4 *3 (-1068))))) +(((*1 *1 *1) + (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1068))))) +(((*1 *2 *2 *3 *3 *4) + (-12 (-5 *4 (-783)) (-4 *3 (-568)) (-5 *1 (-988 *3 *2)) + (-4 *2 (-1262 *3))))) +(((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-377 *3 *4)) + (-4 *3 (-378 *4)))) + ((*1 *2) (-12 (-4 *1 (-378 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1002 *2)) (-4 *2 (-1221))))) (((*1 *2 *3) - (-12 (-5 *3 (-1207 (-656 *4))) (-4 *4 (-862)) - (-5 *2 (-656 (-656 *4))) (-5 *1 (-1206 *4))))) -(((*1 *1 *2 *3) (-12 (-5 *3 (-576)) (-5 *1 (-430 *2)) (-4 *2 (-568))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |lfn| (-656 (-326 (-227)))) (|:| -3537 (-656 (-227))))) - (-5 *2 (-390)) (-5 *1 (-276)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1286 (-326 (-227)))) (-5 *2 (-390)) (-5 *1 (-315))))) -(((*1 *2 *3 *3 *3 *4 *5 *3 *6) - (-12 (-5 *3 (-576)) (-5 *4 (-701 (-227))) (-5 *5 (-227)) - (-5 *6 (-3 (|:| |fn| (-400)) (|:| |fp| (-74 FCN)))) (-5 *2 (-1054)) - (-5 *1 (-758))))) -(((*1 *1 *2) - (-12 (-5 *2 (-656 (-2 (|:| |gen| *3) (|:| -4101 *4)))) - (-4 *3 (-1119)) (-4 *4 (-23)) (-14 *5 *4) (-5 *1 (-661 *3 *4 *5))))) -(((*1 *2 *3 *3 *4 *4 *5 *4 *5 *4 *4 *5 *4) - (-12 (-5 *3 (-1177)) (-5 *4 (-576)) (-5 *5 (-701 (-227))) - (-5 *2 (-1054)) (-5 *1 (-766))))) + (-12 (-5 *3 (-656 *2)) (-4 *2 (-442 *4)) (-5 *1 (-159 *4 *2)) + (-4 *4 (-568))))) (((*1 *2 *1) - (-12 (-4 *1 (-353 *3 *4 *5)) (-4 *3 (-1240)) (-4 *4 (-1262 *3)) - (-4 *5 (-1262 (-419 *4))) (-5 *2 (-112))))) -(((*1 *2 *3 *4 *4 *5 *3 *3 *4 *3 *3 *3) - (-12 (-5 *3 (-576)) (-5 *5 (-701 (-227))) (-5 *4 (-227)) - (-5 *2 (-1054)) (-5 *1 (-764))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1113 (-855 (-227)))) (-5 *2 (-227)) (-5 *1 (-194)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1113 (-855 (-227)))) (-5 *2 (-227)) (-5 *1 (-310)))) + (-12 (-4 *4 (-1119)) (-5 *2 (-902 *3 *4)) (-5 *1 (-898 *3 *4 *5)) + (-4 *3 (-1119)) (-4 *5 (-678 *4)))) ((*1 *2 *3) - (-12 (-5 *3 (-1113 (-855 (-227)))) (-5 *2 (-227)) (-5 *1 (-315))))) -(((*1 *2 *1) - (-12 (-5 *2 (-703 (-885 (-983 *3) (-983 *3)))) (-5 *1 (-983 *3)) - (-4 *3 (-1119))))) -(((*1 *2 *1) - (-12 (-4 *1 (-393 *3 *4)) (-4 *3 (-1068)) (-4 *4 (-1119)) - (-5 *2 (-656 (-2 (|:| |k| *4) (|:| |c| *3)))))) - ((*1 *2 *1) - (-12 (-5 *2 (-656 (-2 (|:| |k| (-906 *3)) (|:| |c| *4)))) - (-5 *1 (-639 *3 *4 *5)) (-4 *3 (-862)) - (-4 *4 (-13 (-174) (-729 (-419 (-576))))) (-14 *5 (-938)))) - ((*1 *2 *1) - (-12 (-5 *2 (-656 (-684 *3))) (-5 *1 (-906 *3)) (-4 *3 (-862))))) + (-12 (-5 *3 (-983 *4)) (-4 *4 (-1119)) (-5 *2 (-1121 *4)) + (-5 *1 (-984 *4))))) +(((*1 *2 *1 *1 *1) + (|partial| -12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1))) + (-4 *1 (-317)))) + ((*1 *2 *1 *1) + (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -4126 *1))) + (-4 *1 (-317))))) +(((*1 *2 *3) + (-12 (-5 *2 (-112)) (-5 *1 (-454 *3)) (-4 *3 (-1262 (-576)))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *5 (-112)) (-4 *4 (-13 (-374) (-860))) (-5 *2 (-430 *3)) + (-5 *1 (-183 *4 *3)) (-4 *3 (-1262 (-171 *4))))) + ((*1 *2 *3 *4) + (-12 (-4 *4 (-13 (-374) (-860))) (-5 *2 (-430 *3)) + (-5 *1 (-183 *4 *3)) (-4 *3 (-1262 (-171 *4)))))) +(((*1 *2 *3 *3 *4) + (-12 (-4 *5 (-464)) (-4 *6 (-805)) (-4 *7 (-862)) + (-4 *3 (-1084 *5 *6 *7)) + (-5 *2 (-656 (-2 (|:| |val| *3) (|:| -3986 *4)))) + (-5 *1 (-1127 *5 *6 *7 *3 *4)) (-4 *4 (-1090 *5 *6 *7 *3))))) +(((*1 *2 *3) + (-12 (-4 *4 (-568)) (-5 *2 (-783)) (-5 *1 (-43 *4 *3)) + (-4 *3 (-429 *4))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-624 *6)) (-4 *6 (-13 (-442 *5) (-27) (-1221))) (-4 *5 (-13 (-464) (-1057 (-576)) (-148) (-651 (-576)))) @@ -4425,59 +4720,44 @@ (-12 (-4 *2 (-966 *3 *4 *5)) (-5 *1 (-1053 *3 *4 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|den| *4)))))) +(((*1 *2 *1) (-12 (-5 *2 (-834)) (-5 *1 (-833))))) +(((*1 *1 *1) + (|partial| -12 (-5 *1 (-1160 *2 *3)) (-4 *2 (-13 (-1119) (-34))) + (-4 *3 (-13 (-1119) (-34)))))) +(((*1 *2 *1) (-12 (-5 *2 (-656 (-885 (-1200) (-783)))) (-5 *1 (-343))))) +(((*1 *2 *3 *4 *5 *6 *7 *6) + (|partial| -12 + (-5 *5 + (-2 (|:| |contp| *3) + (|:| -2089 (-656 (-2 (|:| |irr| *10) (|:| -4270 (-576))))))) + (-5 *6 (-656 *3)) (-5 *7 (-656 *8)) (-4 *8 (-862)) (-4 *3 (-317)) + (-4 *10 (-966 *3 *9 *8)) (-4 *9 (-805)) + (-5 *2 + (-2 (|:| |polfac| (-656 *10)) (|:| |correct| *3) + (|:| |corrfact| (-656 (-1191 *3))))) + (-5 *1 (-637 *8 *9 *3 *10)) (-5 *4 (-656 (-1191 *3)))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-374) (-860))) (-5 *1 (-183 *3 *2)) + (-4 *2 (-1262 (-171 *3)))))) +(((*1 *2 *1) (-12 (-5 *2 (-656 (-960 (-227)))) (-5 *1 (-1287))))) +(((*1 *1 *1 *2) (-12 (-5 *1 (-661 *2 *3 *4)) (-4 *2 (-1119)) (-4 *3 (-23)) (-14 *4 *3)))) -(((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *4 (-1195)) (-5 *5 (-656 (-419 (-969 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(-5 *2 (-656 (-2 (|:| -1567 (-783)) (|:| -2391 *4) (|:| |num| *4)))) + (-5 *2 (-656 (-2 (|:| -3709 (-783)) (|:| -2391 *4) (|:| |num| *4)))) (-4 *4 (-1262 *3)) (-4 *3 (-13 (-374) (-148))) (-5 *1 (-411 *3 *4)))) ((*1 *1 *2 *3 *4) (-12 (-5 *2 (-3 (|:| |fst| (-446)) (|:| -2914 "void"))) @@ -4914,8 +5109,8 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-725 *2 *3 *4)) (-4 *2 (-862)) (-4 *3 (-1119)) (-14 *4 - (-1 (-112) (-2 (|:| -3222 *2) (|:| -1567 *3)) - (-2 (|:| -3222 *2) (|:| -1567 *3)))))) + (-1 (-112) (-2 (|:| -3222 *2) (|:| -3709 *3)) + (-2 (|:| -3222 *2) (|:| -3709 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-518)) (-5 *3 (-1137)) (-5 *1 (-850)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-885 *2 *3)) (-4 *2 (-1236)) (-4 *3 (-1236)))) @@ -4927,11 +5122,11 @@ (-5 *2 (-656 (-1159 *3 *5))) (-5 *1 (-1159 *3 *5)) (-4 *3 (-13 (-1119) (-34))))) ((*1 *2 *3) - (-12 (-5 *3 (-656 (-2 (|:| |val| *4) (|:| -3985 *5)))) + (-12 (-5 *3 (-656 (-2 (|:| |val| *4) (|:| -3986 *5)))) (-4 *4 (-13 (-1119) (-34))) (-4 *5 (-13 (-1119) (-34))) (-5 *2 (-656 (-1159 *4 *5))) (-5 *1 (-1159 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -3985 *4))) + (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -3986 *4))) (-4 *3 (-13 (-1119) (-34))) (-4 *4 (-13 (-1119) (-34))) (-5 *1 (-1159 *3 *4)))) ((*1 *1 *2 *3) @@ -4968,54 +5163,45 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-783)) (-4 *1 (-1274 *3)) (-4 *3 (-1236)))) ((*1 *2 *1) (-12 (-4 *1 (-1274 *2)) (-4 *2 (-1236))))) -(((*1 *2 *3 *3 *4 *3) - (-12 (-5 *3 (-576)) (-5 *4 (-701 (-227))) (-5 *2 (-1054)) - (-5 *1 (-759))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-656 (-874))) (-5 *1 (-1195))))) -(((*1 *1 *1 *1) - (-12 (-5 *1 (-656 *2)) (-4 *2 (-1119)) (-4 *2 (-1236))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-783)) (-4 *5 (-1068)) (-4 *2 (-1262 *5)) - (-5 *1 (-1280 *5 *2 *6 *3)) (-4 *6 (-668 *2)) (-4 *3 (-1277 *5))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1286 (-656 (-2 (|:| -3102 *4) (|:| -3222 (-1139)))))) - (-4 *4 (-360)) (-5 *2 (-783)) (-5 *1 (-357 *4)))) - ((*1 *2) - (-12 (-5 *2 (-783)) (-5 *1 (-362 *3 *4)) (-14 *3 (-938)) - (-14 *4 (-938)))) - ((*1 *2) - (-12 (-5 *2 (-783)) (-5 *1 (-363 *3 *4)) (-4 *3 (-360)) - (-14 *4 - (-3 (-1191 *3) - (-1286 (-656 (-2 (|:| -3102 *3) (|:| -3222 (-1139))))))))) - ((*1 *2) - (-12 (-5 *2 (-783)) (-5 *1 (-364 *3 *4)) (-4 *3 (-360)) - (-14 *4 (-938))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) - (-12 (-5 *3 (-1 (-390) (-390))) (-5 *4 (-390)) - (-5 *2 - (-2 (|:| -3102 *4) (|:| -3311 *4) (|:| |totalpts| (-576)) - (|:| |success| (-112)))) - (-5 *1 (-801)) (-5 *5 (-576))))) -(((*1 *2 *3 *4 *4 *3) - (-12 (-5 *3 (-576)) (-5 *4 (-701 (-227))) (-5 *2 (-1054)) - (-5 *1 (-759))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-227)) (-5 *1 (-228)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-171 (-227))) (-5 *1 (-228)))) +(((*1 *1 *1) (-5 *1 (-1082)))) +(((*1 *1 *1) (-5 *1 (-227))) + ((*1 *2 *2) (-12 (-5 *2 (-227)) (-5 *1 (-228)))) + ((*1 *2 *2) (-12 (-5 *2 (-171 (-227))) (-5 *1 (-228)))) + ((*1 *2 *2) + (-12 (-4 *3 (-568)) (-5 *1 (-443 *3 *2)) (-4 *2 (-442 *3)))) ((*1 *2 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-443 *3 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(-5 *2 (-1191 *1)) - (-4 *1 (-339 *4)))) - ((*1 *2 *1) (-12 (-4 *1 (-339 *3)) (-4 *3 (-374)) (-5 *2 (-1191 *3)))) - ((*1 *2 *1) - (-12 (-4 *1 (-381 *3 *2)) (-4 *3 (-174)) (-4 *3 (-374)) - (-4 *2 (-1262 *3)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1286 *4)) (-4 *4 (-360)) (-5 *2 (-1191 *4)) - (-5 *1 (-540 *4))))) + (-12 (-4 *1 (-566 *3)) (-4 *3 (-13 (-416) (-1221))) (-5 *2 (-112))))) +(((*1 *2 *1) + (-12 (-14 *3 (-656 (-1195))) (-4 *4 (-174)) + (-4 *5 (-243 (-3500 *3) (-783))) + (-14 *6 + (-1 (-112) (-2 (|:| -3222 *2) (|:| -3709 *5)) + (-2 (|:| -3222 *2) (|:| -3709 *5)))) + (-4 *2 (-862)) (-5 *1 (-473 *3 *4 *2 *5 *6 *7)) + (-4 *7 (-966 *4 *5 (-876 *3)))))) +(((*1 *2 *2) + (|partial| -12 (-4 *3 (-1236)) (-5 *1 (-184 *3 *2)) + (-4 *2 (-686 *3))))) (((*1 *1 *2) (-12 (-5 *2 (-1286 *3)) (-4 *3 (-374)) (-14 *6 (-1286 (-701 *3))) (-5 *1 (-44 *3 *4 *5 *6)) (-14 *4 (-938)) (-14 *5 (-656 (-1195))))) @@ -5129,21 +5315,21 @@ ((*1 *1 *2) (-12 (-4 *1 (-385 *2 *3)) (-4 *2 (-862)) (-4 *3 (-174)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1199)) (|:| -4348 (-656 (-340))))) + (-5 *2 (-2 (|:| |localSymbols| (-1199)) (|:| -4346 (-656 (-340))))) (-4 *1 (-394)))) ((*1 *1 *2) (-12 (-5 *2 (-340)) (-4 *1 (-394)))) ((*1 *1 *2) (-12 (-5 *2 (-656 (-340))) (-4 *1 (-394)))) ((*1 *1 *2) (-12 (-5 *2 (-701 (-711))) (-4 *1 (-394)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1199)) (|:| -4348 (-656 (-340))))) + (-5 *2 (-2 (|:| |localSymbols| (-1199)) (|:| -4346 (-656 (-340))))) (-4 *1 (-395)))) ((*1 *1 *2) (-12 (-5 *2 (-340)) (-4 *1 (-395)))) ((*1 *1 *2) (-12 (-5 *2 (-656 (-340))) (-4 *1 (-395)))) ((*1 *2 *3) (-12 (-5 *2 (-406)) (-5 *1 (-405 *3)) (-4 *3 (-1119)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1199)) (|:| -4348 (-656 (-340))))) + (-5 *2 (-2 (|:| |localSymbols| (-1199)) (|:| -4346 (-656 (-340))))) (-4 *1 (-408)))) ((*1 *1 *2) (-12 (-5 *2 (-340)) (-4 *1 (-408)))) ((*1 *1 *2) (-12 (-5 *2 (-656 (-340))) (-4 *1 (-408)))) @@ -5197,7 +5383,7 @@ (-14 *5 (-656 (-1195))) (-14 *6 (-1199)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1199)) (|:| -4348 (-656 (-340))))) + (-5 *2 (-2 (|:| |localSymbols| (-1199)) (|:| -4346 (-656 (-340))))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1195)) (-14 *4 (-3 (|:| |fst| (-446)) (|:| -2914 "void"))) (-14 *5 (-656 (-1195))) (-14 *6 (-1199)))) @@ -5234,14 +5420,14 @@ ((*1 *1 *2) (-12 (-5 *2 (-446)) (-5 *1 (-449)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1199)) (|:| -4348 (-656 (-340))))) + (-5 *2 (-2 (|:| |localSymbols| (-1199)) (|:| -4346 (-656 (-340))))) (-4 *1 (-452)))) ((*1 *1 *2) (-12 (-5 *2 (-340)) (-4 *1 (-452)))) ((*1 *1 *2) (-12 (-5 *2 (-656 (-340))) (-4 *1 (-452)))) ((*1 *1 *2) (-12 (-5 *2 (-1286 (-711))) (-4 *1 (-452)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1199)) (|:| -4348 (-656 (-340))))) + (-5 *2 (-2 (|:| |localSymbols| (-1199)) (|:| -4346 (-656 (-340))))) (-4 *1 (-453)))) ((*1 *1 *2) (-12 (-5 *2 (-340)) (-4 *1 (-453)))) ((*1 *1 *2) (-12 (-5 *2 (-656 (-340))) (-4 *1 (-453)))) @@ -5319,25 +5505,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) - (|:| -1668 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) + (|:| -2104 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| |mdnia| (-2 (|:| |fn| (-326 (-227))) - (|:| -1668 (-656 (-1113 (-855 (-227))))) + (|:| -2104 (-656 (-1113 (-855 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))))) (-5 *1 (-781)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-326 (-227))) - (|:| -1668 (-656 (-1113 (-855 (-227))))) (|:| |abserr| (-227)) + (|:| -2104 (-656 (-1113 (-855 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-781)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) - (|:| -1668 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) + (|:| -2104 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-781)))) ((*1 *2 *3) (-12 (-5 *2 (-786)) (-5 *1 (-785 *3)) (-4 *3 (-1236)))) @@ -5481,80 +5667,109 @@ ((*1 *2 *3 *2 *2 *4 *5) (-12 (-5 *4 (-99 *2)) (-5 *5 (-1 *2 *2)) (-4 *2 (-1068)) (-5 *1 (-865 *2 *3)) (-4 *3 (-864 *2))))) -(((*1 *2) (-12 (-5 *2 (-886)) (-5 *1 (-1289)))) - ((*1 *2 *2) (-12 (-5 *2 (-886)) (-5 *1 (-1289))))) -(((*1 *2 *1 *3) (-12 (-4 *1 (-34)) (-5 *3 (-783)) (-5 *2 (-112)))) - ((*1 *2 *3 *3) - (|partial| -12 (-5 *2 (-112)) (-5 *1 (-1237 *3)) (-4 *3 (-1119)))) - ((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-1 (-112) *3 *3)) (-4 *3 (-1119)) (-5 *2 (-112)) - (-5 *1 (-1237 *3))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-576)) (-5 *2 (-112)) (-5 *1 (-565))))) -(((*1 *2 *1 *1) - (-12 (-4 *3 (-374)) (-4 *3 (-1068)) - (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -4126 *1))) - (-4 *1 (-864 *3))))) -(((*1 *1 *1) (-4 *1 (-641))) - ((*1 *2 *2) - (-12 (-4 *3 (-568)) (-5 *1 (-642 *3 *2)) - (-4 *2 (-13 (-442 *3) (-1021) (-1221)))))) -(((*1 *1 *1 *1) (-4 *1 (-673)))) -(((*1 *2 *1) - (-12 (-4 *1 (-1303 *3 *4)) (-4 *3 (-862)) (-4 *4 (-1068)) - (-5 *2 (-831 *3)))) - ((*1 *2 *1) - (-12 (-4 *2 (-858)) (-5 *1 (-1309 *3 *2)) (-4 *3 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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| (-1176 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2104 + (-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 (-571)))) + ((*1 *2 *1) + (-12 (-4 *1 (-616 *3 *4)) (-4 *3 (-1119)) (-4 *4 (-1236)) + (-5 *2 (-656 *4))))) +(((*1 *2) (-12 (-5 *2 (-1291)) (-5 *1 (-571))))) +(((*1 *2 *2 *2 *2 *2 *2) + (-12 (-4 *2 (-13 (-374) (-10 -8 (-15 ** ($ $ (-419 (-576))))))) + (-5 *1 (-1147 *3 *2)) (-4 *3 (-1262 *2))))) +(((*1 *2 *3 *2) + (-12 (-5 *3 (-656 (-701 *4))) (-5 *2 (-701 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(-174)))) + ((*1 *2 *2 *3) + (-12 + (-5 *2 + (-516 (-419 (-576)) (-245 *5 (-783)) (-876 *4) + (-253 *4 (-419 (-576))))) + (-5 *3 (-656 (-876 *4))) (-14 *4 (-656 (-1195))) (-14 *5 (-783)) + (-5 *1 (-517 *4 *5))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1153 *3)) (-4 *3 (-1068)) (-5 *2 (-656 (-173)))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-227)) (-5 *4 (-576)) (-5 *2 (-1054)) (-5 *1 (-770))))) (((*1 *1 *2 *2 *3) (-12 (-5 *2 (-576)) (-5 *3 (-938)) (-4 *1 (-416)))) ((*1 *1 *2 *2) (-12 (-5 *2 (-576)) (-4 *1 (-416)))) ((*1 *2 *1) @@ -8063,8 +8227,8 @@ (-12 (-5 *1 (-216 *2)) (-4 *2 (-13 (-862) - (-10 -8 (-15 -2794 ((-1177) $ (-1195))) (-15 -1971 ((-1291) $)) - (-15 -1657 ((-1291) $))))))) + (-10 -8 (-15 -2794 ((-1177) $ (-1195))) (-15 -1970 ((-1291) $)) + (-15 -2023 ((-1291) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-304 *2)) (-4 *2 (-21)) (-4 *2 (-1236)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-304 *2)) (-4 *2 (-21)) (-4 *2 (-1236)))) ((*1 *1 *1 *1) @@ -8100,62 +8264,46 @@ (-12 (-5 *2 (-960 *3)) (-4 *1 (-1153 *3)) (-4 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$))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1008)) (-5 *1 (-216 *3)) (-4 *3 (-13 (-862) - (-10 -8 (-15 -2794 ((-1177) $ (-1195))) (-15 -1971 ((-1291) $)) - (-15 -1657 ((-1291) $))))))) + (-10 -8 (-15 -2794 ((-1177) $ (-1195))) (-15 -1970 ((-1291) $)) + (-15 -2023 ((-1291) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-783)) (-5 *1 (-250 *4)) (-4 *4 (-862)))) ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-250 *3)) (-4 *3 (-862)))) @@ -9604,70 +9661,131 @@ (-12 (-5 *2 "rest") (-4 *1 (-1274 *3)) (-4 *3 (-1236)))) ((*1 *2 *1 *3) (-12 (-5 *3 "first") (-4 *1 (-1274 *2)) (-4 *2 (-1236))))) -(((*1 *2 *1) (-12 (-5 *2 (-1291)) (-5 *1 (-834))))) -(((*1 *2 *1) (-12 (-5 *2 (-1291)) (-5 *1 (-834))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-227)) (-5 *5 (-576)) (-5 *2 (-1231 *3)) - (-5 *1 (-802 *3)) (-4 *3 (-993)))) - ((*1 *1 *2 *3 *4) - (-12 (-5 *3 (-656 (-656 (-960 (-227))))) (-5 *4 (-112)) - (-5 *1 (-1231 *2)) (-4 *2 (-993))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-1084 *2 *3 *4)) (-4 *2 (-1068)) (-4 *3 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- (-12 (-5 *2 (-1191 (-507))) (-5 *3 (-624 (-507))) (-5 *1 (-507)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-1286 *4)) (-5 *3 (-938)) (-4 *4 (-360)) - (-5 *1 (-540 *4)))) + (-12 (-5 *2 (-112)) (-5 *1 (-845 *3)) (-4 *3 (-557)) (-4 *3 (-1119)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-855 *3)) (-4 *3 (-557)) (-4 *3 (-1119)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1016 *3)) (-4 *3 (-174)) (-4 *3 (-557)) (-5 *2 (-112)))) ((*1 *2 *3) - (-12 (-4 *4 (-464)) (-4 *5 (-736 *4 *2)) (-4 *2 (-1262 *4)) - (-5 *1 (-787 *4 *2 *5 *3)) (-4 *3 (-1262 *5)))) - ((*1 *2 *1) (-12 (-4 *1 (-809 *2)) (-4 *2 (-174)))) - ((*1 *2 *1) (-12 (-4 *1 (-1016 *2)) (-4 *2 (-174)))) - ((*1 *1 *1) (-4 *1 (-1079)))) -(((*1 *2 *3) - (-12 (-5 *3 (-656 (-2 (|:| |deg| (-783)) (|:| -3789 *5)))) - (-4 *5 (-1262 *4)) (-4 *4 (-360)) (-5 *2 (-656 *5)) - (-5 *1 (-218 *4 *5)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-656 (-2 (|:| -1825 *5) (|:| -3779 (-576))))) - (-5 *4 (-576)) (-4 *5 (-1262 *4)) (-5 *2 (-656 *5)) - (-5 *1 (-708 *5))))) + (-12 (-5 *2 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+ (-4 *4 (-23)) (-14 *5 *4)))) +(((*1 *2 *1 *1) + (-12 (-4 *1 (-1084 *3 *4 *5)) (-4 *3 (-1068)) (-4 *4 (-805)) + (-4 *5 (-862)) (-5 *2 (-112))))) +(((*1 *2 *1 *3) + (-12 (-5 *2 (-656 (-1177))) (-5 *1 (-1082)) (-5 *3 (-1177))))) (((*1 *1) (-4 *1 (-23))) ((*1 *1) (-12 (-4 *1 (-482 *2 *3)) (-4 *2 (-174)) (-4 *3 (-23)))) ((*1 *1) (-5 *1 (-548))) @@ -10013,32 +10156,28 @@ (-12 (-4 *3 (-1119)) (-4 *4 (-13 (-1068) (-899 *3) (-626 *2))) (-5 *2 (-905 *3)) (-5 *1 (-1095 *3 *4 *5)) (-4 *5 (-13 (-442 *4) (-899 *3) (-626 *2)))))) -(((*1 *2 *3) (-12 (-5 *3 (-171 (-576))) (-5 *2 (-112)) (-5 *1 (-458)))) - ((*1 *2 *3) - (-12 - (-5 *3 - (-516 (-419 (-576)) (-245 *5 (-783)) (-876 *4) - (-253 *4 (-419 (-576))))) - (-14 *4 (-656 (-1195))) (-14 *5 (-783)) (-5 *2 (-112)) - (-5 *1 (-517 *4 *5)))) - ((*1 *2 *3) (-12 (-5 *2 (-112)) (-5 *1 (-978 *3)) (-4 *3 (-557)))) - ((*1 *2 *1) (-12 (-4 *1 (-1240)) (-5 *2 (-112))))) -(((*1 *2 *3 *4 *4 *5 *4 *3 *6 *3 *4 *7 *8 *9 *10) - (-12 (-5 *4 (-576)) (-5 *5 (-1177)) (-5 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|upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))) + (-5 *1 (-194))))) (((*1 *2) (-12 (-14 *4 *2) (-4 *5 (-1236)) (-5 *2 (-783)) (-5 *1 (-242 *3 *4 *5)) (-4 *3 (-243 *4 *5)))) @@ -13122,21 +13154,32 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-860) (-374))) (-5 *1 (-1080 *2 *3)) (-4 *3 (-1262 *2))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-999 *2)) (-4 *2 (-1068)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-960 (-227))) (-5 *1 (-1232)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1284 *2)) (-4 *2 (-1236)) (-4 *2 (-1068))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-905 *3)) (-4 *3 (-1119))))) -(((*1 *1 *1 *1) (-5 *1 (-227))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-227)) (-5 *1 (-228)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-171 (-227))) (-5 *1 (-228)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-568)) (-5 *1 (-443 *3 *2)) (-4 *2 (-442 *3)))) - ((*1 *2 *3 *3) - (-12 (-5 *3 (-783)) (-5 *2 (-1 (-390))) (-5 *1 (-1059)))) - ((*1 *1 *1 *1) (-4 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(-568))))) +(((*1 *2 *3) + (-12 (-5 *2 (-430 (-1191 *1))) (-5 *1 (-326 *4)) (-5 *3 (-1191 *1)) + (-4 *4 (-464)) (-4 *4 (-568)) (-4 *4 (-1119)))) + ((*1 *2 *3) + (-12 (-4 *1 (-926)) (-5 *2 (-430 (-1191 *1))) (-5 *3 (-1191 *1))))) (((*1 *2 *1) (-12 (-5 *2 (-656 (-518))) (-5 *1 (-49)))) ((*1 *2 *1) (-12 (-5 *2 (-656 (-888))) (-5 *1 (-495))))) (((*1 *2 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-804)) (-4 *2 (-1068)))) @@ -13150,8 +13193,8 @@ ((*1 *2 *1) (-12 (-14 *3 (-656 (-1195))) (-4 *5 (-243 (-3500 *3) (-783))) (-14 *6 - (-1 (-112) (-2 (|:| -3222 *4) (|:| -1567 *5)) - (-2 (|:| -3222 *4) (|:| -1567 *5)))) + (-1 (-112) (-2 (|:| -3222 *4) (|:| -3709 *5)) + (-2 (|:| -3222 *4) (|:| -3709 *5)))) (-4 *2 (-174)) (-5 *1 (-473 *3 *2 *4 *5 *6 *7)) (-4 *4 (-862)) (-4 *7 (-966 *2 *5 (-876 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-521 *2 *3)) (-4 *3 (-862)) (-4 *2 (-1119)))) @@ -13168,81 +13211,37 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1084 *3 *4 *2)) (-4 *3 (-1068)) (-4 *4 (-805)) (-4 *2 (-862))))) -(((*1 *1 *1 *2) 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(-4 *3 (-1068))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-1177)) (-5 *4 (-1139)) (-5 *2 (-112)) (-5 *1 (-833))))) +(((*1 *1 *2 *3 *4) + (-12 (-14 *5 (-656 (-1195))) (-4 *2 (-174)) + (-4 *4 (-243 (-3500 *5) (-783))) + (-14 *6 + (-1 (-112) (-2 (|:| -3222 *3) (|:| -3709 *4)) + (-2 (|:| -3222 *3) (|:| -3709 *4)))) + (-5 *1 (-473 *5 *2 *3 *4 *6 *7)) (-4 *3 (-862)) + (-4 *7 (-966 *2 *4 (-876 *5)))))) (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1068)) (-4 *3 (-804)))) ((*1 *2 *1) (-12 (-4 *1 (-393 *3 *2)) (-4 *3 (-1068)) (-4 *2 (-1119)))) @@ -13250,8 +13249,8 @@ (-12 (-14 *3 (-656 (-1195))) (-4 *4 (-174)) (-4 *6 (-243 (-3500 *3) (-783))) (-14 *7 - (-1 (-112) (-2 (|:| -3222 *5) (|:| -1567 *6)) - (-2 (|:| -3222 *5) (|:| -1567 *6)))) + (-1 (-112) (-2 (|:| -3222 *5) (|:| -3709 *6)) + (-2 (|:| -3222 *5) (|:| -3709 *6)))) (-5 *2 (-725 *5 *6 *7)) (-5 *1 (-473 *3 *4 *5 *6 *7 *8)) (-4 *5 (-862)) (-4 *8 (-966 *4 *6 (-876 *3))))) ((*1 *2 *1) @@ -13260,134 +13259,96 @@ ((*1 *1 *1) (-12 (-4 *1 (-992 *2 *3 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+ (-5 *3 (-1176 *4)) (-4 *5 (-1277 *4))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1229 *3 *4 *5 *6)) (-4 *3 (-568)) (-4 *4 (-805)) + (-4 *5 (-862)) (-4 *6 (-1084 *3 *4 *5)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-4 *1 (-1229 *4 *5 *6 *3)) (-4 *4 (-568)) (-4 *5 (-805)) + (-4 *6 (-862)) (-4 *3 (-1084 *4 *5 *6)) (-5 *2 (-112))))) (((*1 *2 *3 *2) (-12 (-5 *3 (-656 (-1095 *4 *5 *2))) (-4 *4 (-1119)) (-4 *5 (-13 (-1068) (-899 *4) (-626 (-905 *4)))) @@ -13761,6 +13831,15 @@ (-4 *6 (-13 (-1068) (-899 *5) (-626 (-905 *5)))) (-4 *2 (-13 (-442 *6) (-899 *5) (-626 (-905 *5)))) (-5 *1 (-54 *5 *6 *2))))) +(((*1 *2 *3 *1) + (-12 (|has| *1 (-6 -4462)) (-4 *1 (-501 *3)) (-4 *3 (-1236)) + (-4 *3 (-1119)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-922 *4)) (-4 *4 (-1119)) (-5 *2 (-112)) + (-5 *1 (-921 *4)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-938)) (-5 *2 (-112)) (-5 *1 (-1120 *4 *5)) (-14 *4 *3) + (-14 *5 *3)))) (((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-874) (-874))) (-5 *1 (-115)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-874) (-656 (-874)))) (-5 *1 (-115)))) ((*1 *2 *1) @@ -13769,27 +13848,21 @@ (-12 (-5 *2 (-1291)) (-5 *1 (-216 *3)) (-4 *3 (-13 (-862) - (-10 -8 (-15 -2794 ((-1177) $ (-1195))) (-15 -1971 (*2 $)) - (-15 -1657 (*2 $))))))) + (-10 -8 (-15 -2794 ((-1177) $ (-1195))) (-15 -1970 (*2 $)) + (-15 -2023 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1291)) (-5 *1 (-406)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-576)) (-5 *2 (-1291)) (-5 *1 (-406)))) ((*1 *2 *1) (-12 (-5 *2 (-1291)) (-5 *1 (-514)))) ((*1 *2 *3) (-12 (-5 *3 (-1177)) (-5 *2 (-1291)) (-5 *1 (-722)))) ((*1 *2 *1) (-12 (-5 *2 (-1291)) (-5 *1 (-1216)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-576)) (-5 *2 (-1291)) (-5 *1 (-1216))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-430 *3)) (-4 *3 (-568)) (-5 *1 (-431 *3))))) -(((*1 *1 *1) - (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1068))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1195)) - (-4 *5 (-13 (-317) (-148) (-1057 (-576)) (-651 (-576)))) - (-5 *2 (-598 *3)) (-5 *1 (-438 *5 *3)) - (-4 *3 (-13 (-1221) (-29 *5))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-1195)) (-4 *5 (-13 (-568) (-1057 (-576)) (-148))) - (-5 *2 (-598 (-419 (-969 *5)))) (-5 *1 (-582 *5)) - (-5 *3 (-419 (-969 *5)))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-576)) (-4 *1 (-1246 *4)) (-4 *4 (-1068)) (-4 *4 (-568)) + (-5 *2 (-419 (-969 *4))))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-576)) (-4 *1 (-1246 *4)) (-4 *4 (-1068)) (-4 *4 (-568)) + (-5 *2 (-419 (-969 *4)))))) +(((*1 *1 *2 *1) (-12 (-5 *2 (-1194)) (-5 *1 (-340))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4462)) (-4 *1 (-152 *3)) (-4 *3 (-1236)))) @@ -13802,16 +13875,35 @@ (-4 *5 (-805)) (-4 *3 (-862)) (-4 *2 (-1084 *4 *5 *3)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-783)) (-5 *1 (-1233 *2)) (-4 *2 (-1236))))) -(((*1 *2 *3) (-12 (-5 *3 (-1177)) (-5 *2 (-52)) (-5 *1 (-841))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1279 *3 *2)) - (-4 *2 (-1277 *3))))) -(((*1 *1) (-5 *1 (-449)))) -(((*1 *2 *2 *3) - (|partial| -12 - (-5 *3 (-656 (-2 (|:| |func| *2) (|:| |pole| (-112))))) - (-4 *2 (-13 (-442 *4) (-1021))) (-4 *4 (-568)) - (-5 *1 (-285 *4 *2))))) +(((*1 *2 *3 *3 *3 *3 *4 *3 *5) + (-12 (-5 *3 (-576)) (-5 *4 (-701 (-227))) + (-5 *5 (-3 (|:| |fn| (-400)) (|:| |fp| (-63 LSFUN2)))) + (-5 *2 (-1054)) (-5 *1 (-765))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1119)) (-4 *6 (-1119)) + (-5 *2 (-1 *6 *4 *5)) (-5 *1 (-696 *4 *5 *6)) (-4 *4 (-1119))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1195)) + (-4 *5 (-13 (-317) (-148) (-1057 (-576)) (-651 (-576)))) + (-5 *2 (-598 *3)) (-5 *1 (-438 *5 *3)) + (-4 *3 (-13 (-1221) (-29 *5)))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-1197 (-419 (-576)))) (-5 *1 (-192))))) +(((*1 *2 *3 *4 *5 *6 *7) + (-12 (-5 *3 (-701 *11)) (-5 *4 (-656 (-419 (-969 *8)))) + (-5 *5 (-783)) (-5 *6 (-1177)) (-4 *8 (-13 (-317) (-148))) + (-4 *11 (-966 *8 *10 *9)) (-4 *9 (-13 (-862) (-626 (-1195)))) + (-4 *10 (-805)) + (-5 *2 + (-2 + (|:| |rgl| + (-656 + (-2 (|:| |eqzro| (-656 *11)) (|:| |neqzro| (-656 *11)) + (|:| |wcond| (-656 (-969 *8))) + (|:| |bsoln| + (-2 (|:| |partsol| (-1286 (-419 (-969 *8)))) + (|:| -2437 (-656 (-1286 (-419 (-969 *8)))))))))) + (|:| |rgsz| (-576)))) + (-5 *1 (-941 *8 *9 *10 *11)) (-5 *7 (-576))))) (((*1 *2 *3) (-12 (-5 *3 @@ -13847,42 +13939,41 @@ ((*1 *2 *3) (-12 (-5 *3 (-419 (-969 *4))) (-4 *4 (-568)) (-5 *2 (-656 (-1195))) (-5 *1 (-1062 *4))))) -(((*1 *2) - (-12 (-5 *2 (-419 (-969 *3))) (-5 *1 (-465 *3 *4 *5 *6)) - (-4 *3 (-568)) (-4 *3 (-174)) (-14 *4 (-938)) - (-14 *5 (-656 (-1195))) (-14 *6 (-1286 (-701 *3)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) - (-4 *2 (-13 (-442 *3) (-1021)))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-576)) (-4 *5 (-360)) (-5 *2 (-430 (-1191 (-1191 *5)))) - (-5 *1 (-1234 *5)) (-5 *3 (-1191 (-1191 *5)))))) + (-12 (-5 *3 (-227)) (-5 *4 (-576)) (-5 *2 (-1054)) (-5 *1 (-770))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1236)) (-5 *1 (-613 *3)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1236)) (-5 *1 (-1176 *3))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-568) (-1057 (-576)))) (-4 *5 (-442 *4)) + (-5 *2 (-430 *3)) (-5 *1 (-447 *4 *5 *3)) (-4 *3 (-1262 *5))))) (((*1 *2 *1 *1) - (-12 (-4 *1 (-243 *3 *2)) (-4 *2 (-1236)) (-4 *2 (-1068)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-783)) (-5 *1 (-874)))) - ((*1 *1 *1) (-5 *1 (-874))) - ((*1 *2 *3 *3) - (-12 (-5 *3 (-960 (-227))) (-5 *2 (-227)) (-5 *1 (-1232)))) - ((*1 *2 *1 *1) - (-12 (-4 *1 (-1284 *2)) (-4 *2 (-1236)) (-4 *2 (-1068))))) -(((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1183 *3 *4)) (-14 *3 (-938)) - (-4 *4 (-1068))))) + (-12 (-5 *2 (-112)) (-5 *1 (-1222 *3)) (-4 *3 (-1119))))) (((*1 *2 *3 *3) (-12 (-5 *3 (-783)) (-5 *2 (-1 (-390))) (-5 *1 (-1059))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1191 *4)) (-4 *4 (-360)) (-5 *2 (-975 (-1139))) - (-5 *1 (-357 *4))))) -(((*1 *1 *2) (-12 (-5 *2 (-419 (-576))) (-5 *1 (-219))))) +(((*1 *2 *2) + (-12 (-4 *3 (-1057 (-576))) (-4 *3 (-568)) (-5 *1 (-32 *3 *2)) + (-4 *2 (-442 *3)))) + ((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-1191 *4)) (-5 *1 (-166 *3 *4)) + (-4 *3 (-167 *4)))) + ((*1 *1 *1) (-12 (-4 *1 (-1068)) (-4 *1 (-312)))) + ((*1 *2) (-12 (-4 *1 (-339 *3)) (-4 *3 (-374)) (-5 *2 (-1191 *3)))) + ((*1 *2) (-12 (-4 *1 (-736 *3 *2)) (-4 *3 (-174)) (-4 *2 (-1262 *3)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1087 *3 *2)) (-4 *3 (-13 (-860) (-374))) + (-4 *2 (-1262 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1286 (-656 (-2 (|:| -3103 *4) (|:| -3222 (-1139)))))) + (-4 *4 (-360)) (-5 *2 (-1291)) (-5 *1 (-540 *4))))) +(((*1 *2 *1) + (-12 (-5 *2 (-874)) (-5 *1 (-402 *3 *4 *5)) (-14 *3 (-783)) + (-14 *4 (-783)) (-4 *5 (-174))))) (((*1 *2 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-173)))) ((*1 *2 *1) (-12 (-5 *2 (-1291)) (-5 *1 (-1287)))) ((*1 *2 *1) (-12 (-5 *2 (-1291)) (-5 *1 (-1288))))) -(((*1 *1 *1 *1) - (|partial| -12 (-4 *1 (-864 *2)) (-4 *2 (-1068)) (-4 *2 (-374))))) +(((*1 *1) (-5 *1 (-142)))) (((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1191 (-419 (-1191 *2)))) (-5 *4 (-624 *2)) (-4 *2 (-13 (-442 *5) (-27) (-1221))) @@ -13904,36 +13995,52 @@ ((*1 *2 *3 *4) (-12 (-5 *3 (-419 (-1191 (-419 (-969 *5))))) (-5 *4 (-1195)) (-5 *2 (-419 (-969 *5))) (-5 *1 (-1062 *5)) (-4 *5 (-568))))) -(((*1 *2) (-12 (-5 *2 (-1291)) (-5 *1 (-457 *3)) (-4 *3 (-1068))))) -(((*1 *2 *2) - (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) - (-4 *2 (-13 (-442 *3) (-1021)))))) +(((*1 *2 *3 *3) + (-12 (-4 *3 (-317)) (-4 *3 (-174)) (-4 *4 (-384 *3)) + (-4 *5 (-384 *3)) (-5 *2 (-2 (|:| -2287 *3) (|:| -3588 *3))) + (-5 *1 (-700 *3 *4 *5 *6)) (-4 *6 (-699 *3 *4 *5)))) + ((*1 *2 *3 *3) + (-12 (-5 *2 (-2 (|:| -2287 *3) (|:| -3588 *3))) (-5 *1 (-712 *3)) + (-4 *3 (-317))))) +(((*1 *2 *2 *3) + (|partial| -12 (-5 *2 (-419 (-969 *4))) (-5 *3 (-1195)) + (-4 *4 (-13 (-568) (-1057 (-576)) (-148))) (-5 *1 (-582 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-173)))) + ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1231 *3)) (-4 *3 (-993))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1236)) (-5 *1 (-613 *3)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1236)) (-5 *1 (-1176 *3))))) -(((*1 *2 *3 *3 *3) - (|partial| -12 (-4 *4 (-13 (-374) (-148) (-1057 (-576)))) - (-4 *5 (-1262 *4)) (-5 *2 (-656 (-419 *5))) (-5 *1 (-1035 *4 *5)) - (-5 *3 (-419 *5))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-1084 *2 *3 *4)) (-4 *2 (-1068)) (-4 *3 (-805)) - (-4 *4 (-862)))) - ((*1 *2 *2 *1) - (-12 (-4 *1 (-1229 *3 *4 *5 *2)) (-4 *3 (-568)) (-4 *4 (-805)) - (-4 *5 (-862)) (-4 *2 (-1084 *3 *4 *5))))) -(((*1 *2 *3) - (-12 (-5 *2 (-576)) (-5 *1 (-457 *3)) (-4 *3 (-416)) (-4 *3 (-1068))))) -(((*1 *2 *2 *3 *4) - (|partial| -12 (-5 *3 (-783)) (-4 *4 (-13 (-568) (-148))) - (-5 *1 (-1256 *4 *2)) (-4 *2 (-1262 *4))))) -(((*1 *2 *3) - (-12 (-4 *1 (-353 *4 *3 *5)) (-4 *4 (-1240)) (-4 *3 (-1262 *4)) - (-4 *5 (-1262 (-419 *3))) (-5 *2 (-112)))) - ((*1 *2 *3) - (-12 (-4 *1 (-353 *3 *4 *5)) (-4 *3 (-1240)) (-4 *4 (-1262 *3)) - (-4 *5 (-1262 (-419 *4))) (-5 *2 (-112))))) -(((*1 *2 *3) (-12 (-5 *3 (-1177)) (-5 *2 (-52)) (-5 *1 (-1214))))) +(((*1 *2 *3 *4 *4 *4) + (-12 (-5 *3 (-656 *8)) (-5 *4 (-112)) (-4 *8 (-1084 *5 *6 *7)) + (-4 *5 (-464)) (-4 *6 (-805)) (-4 *7 (-862)) + (-5 *2 (-656 (-1046 *5 *6 *7 *8))) (-5 *1 (-1046 *5 *6 *7 *8)))) + ((*1 *2 *3 *4 *4 *4) + (-12 (-5 *3 (-656 *8)) (-5 *4 (-112)) (-4 *8 (-1084 *5 *6 *7)) + (-4 *5 (-464)) (-4 *6 (-805)) (-4 *7 (-862)) + (-5 *2 (-656 (-1165 *5 *6 *7 *8))) (-5 *1 (-1165 *5 *6 *7 *8))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1002 *2)) (-4 *2 (-1221))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-568)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -2736 *4))) + (-5 *1 (-988 *4 *3)) (-4 *3 (-1262 *4))))) +(((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-573))))) +(((*1 *2 *1) + (-12 (-5 *2 (-656 (-2 (|:| |k| (-1195)) (|:| |c| (-1308 *3))))) + (-5 *1 (-1308 *3)) (-4 *3 (-1068)))) + ((*1 *2 *1) + (-12 (-5 *2 (-656 (-2 (|:| |k| *3) (|:| |c| (-1310 *3 *4))))) + (-5 *1 (-1310 *3 *4)) (-4 *3 (-862)) (-4 *4 (-1068))))) +(((*1 *2 *2 *2 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-1066))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-1195)) (-5 *5 (-1113 (-227))) (-5 *2 (-944)) + (-5 *1 (-942 *3)) (-4 *3 (-626 (-548))))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-1195)) (-5 *2 (-944)) (-5 *1 (-942 *3)) + (-4 *3 (-626 (-548))))) + ((*1 *1 *2) (-12 (-5 *2 (-1 (-227) (-227))) (-5 *1 (-944)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1 (-227) (-227))) (-5 *3 (-1113 (-227))) + (-5 *1 (-944))))) (((*1 *1 *2 *3) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1068)) (-4 *3 (-804)))) ((*1 *1 *2 *3) @@ -13943,8 +14050,8 @@ (-12 (-5 *3 (-725 *5 *6 *7)) (-4 *5 (-862)) (-4 *6 (-243 (-3500 *4) (-783))) (-14 *7 - (-1 (-112) (-2 (|:| -3222 *5) (|:| -1567 *6)) - (-2 (|:| -3222 *5) (|:| -1567 *6)))) + (-1 (-112) (-2 (|:| -3222 *5) (|:| -3709 *6)) + (-2 (|:| -3222 *5) (|:| -3709 *6)))) (-14 *4 (-656 (-1195))) (-4 *2 (-174)) (-5 *1 (-473 *4 *2 *5 *6 *7 *8)) (-4 *8 (-966 *2 *6 (-876 *4))))) ((*1 *1 *2 *3) @@ -13974,12 +14081,6 @@ ((*1 *1 *1 *2 *3) (-12 (-4 *1 (-992 *4 *3 *2)) (-4 *4 (-1068)) (-4 *3 (-804)) (-4 *2 (-862))))) -(((*1 *2 *3 *3 *3 *4 *4 *4 *3) - (-12 (-5 *3 (-576)) (-5 *4 (-701 (-227))) (-5 *2 (-1054)) - (-5 *1 (-764))))) -(((*1 *2 *3) - (-12 (-5 *3 (-938)) (-5 *2 (-1191 *4)) (-5 *1 (-368 *4)) - (-4 *4 (-360))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-938)) (-4 *6 (-568)) (-5 *2 (-656 (-326 *6))) (-5 *1 (-223 *5 *6)) (-5 *3 (-326 *6)) (-4 *5 (-1068)))) @@ -14005,70 +14106,109 @@ ((*1 *2 *1) (-12 (-5 *2 (-1301 *3 *4)) (-5 *1 (-1310 *3 *4)) (-4 *3 (-862)) (-4 *4 (-1068))))) -(((*1 *1 *1 *1) (-4 *1 (-986)))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1002 *2)) (-4 *2 (-1221))))) -(((*1 *2) - (-12 (-5 *2 (-701 (-927 *3))) (-5 *1 (-362 *3 *4)) (-14 *3 (-938)) - (-14 *4 (-938)))) - ((*1 *2) - (-12 (-5 *2 (-701 *3)) (-5 *1 (-363 *3 *4)) (-4 *3 (-360)) - (-14 *4 - (-3 (-1191 *3) - (-1286 (-656 (-2 (|:| -3102 *3) (|:| -3222 (-1139))))))))) - ((*1 *2) - (-12 (-5 *2 (-701 *3)) (-5 *1 (-364 *3 *4)) (-4 *3 (-360)) - (-14 *4 (-938))))) -(((*1 *2 *2 *3 *3) - (-12 (-5 *3 (-576)) (-4 *4 (-13 (-568) (-148))) (-5 *1 (-549 *4 *2)) - (-4 *2 (-1277 *4)))) - ((*1 *2 *2 *3 *3) - (-12 (-5 *3 (-576)) (-4 *4 (-13 (-374) (-379) (-626 *3))) - 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*2 (-171 (-227))) (-5 *1 (-228)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-568)) (-5 *1 (-443 *3 *2)) (-4 *2 (-442 *3)))) + ((*1 *2 *3 *3) + (-12 (-5 *3 (-783)) (-5 *2 (-1 (-390))) (-5 *1 (-1059)))) + ((*1 *1 *1 *1) (-4 *1 (-1158)))) +(((*1 *2 *2) + (-12 (-5 *2 (-960 *3)) (-4 *3 (-13 (-374) (-1221) (-1021))) + (-5 *1 (-178 *3))))) +(((*1 *2 *3) + (-12 (-4 *4 (-1068)) (-4 *3 (-1262 *4)) (-4 *2 (-1277 *4)) + (-5 *1 (-1280 *4 *3 *5 *2)) (-4 *5 (-668 *3))))) +(((*1 *2 *2) + (-12 (-4 *3 (-464)) (-5 *1 (-1227 *3 *2)) + (-4 *2 (-13 (-442 *3) (-1221)))))) (((*1 *2 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-568) (-1057 (-576)))) (-5 *2 (-326 *4)) @@ -14417,56 +14578,32 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-464) (-1057 (-576)) (-651 (-576)))) (-5 *1 (-1225 *3 *2)) (-4 *2 (-13 (-27) (-1221) (-442 *3)))))) -(((*1 *2 *3 *4 *4 *5 *3 *3) - (-12 (-5 *3 (-576)) (-5 *4 (-701 (-227))) (-5 *5 (-227)) - (-5 *2 (-1054)) (-5 *1 (-764))))) (((*1 *2 *3) - (-12 (-5 *3 (-1286 (-326 (-227)))) + (-12 (-4 *4 (-13 (-568) (-1057 (-576)))) (-4 *5 (-442 *4)) (-5 *2 - (-2 (|:| |additions| (-576)) (|:| |multiplications| (-576)) - (|:| |exponentiations| (-576)) (|:| |functionCalls| (-576)))) - (-5 *1 (-315))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-656 (-1200))) (-5 *1 (-1200)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-518)) (-5 *3 (-656 (-1200))) (-5 *1 (-1200))))) + (-3 (|:| |overq| (-1191 (-419 (-576)))) + (|:| |overan| (-1191 (-48))) (|:| -4194 (-112)))) + (-5 *1 (-447 *4 *5 *3)) (-4 *3 (-1262 *5))))) +(((*1 *2) + (-12 (-4 *2 (-13 (-442 *3) (-1021))) (-5 *1 (-285 *3 *2)) + (-4 *3 (-568))))) (((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *2 *6)) (-5 *4 (-1 *6 *5)) (-4 *5 (-1119)) (-4 *6 (-1119)) (-4 *2 (-1119)) (-5 *1 (-692 *5 *6 *2))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-568) (-148))) (-5 *2 (-656 *3)) - (-5 *1 (-1256 *4 *3)) (-4 *3 (-1262 *4))))) (((*1 *2 *1) - (|partial| -12 (-4 *3 (-1131)) (-4 *3 (-1119)) (-5 *2 (-656 *1)) - (-4 *1 (-442 *3)))) - ((*1 *2 *1) - (|partial| -12 (-5 *2 (-656 (-905 *3))) 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(-1236)) (-5 *2 (-112)) + (-5 *1 (-1176 *4))))) +(((*1 *1 *2) + (-12 (-5 *2 (-701 *5)) (-4 *5 (-1068)) (-5 *1 (-1073 *3 *4 *5)) + (-14 *3 (-783)) (-14 *4 (-783))))) +(((*1 *2) (-12 (-5 *2 (-1291)) (-5 *1 (-1195))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-112) (-115) (-115))) (-5 *1 (-115))))) (((*1 *2 *3) - (-12 (-5 *2 (-171 *4)) (-5 *1 (-183 *4 *3)) - (-4 *4 (-13 (-374) (-860))) (-4 *3 (-1262 *2))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1229 *2 *3 *4 *5)) (-4 *2 (-568)) (-4 *3 (-805)) - (-4 *4 (-862)) (-4 *5 (-1084 *2 *3 *4))))) + (-12 (-5 *3 (-656 (-656 (-656 *4)))) (-5 *2 (-656 (-656 *4))) + (-5 *1 (-1206 *4)) (-4 *4 (-862))))) (((*1 *1 *1) (-12 (-5 *1 (-350 *2 *3 *4)) (-14 *2 (-656 (-1195))) (-14 *3 (-656 (-1195))) (-4 *4 (-399)))) @@ -14476,10 +14613,17 @@ ((*1 *1 *2) (-12 (-5 *2 (-419 (-576))) (-4 *1 (-1031)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1031)) (-5 *2 (-938)))) ((*1 *1 *1) (-4 *1 (-1031)))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-541))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-289))))) (((*1 *2 *1) - (-12 (-5 *2 (-1176 (-419 *3))) (-5 *1 (-176 *3)) (-4 *3 (-317))))) + (-12 (-4 *1 (-616 *2 *3)) (-4 *3 (-1236)) (-4 *2 (-1119)) + (-4 *2 (-862))))) +(((*1 *2 *2 *3 *3) + (|partial| -12 (-5 *3 (-1195)) + (-4 *4 (-13 (-317) (-148) (-1057 (-576)) (-651 (-576)))) + (-5 *1 (-587 *4 *2)) + (-4 *2 (-13 (-1221) (-976) (-1158) (-29 *4)))))) +(((*1 *2 *1) + (-12 (-4 *1 (-339 *3)) (-4 *3 (-374)) (-4 *3 (-379)) + (-5 *2 (-1191 *3))))) (((*1 *2 *3) (-12 (-5 *3 (-938)) (-5 *2 (-1191 *4)) (-5 *1 (-368 *4)) (-4 *4 (-360)))) @@ -14497,23 +14641,34 @@ (-12 (-5 *3 (-576)) (-5 *2 (-922 *4)) (-5 *1 (-921 *4)) (-4 *4 (-1119)))) ((*1 *1) (-12 (-4 *1 (-1011 *2)) (-4 *2 (-557)) (-4 *2 (-568))))) -(((*1 *2 *1) (-12 (-5 *2 (-576)) (-5 *1 (-834))))) -(((*1 *2 *1) (-12 (-5 *2 (-1291)) (-5 *1 (-834))))) -(((*1 *2 *1) - (-12 (-4 *1 (-375 *3 *4)) (-4 *3 (-1119)) (-4 *4 (-1119)) - (-5 *2 (-1177))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1200))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-783)) (-5 *1 (-129))))) -(((*1 *1) (-5 *1 (-571)))) +(((*1 *2 *3) + (|partial| -12 (-4 *4 (-1240)) (-4 *5 (-1262 *4)) + (-5 *2 (-2 (|:| |radicand| (-419 *5)) (|:| |deg| (-783)))) + (-5 *1 (-149 *4 *5 *3)) (-4 *3 (-1262 (-419 *5)))))) +(((*1 *2 *3 *4 *5 *6) + (|partial| -12 (-5 *4 (-1195)) (-5 *6 (-656 (-624 *3))) + (-5 *5 (-624 *3)) (-4 *3 (-13 (-27) (-1221) (-442 *7))) + (-4 *7 (-13 (-464) (-148) (-1057 (-576)) (-651 (-576)))) + (-5 *2 (-2 (|:| -3160 *3) (|:| |coeff| *3))) + (-5 *1 (-569 *7 *3))))) +(((*1 *2 *3) + (-12 (-4 *4 (-1236)) (-5 *2 (-783)) (-5 *1 (-184 *4 *3)) + (-4 *3 (-686 *4))))) +(((*1 *1 *2) (-12 (-5 *2 (-656 (-874))) (-5 *1 (-874))))) +(((*1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1236))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-464)) (-4 *5 (-805)) (-4 *6 (-862)) - (-4 *7 (-1084 *4 *5 *6)) (-5 *2 (-112)) - (-5 *1 (-1007 *4 *5 *6 *7 *3)) (-4 *3 (-1090 *4 *5 *6 *7)))) - ((*1 *2 *3 *3) - (-12 (-4 *4 (-464)) (-4 *5 (-805)) (-4 *6 (-862)) - (-4 *7 (-1084 *4 *5 *6)) (-5 *2 (-112)) - (-5 *1 (-1126 *4 *5 *6 *7 *3)) (-4 *3 (-1090 *4 *5 *6 *7))))) -(((*1 *2 *1) (-12 (-5 *1 (-1045 *2)) (-4 *2 (-1236))))) + (-12 (-4 *4 (-568)) (-5 *2 (-656 *3)) (-5 *1 (-988 *4 *3)) + (-4 *3 (-1262 *4))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-568)) + (-5 *2 + (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3))) + (-5 *1 (-988 *4 *3)) (-4 *3 (-1262 *4))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-1191 *1)) (-4 *1 (-464)))) + ((*1 *2 *2 *2) + (-12 (-5 *2 (-1191 *6)) (-4 *6 (-966 *5 *3 *4)) (-4 *3 (-805)) + (-4 *4 (-862)) (-4 *5 (-926)) (-5 *1 (-469 *3 *4 *5 *6)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-1191 *1)) (-4 *1 (-926))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-656 (-48))) (-5 *2 (-430 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1262 (-48))))) @@ -14654,36 +14809,46 @@ ((*1 *2 *1) (-12 (-5 *2 (-430 *1)) (-4 *1 (-1240)))) ((*1 *2 *3) (-12 (-5 *2 (-430 *3)) (-5 *1 (-1251 *3)) (-4 *3 (-1262 (-576)))))) -(((*1 *2) (-12 (-5 *2 (-1177)) (-5 *1 (-1205))))) -(((*1 *2 *2) - (-12 (-4 *3 (-568)) (-4 *4 (-1011 *3)) (-5 *1 (-143 *3 *4 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