diff options
Diffstat (limited to 'src/share/algebra')
| -rw-r--r-- | src/share/algebra/browse.daase | 764 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1128 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1287 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8310 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 31353 |
5 files changed, 21447 insertions, 21395 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 05cfd01d..48298217 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2238320 . 3419278780) +(2238314 . 3420122812) (-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 NIL (-19 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."))) -((-4255 . T) (-4254 . T) (-2341 . T)) +((-4255 . T) (-4254 . T) (-1996 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) @@ -46,13 +46,13 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4251 . T) (-4249 . T) (-4248 . T) ((-4256 "*") . T) (-4247 . T) (-4252 . T) (-4246 . T) (-2341 . T)) +((-4251 . T) (-4249 . T) (-4248 . T) ((-4256 "*") . T) (-4247 . T) (-4252 . T) (-4246 . T) (-1996 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,{}x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) NIL NIL -(-31 R -1896) +(-31 R -1346) ((|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 -967) (QUOTE (-525))))) @@ -62,7 +62,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4254))) (-33) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-2341 . T)) +((-1996 . T)) NIL (-34) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) @@ -70,7 +70,7 @@ NIL NIL (-35 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4254 . T) (-4255 . T) (-2341 . T)) +((-4254 . T) (-4255 . T) (-1996 . T)) NIL (-36 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) @@ -84,11 +84,11 @@ 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 -(-39 -1896 UP UPUP -1690) +(-39 -1346 UP UPUP -2238) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4247 |has| (-385 |#2|) (-341)) (-4252 |has| (-385 |#2|) (-341)) (-4246 |has| (-385 |#2|) (-341)) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| (-385 |#2|) (QUOTE (-136))) (|HasCategory| (-385 |#2|) (QUOTE (-138))) (|HasCategory| (-385 |#2|) (QUOTE (-327))) (-3215 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-3215 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-3215 (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-385 |#2|) (QUOTE (-327))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3215 (|HasCategory| (-385 |#2|) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341))))) -(-40 R -1896) +((|HasCategory| (-385 |#2|) (QUOTE (-136))) (|HasCategory| (-385 |#2|) (QUOTE (-138))) (|HasCategory| (-385 |#2|) (QUOTE (-327))) (-3309 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-3309 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-3309 (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-385 |#2|) (QUOTE (-327))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3309 (|HasCategory| (-385 |#2|) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341))))) +(-40 R -1346) ((|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 (-429))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))))) @@ -107,7 +107,7 @@ NIL (-44 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4254 . T) (-4255 . T)) -((-3215 (-12 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3160) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3978) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3160) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3978) (|devaluate| |#2|))))))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (-12 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3160) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3978) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3946) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3946) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#2|))))))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (-12 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3946) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797))))) (-45 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -140,7 +140,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-53 |Base| R -1896) +(-53 |Base| R -1346) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -150,7 +150,7 @@ NIL NIL (-55 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4254 . T) (-4255 . T) (-2341 . T)) +((-4254 . T) (-4255 . T) (-1996 . T)) NIL (-56 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) @@ -159,64 +159,64 @@ NIL (-57 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4255 . T) (-4254 . T)) -((-3215 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3215 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3309 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-58 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) -(-59 -3515) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +(-59 -1310) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-60 -3515) +(-60 -1310) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-61 -3515) +(-61 -1310) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -3515) +(-62 -1310) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-63 -3515) +(-63 -1310) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -3515) +(-64 -1310) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -3515) +(-65 -1310) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -3515) +(-66 -1310) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-67 -3515) +(-67 -1310) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-68 -3515) +(-68 -1310) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-69 -3515) +(-69 -1310) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-70 -3515) +(-70 -1310) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-71 -3515) +(-71 -1310) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-72 -3515) +(-72 -1310) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -228,55 +228,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-75 -3515) +(-75 -1310) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-76 -3515) +(-76 -1310) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-77 -3515) +(-77 -1310) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-78 -3515) +(-78 -1310) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-79 -3515) +(-79 -1310) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -3515) +(-80 -1310) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -3515) +(-81 -1310) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-82 -3515) +(-82 -1310) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -3515) +(-83 -1310) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -3515) +(-84 -1310) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -3515) +(-85 -1310) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -3515) +(-86 -1310) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-87 -3515) +(-87 -1310) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -287,7 +287,7 @@ NIL (-89 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-90 S) ((|constructor| (NIL "Category for the inverse trigonometric functions.")) (|atan| (($ $) "\\spad{atan(x)} returns the arc-tangent of \\spad{x}.")) (|asin| (($ $) "\\spad{asin(x)} returns the arc-sine of \\spad{x}.")) (|asec| (($ $) "\\spad{asec(x)} returns the arc-secant of \\spad{x}.")) (|acsc| (($ $) "\\spad{acsc(x)} returns the arc-cosecant of \\spad{x}.")) (|acot| (($ $) "\\spad{acot(x)} returns the arc-cotangent of \\spad{x}.")) (|acos| (($ $) "\\spad{acos(x)} returns the arc-cosine of \\spad{x}."))) NIL @@ -323,7 +323,7 @@ NIL (-98 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-99 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -338,12 +338,12 @@ NIL NIL (-102 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4255 . T) (-2341 . T)) +((-4255 . T) (-1996 . T)) NIL (-103) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion.")) (|coerce| (((|RadixExpansion| 2) $) "\\spad{coerce(b)} converts a binary expansion to a radix expansion with base 2.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(b)} converts a binary expansion to a rational number."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| (-525) (QUOTE (-843))) (|HasCategory| (-525) (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-952))) (|HasCategory| (-525) (QUOTE (-762))) (-3215 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1066))) (|HasCategory| (-525) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1090)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-525) (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-843)))) (|HasCategory| (-525) (QUOTE (-136))))) +((|HasCategory| (-525) (QUOTE (-843))) (|HasCategory| (-525) (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-952))) (|HasCategory| (-525) (QUOTE (-762))) (-3309 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1066))) (|HasCategory| (-525) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1090)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-525) (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-843)))) (|HasCategory| (-525) (QUOTE (-136))))) (-104) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -372,7 +372,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-111 -1896 UP) +(-111 -1346 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 @@ -383,14 +383,14 @@ NIL (-113 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| (-112 |#1|) (QUOTE (-843))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| (-112 |#1|) (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-138))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-112 |#1|) (QUOTE (-952))) (|HasCategory| (-112 |#1|) (QUOTE (-762))) (-3215 (|HasCategory| (-112 |#1|) (QUOTE (-762))) (|HasCategory| (-112 |#1|) (QUOTE (-789)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (QUOTE (-1066))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (QUOTE (-213))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -486) (QUOTE (-1090)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -288) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -265) (LIST (QUOTE -112) (|devaluate| |#1|)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (QUOTE (-286))) (|HasCategory| (-112 |#1|) (QUOTE (-510))) (|HasCategory| (-112 |#1|) (QUOTE (-789))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-843)))) (|HasCategory| (-112 |#1|) (QUOTE (-136))))) +((|HasCategory| (-112 |#1|) (QUOTE (-843))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| (-112 |#1|) (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-138))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-112 |#1|) (QUOTE (-952))) (|HasCategory| (-112 |#1|) (QUOTE (-762))) (-3309 (|HasCategory| (-112 |#1|) (QUOTE (-762))) (|HasCategory| (-112 |#1|) (QUOTE (-789)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (QUOTE (-1066))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (QUOTE (-213))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -486) (QUOTE (-1090)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -288) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -265) (LIST (QUOTE -112) (|devaluate| |#1|)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (QUOTE (-286))) (|HasCategory| (-112 |#1|) (QUOTE (-510))) (|HasCategory| (-112 |#1|) (QUOTE (-789))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-843)))) (|HasCategory| (-112 |#1|) (QUOTE (-136))))) (-114 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL ((|HasAttribute| |#1| (QUOTE -4255))) (-115 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) -((-2341 . T)) +((-1996 . T)) NIL (-116 UP) ((|constructor| (NIL "\\indented{1}{Author: Frederic Lehobey,{} James \\spad{H}. Davenport} Date Created: 28 June 1994 Date Last Updated: 11 July 1997 Basic Operations: brillhartIrreducible? Related Domains: Also See: AMS Classifications: Keywords: factorization Examples: References: [1] John Brillhart,{} Note on Irreducibility Testing,{} Mathematics of Computation,{} vol. 35,{} num. 35,{} Oct. 1980,{} 1379-1381 [2] James Davenport,{} On Brillhart Irreducibility. To appear. [3] John Brillhart,{} On the Euler and Bernoulli polynomials,{} \\spad{J}. Reine Angew. Math.,{} \\spad{v}. 234,{} (1969),{} \\spad{pp}. 45-64")) (|noLinearFactor?| (((|Boolean|) |#1|) "\\spad{noLinearFactor?(p)} returns \\spad{true} if \\spad{p} can be shown to have no linear factor by a theorem of Lehmer,{} \\spad{false} else. \\spad{I} insist on the fact that \\spad{false} does not mean that \\spad{p} has a linear factor.")) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{brillhartTrials(n)} sets to \\spad{n} the number of tests in \\spadfun{brillhartIrreducible?} and returns the previous value.") (((|NonNegativeInteger|)) "\\spad{brillhartTrials()} returns the number of tests in \\spadfun{brillhartIrreducible?}.")) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) "\\spad{brillhartIrreducible?(p,{}noLinears)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} else. If \\spad{noLinears} is \\spad{true},{} we are being told \\spad{p} has no linear factors \\spad{false} does not mean that \\spad{p} is reducible.") (((|Boolean|) |#1|) "\\spad{brillhartIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} is inconclusive."))) @@ -399,14 +399,14 @@ NIL (-117 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-118 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-119) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4255 . T) (-4254 . T) (-2341 . T)) +((-4255 . T) (-4254 . T) (-1996 . T)) NIL (-120 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -414,20 +414,20 @@ NIL NIL (-121 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4254 . T) (-4255 . T) (-2341 . T)) +((-4254 . T) (-4255 . T) (-1996 . T)) NIL (-122 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-123 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-124) ((|constructor| (NIL "ByteArray provides datatype for fix-sized buffer of bytes."))) ((-4255 . T) (-4254 . T)) -((-3215 (-12 (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (-12 (|HasCategory| (-125) (QUOTE (-1019))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125)))))) (-3215 (-12 (|HasCategory| (-125) (QUOTE (-1019))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (|HasCategory| (-125) (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-125) (LIST (QUOTE -567) (QUOTE (-501)))) (-3215 (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-125) (QUOTE (-1019)))) (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-125) (QUOTE (-1019))) (-12 (|HasCategory| (-125) (QUOTE (-1019))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (|HasCategory| (-125) (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (-12 (|HasCategory| (-125) (QUOTE (-1019))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125)))))) (-3309 (-12 (|HasCategory| (-125) (QUOTE (-1019))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (|HasCategory| (-125) (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-125) (LIST (QUOTE -567) (QUOTE (-501)))) (-3309 (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-125) (QUOTE (-1019)))) (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-125) (QUOTE (-1019))) (-12 (|HasCategory| (-125) (QUOTE (-1019))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (|HasCategory| (-125) (LIST (QUOTE -566) (QUOTE (-797))))) (-125) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|coerce| (($ (|NonNegativeInteger|)) "\\spad{coerce(x)} has the same effect as byte(\\spad{x}).")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -444,11 +444,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4256 "*") . T)) NIL -(-129 |minix| -3815 S T$) +(-129 |minix| -3339 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-130 |minix| -3815 R) +(-130 |minix| -3339 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -459,7 +459,7 @@ NIL (-132) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4254 . T) (-4244 . T) (-4255 . T)) -((-3215 (-12 (|HasCategory| (-135) (QUOTE (-346))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1019))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-135) (QUOTE (-346))) (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1019))) (-12 (|HasCategory| (-135) (QUOTE (-1019))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| (-135) (QUOTE (-346))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1019))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-135) (QUOTE (-346))) (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1019))) (-12 (|HasCategory| (-135) (QUOTE (-1019))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-797))))) (-133 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -484,7 +484,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4251 . T)) NIL -(-139 -1896 UP UPUP) +(-139 -1346 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 @@ -498,7 +498,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasAttribute| |#1| (QUOTE -4254))) (-142 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) -((-2341 . T)) +((-1996 . T)) NIL (-143 |n| K Q) ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,{}[i1,{}i2,{}...,{}iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,{}[i1,{}i2,{}...,{}iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) @@ -516,7 +516,7 @@ 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 -(-147 R -1896) +(-147 R -1346) ((|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 @@ -546,7 +546,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-843))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-1112))) (|HasCategory| |#2| (QUOTE (-985))) (|HasCategory| |#2| (QUOTE (-952))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-341))) (|HasAttribute| |#2| (QUOTE -4250)) (|HasAttribute| |#2| (QUOTE -4253)) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-789)))) (-154 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4247 -3215 (|has| |#1| (-517)) (-12 (|has| |#1| (-286)) (|has| |#1| (-843)))) (-4252 |has| |#1| (-341)) (-4246 |has| |#1| (-341)) (-4250 |has| |#1| (-6 -4250)) (-4253 |has| |#1| (-6 -4253)) (-2381 . T) (-2341 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) +((-4247 -3309 (|has| |#1| (-517)) (-12 (|has| |#1| (-286)) (|has| |#1| (-843)))) (-4252 |has| |#1| (-341)) (-4246 |has| |#1| (-341)) (-4250 |has| |#1| (-6 -4250)) (-4253 |has| |#1| (-6 -4253)) (-2047 . T) (-1996 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL (-155 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -558,8 +558,8 @@ NIL NIL (-157 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4247 -3215 (|has| |#1| (-517)) (-12 (|has| |#1| (-286)) (|has| |#1| (-843)))) (-4252 |has| |#1| (-341)) (-4246 |has| |#1| (-341)) (-4250 |has| |#1| (-6 -4250)) (-4253 |has| |#1| (-6 -4253)) (-2381 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327))) (-3215 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3215 (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-213))) (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (QUOTE (-346)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (QUOTE (-770)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (QUOTE (-789)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (QUOTE (-952)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (QUOTE (-1112)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -567) 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T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) +((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327))) (-3309 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3309 (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-213))) (-12 (|HasCategory| |#1| 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(QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-770))) (|HasCategory| |#1| (QUOTE (-985))) (-12 (|HasCategory| |#1| (QUOTE (-985))) (|HasCategory| |#1| (QUOTE (-1112)))) (|HasCategory| |#1| (QUOTE (-510))) (-3309 (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-843))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-341)))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-213))) (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasAttribute| |#1| (QUOTE -4250)) (|HasAttribute| |#1| (QUOTE -4253)) (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341)))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090))))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-327))))) (-158 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -608,7 +608,7 @@ NIL ((|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain")) (|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments returns} the list of syntax objects for the arguments used to invoke the constructor.")) (|constructorName| (((|Symbol|) $) "\\spad{constructorName c} returns the name of the constructor"))) NIL NIL -(-170 R -1896) +(-170 R -1346) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -712,19 +712,19 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -(-196 -1896 UP UPUP R) +(-196 -1346 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 -(-197 -1896 FP) +(-197 -1346 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 (-198) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion.")) (|coerce| (((|RadixExpansion| 10) $) "\\spad{coerce(d)} converts a decimal expansion to a radix expansion with base 10.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(d)} converts a decimal expansion to a rational number."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| (-525) (QUOTE (-843))) (|HasCategory| (-525) (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-952))) (|HasCategory| (-525) (QUOTE (-762))) (-3215 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1066))) (|HasCategory| (-525) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1090)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-525) (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-843)))) (|HasCategory| (-525) (QUOTE (-136))))) -(-199 R -1896) +((|HasCategory| (-525) (QUOTE (-843))) (|HasCategory| (-525) (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-952))) (|HasCategory| (-525) (QUOTE (-762))) (-3309 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1066))) (|HasCategory| (-525) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1090)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-525) (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-843)))) (|HasCategory| (-525) (QUOTE (-136))))) +(-199 R -1346) ((|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 @@ -739,18 +739,18 @@ NIL (-202 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-203 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4251 . T)) NIL -(-204 R -1896) +(-204 R -1346) ((|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 (-205) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|hash| (((|Integer|) $) "\\spad{hash(x)} returns the hash key for \\spad{x}")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-2371 . T) (-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) +((-2038 . T) (-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL (-206) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) @@ -759,14 +759,14 @@ NIL (-207 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,{}Y,{}Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4256 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4256 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-208 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL NIL (-209 S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) -((-4255 . T) (-2341 . T)) +((-4255 . T) (-1996 . T)) NIL (-210 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) @@ -790,28 +790,28 @@ NIL ((|HasAttribute| |#1| (QUOTE -4254))) (-215 S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) -((-4255 . T) (-2341 . T)) +((-4255 . T) (-1996 . T)) NIL (-216) ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-217 S -3815 R) +(-217 S -3339 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL ((|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (QUOTE (-735))) (|HasCategory| |#3| (QUOTE (-787))) (|HasAttribute| |#3| (QUOTE -4251)) (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (QUOTE (-346))) (|HasCategory| |#3| (QUOTE (-669))) (|HasCategory| |#3| (QUOTE (-126))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-976))) (|HasCategory| |#3| (QUOTE (-1019)))) -(-218 -3815 R) +(-218 -3339 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4248 |has| |#2| (-976)) (-4249 |has| |#2| (-976)) (-4251 |has| |#2| (-6 -4251)) ((-4256 "*") |has| |#2| (-160)) (-4254 . T) (-2341 . T)) +((-4248 |has| |#2| (-976)) (-4249 |has| |#2| (-976)) (-4251 |has| |#2| (-6 -4251)) ((-4256 "*") |has| |#2| (-160)) (-4254 . T) (-1996 . T)) NIL -(-219 -3815 A B) +(-219 -3339 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-220 -3815 R) +(-220 -3339 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) ((-4248 |has| |#2| (-976)) (-4249 |has| |#2| (-976)) (-4251 |has| |#2| (-6 -4251)) ((-4256 "*") |has| |#2| (-160)) (-4254 . 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(NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -826,12 +826,12 @@ NIL NIL (-224 S) ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,{}v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,{}v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) -((-2341 . T)) +((-1996 . T)) NIL (-225 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}")) (|coerce| (((|List| |#1|) $) "\\spad{coerce(x)} returns the list of elements in \\spad{x}") (($ (|List| |#1|)) "\\spad{coerce(l)} creates a datalist from \\spad{l}"))) ((-4255 . T) (-4254 . T)) -((-3215 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3215 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3309 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-226 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -839,19 +839,19 @@ NIL (-227 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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|#3| (LIST (QUOTE -967) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-787))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-976))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-1019))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525)))))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#3| (QUOTE (-669))) (-12 (|HasCategory| |#3| (QUOTE (-976))) (|HasCategory| |#3| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-976))) (|HasCategory| |#3| (LIST (QUOTE -834) (QUOTE (-1090))))) (-12 (|HasCategory| |#3| (QUOTE (-213))) (|HasCategory| |#3| (QUOTE (-976)))) (-3309 (|HasCategory| |#3| (QUOTE (-976))) (-12 (|HasCategory| |#3| (QUOTE (-1019))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525)))))) (-12 (|HasCategory| |#3| (QUOTE (-1019))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#3| (QUOTE (-1019)))) (-3309 (|HasAttribute| |#3| (QUOTE -4251)) (-12 (|HasCategory| |#3| (QUOTE (-213))) (|HasCategory| |#3| (QUOTE (-976)))) (-12 (|HasCategory| |#3| (QUOTE (-976))) (|HasCategory| |#3| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-976))) (|HasCategory| |#3| (LIST (QUOTE -834) (QUOTE (-1090)))))) (|HasCategory| |#3| (QUOTE (-126))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1019))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -566) (QUOTE (-797))))) (-231 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -862,7 +862,7 @@ NIL NIL (-233 S) ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) -((-4254 . T) (-4255 . T) (-2341 . T)) +((-4254 . T) (-4255 . T) (-1996 . T)) NIL (-234) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g),{}a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -903,7 +903,7 @@ NIL (-243 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4252 |has| |#1| (-6 -4252)) (-4249 . T) (-4248 . T) (-4251 . T)) -((|HasCategory| |#1| (QUOTE (-843))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#3| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#3| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#3| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#3| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#3| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-341))) (-3215 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4252)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-843))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#3| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#3| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#3| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#3| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#3| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-341))) (-3309 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4252)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136))))) (-244 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -948,11 +948,11 @@ 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 -(-255 R -1896) +(-255 R -1346) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-256 R -1896) +(-256 R -1346) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -974,7 +974,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1019)))) (-261 S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) -((-4255 . T) (-2341 . T)) +((-4255 . T) (-1996 . T)) NIL (-262 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) @@ -1000,7 +1000,7 @@ 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 -(-268 S R |Mod| -3934 -1440 |exactQuo|) +(-268 S R |Mod| -3988 -1932 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL @@ -1022,21 +1022,21 @@ NIL NIL (-273 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3160) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3978) (|devaluate| |#2|)))))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1019))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3946) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#2|)))))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1019))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797))))) (-275) ((|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 -(-276 -1896 S) +(-276 -1346 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 -(-277 E -1896) +(-277 E -1346) ((|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 @@ -1084,7 +1084,7 @@ 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 -(-289 -1896) +(-289 -1346) ((|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 @@ -1095,7 +1095,7 @@ NIL (-291 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-843))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-952))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-762))) (-3215 (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-762))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-789)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-1066))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-213))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -486) (QUOTE (-1090)) (LIST (QUOTE -1158) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -288) (LIST (QUOTE -1158) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -265) (LIST (QUOTE -1158) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1158) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-286))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-510))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-789))) (-12 (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-843))) (|HasCategory| $ (QUOTE (-136)))) (-3215 (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (-12 (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-843))) (|HasCategory| $ (QUOTE (-136)))))) +((|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-843))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-952))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-762))) (-3309 (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-762))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-789)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-1066))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-213))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -486) (QUOTE (-1090)) (LIST (QUOTE -1158) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -288) (LIST (QUOTE -1158) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (LIST (QUOTE -265) (LIST (QUOTE -1158) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1158) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-286))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-510))) (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-789))) (-12 (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-843))) (|HasCategory| $ (QUOTE (-136)))) (-3309 (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (-12 (|HasCategory| (-1158 |#1| |#2| |#3| |#4|) (QUOTE (-843))) (|HasCategory| $ (QUOTE (-136)))))) (-292 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1106,9 +1106,9 @@ NIL NIL (-294 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4251 -3215 (-2385 (|has| |#1| (-976)) (|has| |#1| (-588 (-525)))) (-12 (|has| |#1| (-517)) (-3215 (-2385 (|has| |#1| (-976)) (|has| |#1| (-588 (-525)))) (|has| |#1| (-976)) (|has| |#1| (-450)))) (|has| |#1| (-976)) (|has| |#1| (-450))) (-4249 |has| |#1| (-160)) (-4248 |has| |#1| (-160)) ((-4256 "*") |has| |#1| (-517)) (-4247 |has| |#1| (-517)) (-4252 |has| 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(QUOTE (-976))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))))) (-3309 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-976)))) (-3309 (-12 (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| $ (QUOTE (-976))) (|HasCategory| $ (LIST (QUOTE -967) (QUOTE (-525))))) +(-295 R -1346) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1119,7 +1119,7 @@ NIL (-297 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."))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4252 |has| |#1| (-341)) (-4246 |has| |#1| (-341)) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-341))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3215 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -4044) (LIST (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3215 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-892))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2313) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (LIST (QUOTE -3122) (LIST (LIST (QUOTE -592) (QUOTE (-1090))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-341))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3309 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -1908) (LIST (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3309 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-892))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -3766) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (LIST (QUOTE -4104) (LIST (LIST (QUOTE -592) (QUOTE (-1090))) (|devaluate| |#1|))))))) (-298 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1151,12 +1151,12 @@ NIL (-305 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) ((-4255 . T) (-4254 . T)) -((-3215 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3215 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) -(-306 S -1896) +((-3309 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3309 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +(-306 S -1346) ((|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 (-346)))) -(-307 -1896) +(-307 -1346) ((|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."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL @@ -1176,15 +1176,15 @@ 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 -(-312 S -1896 UP UPUP R) +(-312 S -1346 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 -(-313 -1896 UP UPUP R) +(-313 -1346 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 -(-314 -1896 UP UPUP R) +(-314 -1346 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 @@ -1204,26 +1204,26 @@ NIL ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-319 S -1896 UP UPUP) +(-319 S -1346 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|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 (-346))) (|HasCategory| |#2| (QUOTE (-341)))) -(-320 -1896 UP UPUP) +(-320 -1346 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|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."))) ((-4247 |has| (-385 |#2|) (-341)) (-4252 |has| (-385 |#2|) (-341)) (-4246 |has| (-385 |#2|) (-341)) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL (-321 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((-3215 (|HasCategory| (-844 |#1|) (QUOTE (-136))) (|HasCategory| (-844 |#1|) (QUOTE (-346)))) (|HasCategory| (-844 |#1|) (QUOTE (-138))) (|HasCategory| (-844 |#1|) (QUOTE (-346))) (|HasCategory| (-844 |#1|) (QUOTE (-136)))) +((-3309 (|HasCategory| (-844 |#1|) (QUOTE (-136))) (|HasCategory| (-844 |#1|) (QUOTE (-346)))) (|HasCategory| (-844 |#1|) (QUOTE (-138))) (|HasCategory| (-844 |#1|) (QUOTE (-346))) (|HasCategory| (-844 |#1|) (QUOTE (-136)))) (-322 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((-3215 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3309 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) (-323 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((-3215 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3309 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) (-324 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1240,31 +1240,31 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL -(-328 R UP -1896) +(-328 R UP -1346) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-329 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((-3215 (|HasCategory| (-844 |#1|) (QUOTE (-136))) (|HasCategory| (-844 |#1|) (QUOTE (-346)))) (|HasCategory| (-844 |#1|) (QUOTE (-138))) (|HasCategory| (-844 |#1|) (QUOTE (-346))) (|HasCategory| (-844 |#1|) (QUOTE (-136)))) +((-3309 (|HasCategory| (-844 |#1|) (QUOTE (-136))) (|HasCategory| (-844 |#1|) (QUOTE (-346)))) (|HasCategory| (-844 |#1|) (QUOTE (-138))) (|HasCategory| (-844 |#1|) (QUOTE (-346))) (|HasCategory| (-844 |#1|) (QUOTE (-136)))) (-330 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((-3215 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3309 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) (-331 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((-3215 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3309 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) (-332 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((-3215 (|HasCategory| (-844 |#1|) (QUOTE (-136))) (|HasCategory| (-844 |#1|) (QUOTE (-346)))) (|HasCategory| (-844 |#1|) (QUOTE (-138))) (|HasCategory| (-844 |#1|) (QUOTE (-346))) (|HasCategory| (-844 |#1|) (QUOTE (-136)))) +((-3309 (|HasCategory| (-844 |#1|) (QUOTE (-136))) (|HasCategory| (-844 |#1|) (QUOTE (-346)))) (|HasCategory| (-844 |#1|) (QUOTE (-138))) (|HasCategory| (-844 |#1|) (QUOTE (-346))) (|HasCategory| (-844 |#1|) (QUOTE (-136)))) (-333 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((-3215 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) -(-334 -1896 GF) +((-3309 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +(-334 -1346 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 @@ -1272,14 +1272,14 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-336 -1896 FP FPP) +(-336 -1346 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-337 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((-3215 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3309 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) (-338 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL @@ -1334,7 +1334,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4255)) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1019)))) (-351 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4254 . T) (-2341 . T)) +((-4254 . T) (-1996 . T)) NIL (-352 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) @@ -1358,7 +1358,7 @@ NIL NIL (-357) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4237 . T) (-4245 . T) (-2371 . T) (-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) +((-4237 . T) (-4245 . T) (-2038 . T) (-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL (-358 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1374,11 +1374,11 @@ NIL NIL (-361) ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-2341 . T)) +((-1996 . T)) NIL (-362) ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2341 . T)) +((-1996 . T)) NIL (-363 R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) @@ -1408,7 +1408,7 @@ 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 -(-370 -1896 UP UPUP R) +(-370 -1346 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 @@ -1422,27 +1422,27 @@ NIL NIL (-373) ((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram."))) -((-2341 . T)) +((-1996 . T)) NIL (-374) ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2341 . T)) +((-1996 . T)) NIL (-375) ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) NIL NIL -(-376 -3515 |returnType| -3362 |symbols|) +(-376 -1310 |returnType| -4031 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-377 -1896 UP) +(-377 -1346 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-378 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-2341 . T)) +((-1996 . T)) NIL (-379 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1458,7 +1458,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4237)) (|HasAttribute| |#1| (QUOTE -4245))) (-382) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-2371 . T) (-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) +((-2038 . T) (-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL (-383 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) @@ -1471,7 +1471,7 @@ NIL (-385 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4241 -12 (|has| |#1| (-6 -4252)) (|has| |#1| (-429)) (|has| |#1| (-6 -4241))) (-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-762))) (-3215 (|HasCategory| |#1| (QUOTE (-762))) (|HasCategory| |#1| (QUOTE (-789)))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-1066))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (-3215 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770))))) (-3215 (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-510))) (-12 (|HasAttribute| |#1| (QUOTE -4252)) (|HasAttribute| |#1| (QUOTE -4241)) (|HasCategory| |#1| (QUOTE (-429)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-762))) (-3309 (|HasCategory| |#1| (QUOTE (-762))) (|HasCategory| |#1| (QUOTE (-789)))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-1066))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (-3309 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770))))) (-3309 (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-510))) (-12 (|HasAttribute| |#1| (QUOTE -4252)) (|HasAttribute| |#1| (QUOTE -4241)) (|HasCategory| |#1| (QUOTE (-429)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136))))) (-386 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1492,11 +1492,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-391 R -1896 UP A) +(-391 R -1346 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4251 . T)) NIL -(-392 R -1896 UP A |ibasis|) +(-392 R -1346 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 -967) (|devaluate| |#2|)))) @@ -1515,7 +1515,7 @@ NIL (-396 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) ((-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1090)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -288) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -265) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-1130))) (-3215 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-429)))) +((|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1090)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -288) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -265) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-1130))) (-3309 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-429)))) (-397 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}."))) NIL @@ -1542,9 +1542,9 @@ NIL ((|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-346)))) (-403 S) ((|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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4254 . T) (-4244 . T) (-4255 . T) (-2341 . T)) +((-4254 . T) (-4244 . T) (-4255 . T) (-1996 . T)) NIL -(-404 R -1896) +(-404 R -1346) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1552,7 +1552,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4241 -12 (|has| |#1| (-6 -4241)) (|has| |#2| (-6 -4241))) (-4248 . T) (-4249 . T) (-4251 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4241)) (|HasAttribute| |#2| (QUOTE -4241)))) -(-406 R -1896) +(-406 R -1346) ((|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 @@ -1562,17 +1562,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-976))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (-408 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4251 -3215 (|has| |#1| (-976)) (|has| |#1| (-450))) (-4249 |has| |#1| (-160)) (-4248 |has| |#1| (-160)) ((-4256 "*") |has| |#1| (-517)) (-4247 |has| |#1| (-517)) (-4252 |has| |#1| (-517)) (-4246 |has| |#1| (-517)) (-2341 . T)) +((-4251 -3309 (|has| |#1| (-976)) (|has| |#1| (-450))) (-4249 |has| |#1| (-160)) (-4248 |has| |#1| (-160)) ((-4256 "*") |has| |#1| (-517)) (-4247 |has| |#1| (-517)) (-4252 |has| |#1| (-517)) (-4246 |has| |#1| (-517)) (-1996 . T)) NIL -(-409 R -1896) +(-409 R -1346) ((|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 -(-410 R -1896) +(-410 R -1346) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-411 R -1896) +(-411 R -1346) ((|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 @@ -1580,7 +1580,7 @@ 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 -(-413 R -1896 UP) +(-413 R -1346 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 -967) (QUOTE (-47))))) @@ -1598,17 +1598,17 @@ NIL NIL (-417) ((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-2341 . T)) +((-1996 . T)) NIL (-418) ((|constructor| (NIL "\\axiomType{FortranVectorFunctionCategory} is the catagory of arguments to NAG Library routines which return the values of vectors of functions.")) (|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2341 . T)) +((-1996 . T)) NIL (-419 UP) ((|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 -(-420 R UP -1896) +(-420 R UP -1346) ((|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 @@ -1655,7 +1655,7 @@ NIL (-431 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4256 "*") |has| |#2| (-160)) (-4247 |has| |#2| (-517)) (-4252 |has| |#2| (-6 -4252)) (-4249 . T) (-4248 . T) (-4251 . T)) -((|HasCategory| |#2| (QUOTE (-843))) (-3215 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-843)))) (-3215 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-843)))) (-3215 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-843)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3215 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (-3215 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#2| (QUOTE -4252)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-843)))) (|HasCategory| |#2| (QUOTE (-136))))) +((|HasCategory| |#2| (QUOTE (-843))) (-3309 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-843)))) (-3309 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-843)))) (-3309 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-843)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3309 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (-3309 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#2| (QUOTE -4252)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-843)))) (|HasCategory| |#2| (QUOTE (-136))))) (-432 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1720,7 +1720,7 @@ 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 -(-448 |lv| -1896 R) +(-448 |lv| -1346 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 @@ -1735,11 +1735,11 @@ NIL (-451 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4252 |has| |#1| (-341)) (-4246 |has| |#1| (-341)) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-341))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3215 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -4044) (LIST (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3215 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-892))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2313) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (LIST (QUOTE -3122) (LIST (LIST (QUOTE -592) (QUOTE (-1090))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-341))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3309 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -1908) (LIST (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3309 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-892))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -3766) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (LIST (QUOTE -4104) (LIST (LIST (QUOTE -592) (QUOTE (-1090))) (|devaluate| |#1|))))))) (-452 |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."))) ((-4255 . T)) -((-12 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3160) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3978) (|devaluate| |#2|)))))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-789))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3946) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#2|)))))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-789))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797))))) (-453 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4255 . T) (-4254 . T)) @@ -1751,7 +1751,7 @@ NIL (-455 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3160) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3978) (|devaluate| |#2|)))))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1019))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3946) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#2|)))))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1019))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797))))) (-456) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1759,16 +1759,16 @@ NIL (-457 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4256 "*") |has| |#2| (-160)) (-4247 |has| |#2| (-517)) (-4252 |has| |#2| (-6 -4252)) (-4249 . T) (-4248 . T) (-4251 . 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((|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}."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) -(-460 -1896 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +(-460 -1346 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 @@ -1779,14 +1779,14 @@ NIL (-462) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion.")) (|coerce| (((|RadixExpansion| 16) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a radix expansion with base 16.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| (-525) (QUOTE (-843))) (|HasCategory| (-525) (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-952))) (|HasCategory| (-525) (QUOTE (-762))) (-3215 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1066))) (|HasCategory| (-525) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1090)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-525) (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-843)))) (|HasCategory| (-525) (QUOTE (-136))))) +((|HasCategory| (-525) (QUOTE (-843))) (|HasCategory| (-525) (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-952))) (|HasCategory| (-525) (QUOTE (-762))) (-3309 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1066))) (|HasCategory| (-525) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1090)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-525) (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-843)))) (|HasCategory| (-525) (QUOTE (-136))))) (-463 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL ((|HasAttribute| |#1| (QUOTE -4254)) (|HasAttribute| |#1| (QUOTE -4255)) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (-464 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-2341 . T)) +((-1996 . T)) NIL (-465 S) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) @@ -1796,7 +1796,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-467 -1896 UP |AlExt| |AlPol|) +(-467 -1346 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 @@ -1807,16 +1807,16 @@ NIL (-469 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4255 . T) (-4254 . T)) -((-3215 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3215 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3309 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-470 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-471 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented"))) NIL NIL -(-472 R UP -1896) +(-472 R UP -1346) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1836,7 +1836,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-477 -1896 |Expon| |VarSet| |DPoly|) +(-477 -1346 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -567) (QUOTE (-1090))))) @@ -1883,19 +1883,19 @@ NIL (-488 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4255 . T) (-4254 . T)) -((-3215 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3215 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3309 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-489 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((-3215 (|HasCategory| (-538 |#1|) (QUOTE (-136))) (|HasCategory| (-538 |#1|) (QUOTE (-346)))) (|HasCategory| (-538 |#1|) (QUOTE (-138))) (|HasCategory| (-538 |#1|) (QUOTE (-346))) (|HasCategory| (-538 |#1|) (QUOTE (-136)))) +((-3309 (|HasCategory| (-538 |#1|) (QUOTE (-136))) (|HasCategory| (-538 |#1|) (QUOTE (-346)))) (|HasCategory| (-538 |#1|) (QUOTE (-138))) (|HasCategory| (-538 |#1|) (QUOTE (-346))) (|HasCategory| (-538 |#1|) (QUOTE (-136)))) (-490 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-491 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) ((-4255 . T) (-4254 . T)) -((-3215 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3215 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3309 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-492 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -1907,7 +1907,7 @@ NIL (-494 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4256 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4256 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-495 GF) ((|constructor| (NIL "InnerNormalBasisFieldFunctions(\\spad{GF}) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,{}n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,{}n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{\\spad{**}}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,{}e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,{}e,{}d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in \\spad{GF}(2^m) using normal bases\",{} Information and Computation 78,{} \\spad{pp}.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,{}e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,{}n,{}k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in \\spad{GF}(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} \\spad{pp}.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,{}...,{}vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,{}m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,{}p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field \\spad{GF}."))) NIL @@ -1920,7 +1920,7 @@ NIL ((|constructor| (NIL "converts entire exponents to OutputForm"))) NIL NIL -(-498 K -1896 |Par|) +(-498 K -1346 |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 @@ -1940,7 +1940,7 @@ 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 -(-503 K -1896 |Par|) +(-503 K -1346 |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 @@ -1975,12 +1975,12 @@ NIL (-511 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3160) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3978) (|devaluate| |#2|)))))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1019))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797))))) -(-512 R -1896) +((-12 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3946) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#2|)))))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1019))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797))))) +(-512 R -1346) ((|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 -(-513 R0 -1896 UP UPUP R) +(-513 R0 -1346 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 @@ -1990,7 +1990,7 @@ NIL NIL (-515 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,{}f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,{}sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,{}sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-2371 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) +((-2038 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL (-516 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -2000,7 +2000,7 @@ 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."))) ((-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL -(-518 R -1896) +(-518 R -1346) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2012,7 +2012,7 @@ 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 -(-521 R -1896 L) +(-521 R -1346 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -602) (|devaluate| |#2|)))) @@ -2020,11 +2020,11 @@ 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 -(-523 -1896 UP UPUP R) +(-523 -1346 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 -(-524 -1896 UP) +(-524 -1346 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 @@ -2036,15 +2036,15 @@ 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 -(-527 R -1896 L) +(-527 R -1346 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -602) (|devaluate| |#2|)))) -(-528 R -1896) +(-528 R -1346) ((|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 -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1054)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-578))))) -(-529 -1896 UP) +(-529 -1346 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2052,27 +2052,27 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-531 -1896) +(-531 -1346) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-532 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-2371 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) +((-2038 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL (-533) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-534 R -1896) +(-534 R -1346) ((|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 -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-263))) (|HasCategory| |#2| (QUOTE (-578))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-263)))) (|HasCategory| |#1| (QUOTE (-517)))) -(-535 -1896 UP) +(-535 -1346 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-536 R -1896) +(-536 R -1346) ((|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 @@ -2088,15 +2088,15 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-540 R -1896) +(-540 R -1346) ((|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 -(-541 E -1896) +(-541 E -1346) ((|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 -(-542 -1896) +(-542 -1346) ((|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}."))) ((-4249 . T) (-4248 . T)) ((|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-1090))))) @@ -2123,7 +2123,7 @@ NIL (-548 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4255 . T) (-4254 . T)) -((-3215 (-12 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1019))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (-3215 (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-797)))) (-12 (|HasCategory| (-135) (QUOTE (-1019))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -567) (QUOTE (-501)))) (-3215 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1019)))) (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1019))) (-12 (|HasCategory| (-135) (QUOTE (-1019))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1019))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (-3309 (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-797)))) (-12 (|HasCategory| (-135) (QUOTE (-1019))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -567) (QUOTE (-501)))) (-3309 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1019)))) (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1019))) (-12 (|HasCategory| (-135) (QUOTE (-1019))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-797))))) (-549 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL @@ -2131,7 +2131,7 @@ NIL (-550 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,{}r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,{}r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,{}refer,{}var,{}cen,{}r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,{}g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,{}g,{}taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,{}f)} returns the series \\spad{sum(fn(n) * an * x^n,{}n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,{}n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,{}str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-525)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-525)) (|devaluate| |#1|)))) (|HasCategory| (-525) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -4044) (LIST (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-525)))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-525)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-525)) (|devaluate| |#1|)))) (|HasCategory| (-525) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -1908) (LIST (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-525)))))) (-551 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) ((-4249 |has| |#1| (-517)) (-4248 |has| |#1| (-517)) ((-4256 "*") |has| |#1| (-517)) (-4247 |has| |#1| (-517)) (-4251 . T)) @@ -2144,7 +2144,7 @@ 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 -(-554 R -1896 FG) +(-554 R -1346 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2155,14 +2155,14 @@ NIL (-556 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4255 . T) (-4254 . T)) -((-3215 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3215 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-976))) (-12 (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-976)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3309 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-976))) (-12 (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-976)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-557 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL ((|HasAttribute| |#1| (QUOTE -4255)) (|HasCategory| |#2| (QUOTE (-789))) (|HasAttribute| |#1| (QUOTE -4254)) (|HasCategory| |#3| (QUOTE (-1019)))) (-558 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-2341 . T)) +((-1996 . T)) NIL (-559) ((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes.")) (|coerce| (($ (|Byte|)) "\\spad{coerce(x)} the numerical byte value into a \\spad{JVM} bytecode."))) @@ -2170,19 +2170,19 @@ NIL NIL (-560 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)."))) -((-4251 -3215 (-2385 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4249 . T) (-4248 . T)) -((-3215 (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) +((-4251 -3309 (-1341 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4249 . T) (-4248 . T)) +((-3309 (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-561 |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."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3160) (QUOTE (-1073))) (LIST (QUOTE |:|) (QUOTE -3978) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| (-1073) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3946) (QUOTE (-1073))) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| (-1073) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (LIST (QUOTE -566) (QUOTE (-797))))) (-562 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL NIL (-563 |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) -((-4255 . T) (-2341 . T)) +((-4255 . T) (-1996 . T)) NIL (-564 R S) ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) @@ -2200,7 +2200,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-568 -1896 UP) +(-568 -1346 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2216,7 +2216,7 @@ 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}."))) ((-4248 . T) (-4249 . T) (-4251 . T)) ((|HasCategory| |#1| (QUOTE (-787)))) -(-572 R -1896) +(-572 R -1346) ((|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 @@ -2244,18 +2244,18 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-579 R -1896) +(-579 R -1346) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-580 |lv| -1896) +(-580 |lv| -1346) ((|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 (-581) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-4255 . T)) -((-12 (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 (-51))) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3160) (QUOTE (-1073))) (LIST (QUOTE |:|) (QUOTE -3978) (QUOTE (-51))))))) (-3215 (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 (-51))) (QUOTE (-1019))) (|HasCategory| (-51) (QUOTE (-1019)))) (-3215 (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 (-51))) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 (-51))) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-51) (QUOTE (-1019))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1019))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-1073) (QUOTE (-789))) (-3215 (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 (-51))) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-51) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 (-51))) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 (-51))) (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 (-51))) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3946) (QUOTE (-1073))) (LIST (QUOTE |:|) (QUOTE -2511) (QUOTE (-51))))))) (-3309 (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 (-51))) (QUOTE (-1019))) (|HasCategory| (-51) (QUOTE (-1019)))) (-3309 (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 (-51))) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 (-51))) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-51) (QUOTE (-1019))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1019))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-1073) (QUOTE (-789))) (-3309 (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 (-51))) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-51) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 (-51))) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 (-51))) (LIST (QUOTE -566) (QUOTE (-797))))) (-582 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2266,8 +2266,8 @@ NIL NIL (-584 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4251 -3215 (-2385 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4249 . T) (-4248 . T)) -((-3215 (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) +((-4251 -3309 (-1341 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4249 . T) (-4248 . T)) +((-3309 (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-585 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit \\spad{lim(x -> a,{}f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),{}x=a,{}\"left\")} computes the left hand real limit \\spad{lim(x -> a-,{}f(x))}; \\spad{limit(f(x),{}x=a,{}\"right\")} computes the right hand real limit \\spad{lim(x -> a+,{}f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}."))) NIL @@ -2279,7 +2279,7 @@ NIL (-587 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-2823 (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-341)))) +((-2480 (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-341)))) (-588 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4251 . T)) @@ -2299,11 +2299,11 @@ NIL (-592 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) ((-4255 . T) (-4254 . T)) -((-3215 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3215 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-770))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3309 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-770))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-593 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-594 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2318,9 +2318,9 @@ NIL ((|HasAttribute| |#1| (QUOTE -4255))) (-597 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) -((-2341 . T)) +((-1996 . T)) NIL -(-598 R -1896 L) +(-598 R -1346 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 @@ -2340,11 +2340,11 @@ 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}."))) ((-4248 . T) (-4249 . T) (-4251 . T)) NIL -(-603 -1896 UP) +(-603 -1346 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)))) -(-604 A -3966) +(-604 A -1254) ((|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}}"))) ((-4248 . T) (-4249 . T) (-4251 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-341)))) @@ -2378,13 +2378,13 @@ NIL NIL (-612 S) ((|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}."))) -((-4255 . T) (-4254 . T) (-2341 . T)) +((-4255 . T) (-4254 . T) (-1996 . T)) NIL -(-613 -1896) +(-613 -1346) ((|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 -(-614 -1896 |Row| |Col| M) +(-614 -1346 |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 @@ -2395,7 +2395,7 @@ NIL (-616 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,{}R) b - b *\\$SQMATRIX(n,{}R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) ((-4251 . T) (-4254 . T) (-4248 . T) (-4249 . T)) -((|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE (-4256 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-525)))) (-3215 (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-517))) (-3215 (|HasAttribute| |#2| (QUOTE (-4256 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#2| (QUOTE (-213)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-160)))) +((|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE (-4256 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-525)))) (-3309 (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-517))) (-3309 (|HasAttribute| |#2| (QUOTE (-4256 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#2| (QUOTE (-213)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-160)))) (-617 |VarSet|) ((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} \\spad{<=} \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.\\spad{fr}).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(\\spad{vl},{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList1(\\spad{vl},{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL @@ -2406,12 +2406,12 @@ NIL NIL (-619 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}."))) -((-2341 . T)) +((-1996 . T)) NIL (-620 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,{}x,{}y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,{}i,{}j,{}k,{}s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,{}i,{}j,{}k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,{}y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,{}j,{}k)} create a matrix with all zero terms"))) NIL -((-3215 (-12 (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (QUOTE (-976))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (QUOTE (-976))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-621 |VarSet|) ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{\\spad{y*z}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) NIL @@ -2450,7 +2450,7 @@ NIL ((|HasAttribute| |#2| (QUOTE (-4256 "*"))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-517)))) (-630 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4254 . T) (-4255 . T) (-2341 . T)) +((-4254 . T) (-4255 . T) (-1996 . T)) NIL (-631 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,{}a,{}i,{}j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,{}a,{}i,{}j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,{}i,{}j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) @@ -2459,12 +2459,12 @@ NIL (-632 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) ((-4254 . T) (-4255 . T)) -((-3215 (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4256 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4256 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-633 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL NIL -(-634 S -1896 FLAF FLAS) +(-634 S -1346 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 @@ -2474,11 +2474,11 @@ NIL NIL (-636) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4247 . T) (-4252 |has| (-641) (-341)) (-4246 |has| (-641) (-341)) (-2381 . T) (-4253 |has| (-641) (-6 -4253)) (-4250 |has| (-641) (-6 -4250)) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| (-641) (QUOTE (-138))) (|HasCategory| (-641) (QUOTE (-136))) (|HasCategory| (-641) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-641) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-641) (QUOTE (-346))) (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-641) (QUOTE (-213))) (-3215 (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (QUOTE (-327)))) (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (LIST (QUOTE -265) (QUOTE (-641)) (QUOTE (-641)))) (|HasCategory| (-641) (LIST (QUOTE -288) (QUOTE (-641)))) (|HasCategory| (-641) (LIST (QUOTE -486) (QUOTE (-1090)) (QUOTE (-641)))) (|HasCategory| (-641) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| (-641) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| (-641) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| (-641) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (-3215 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (QUOTE (-327)))) (|HasCategory| (-641) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-641) (QUOTE (-952))) (|HasCategory| (-641) (QUOTE (-1112))) (-12 (|HasCategory| (-641) (QUOTE (-933))) (|HasCategory| (-641) (QUOTE (-1112)))) (-3215 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-843)))) (|HasCategory| (-641) (QUOTE (-341))) (-12 (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (QUOTE (-843))))) (-3215 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-843)))) (-12 (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (QUOTE (-843)))) (-12 (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (QUOTE (-843))))) (|HasCategory| (-641) (QUOTE (-510))) (-12 (|HasCategory| (-641) (QUOTE (-985))) (|HasCategory| (-641) (QUOTE (-1112)))) (|HasCategory| (-641) (QUOTE (-985))) (-3215 (|HasCategory| (-641) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-641) (QUOTE (-341)))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-843))) (-3215 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-843)))) (|HasCategory| (-641) (QUOTE (-341)))) (-3215 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-843)))) (|HasCategory| (-641) (QUOTE (-517)))) (-12 (|HasCategory| (-641) (QUOTE (-213))) (|HasCategory| (-641) (QUOTE (-341)))) (-12 (|HasCategory| (-641) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-641) (QUOTE (-341)))) (|HasCategory| (-641) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-641) (QUOTE (-789))) (|HasCategory| (-641) (QUOTE (-517))) (|HasAttribute| (-641) (QUOTE -4253)) (|HasAttribute| (-641) (QUOTE -4250)) (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-843)))) (|HasCategory| (-641) (QUOTE (-136)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-843)))) (|HasCategory| (-641) (QUOTE (-327))))) +((-4247 . T) (-4252 |has| (-641) (-341)) (-4246 |has| (-641) (-341)) (-2047 . T) (-4253 |has| (-641) (-6 -4253)) (-4250 |has| (-641) (-6 -4250)) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) +((|HasCategory| (-641) (QUOTE (-138))) (|HasCategory| (-641) (QUOTE (-136))) (|HasCategory| (-641) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-641) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-641) (QUOTE (-346))) (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-641) (QUOTE (-213))) (-3309 (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (QUOTE (-327)))) (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (LIST (QUOTE -265) (QUOTE (-641)) (QUOTE (-641)))) (|HasCategory| (-641) (LIST (QUOTE -288) (QUOTE (-641)))) (|HasCategory| (-641) (LIST (QUOTE -486) (QUOTE (-1090)) (QUOTE (-641)))) (|HasCategory| (-641) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| (-641) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| (-641) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| (-641) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (-3309 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (QUOTE (-327)))) (|HasCategory| (-641) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-641) (QUOTE (-952))) (|HasCategory| (-641) (QUOTE (-1112))) (-12 (|HasCategory| (-641) (QUOTE (-933))) (|HasCategory| (-641) (QUOTE (-1112)))) (-3309 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-843)))) (|HasCategory| (-641) (QUOTE (-341))) (-12 (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (QUOTE (-843))))) (-3309 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-843)))) (-12 (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (QUOTE (-843)))) (-12 (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (QUOTE (-843))))) (|HasCategory| (-641) (QUOTE (-510))) (-12 (|HasCategory| (-641) (QUOTE (-985))) (|HasCategory| (-641) (QUOTE (-1112)))) (|HasCategory| (-641) (QUOTE (-985))) (-3309 (|HasCategory| (-641) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-641) (QUOTE (-341)))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-843))) (-3309 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-843)))) (|HasCategory| (-641) (QUOTE (-341)))) (-3309 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-843)))) (|HasCategory| (-641) (QUOTE (-517)))) (-12 (|HasCategory| (-641) (QUOTE (-213))) (|HasCategory| (-641) (QUOTE (-341)))) (-12 (|HasCategory| (-641) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-641) (QUOTE (-341)))) (|HasCategory| (-641) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-641) (QUOTE (-789))) (|HasCategory| (-641) (QUOTE (-517))) (|HasAttribute| (-641) (QUOTE -4253)) (|HasAttribute| (-641) (QUOTE -4250)) (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-843)))) (|HasCategory| (-641) (QUOTE (-136)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-843)))) (|HasCategory| (-641) (QUOTE (-327))))) (-637 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,{}d,{}n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) -((-4255 . T) (-2341 . T)) +((-4255 . T) (-1996 . T)) NIL (-638 U) ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,{}n,{}g,{}p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl,{} p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,{}p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,{}p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,{}p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,{}f2,{}p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) @@ -2488,13 +2488,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) NIL NIL -(-640 OV E -1896 PG) +(-640 OV E -1346 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 (-641) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-2371 . T) (-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) +((-2038 . T) (-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL (-642 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m,{} d,{} p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,{}p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m,{} d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2524,7 +2524,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-649 S -1990 I) +(-649 S -1424 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr,{} x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2544,14 +2544,14 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-654 R |Mod| -3934 -1440 |exactQuo|) +(-654 R |Mod| -3988 -1932 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL (-655 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|coerce| (($ |#2|) "\\spad{coerce(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4250 |has| |#1| (-341)) (-4252 |has| |#1| (-6 -4252)) (-4249 . T) (-4248 . T) (-4251 . T)) -((|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-327))) (-3215 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4252)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-327))) (-3309 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4252)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136))))) (-656 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|coerce| (((|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)) $) "\\spad{coerce(x)} \\undocumented") (($ (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) "\\spad{coerce(x)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2560,7 +2560,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4249 |has| |#1| (-160)) (-4248 |has| |#1| (-160)) (-4251 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138)))) -(-658 R |Mod| -3934 -1440 |exactQuo|) +(-658 R |Mod| -3988 -1932 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4251 . T)) NIL @@ -2572,7 +2572,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4249 . T) (-4248 . T)) NIL -(-661 -1896) +(-661 -1346) ((|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]]}."))) ((-4251 . T)) NIL @@ -2608,7 +2608,7 @@ 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.")) (** (($ $ (|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 -(-670 -1896 UP) +(-670 -1346 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 @@ -2627,7 +2627,7 @@ NIL (-674 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) (((-4256 "*") |has| |#2| (-160)) (-4247 |has| |#2| (-517)) (-4252 |has| |#2| (-6 -4252)) (-4249 . T) (-4248 . T) (-4251 . T)) -((|HasCategory| |#2| (QUOTE (-843))) (-3215 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-843)))) (-3215 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-843)))) (-3215 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-843)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3215 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (-3215 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#2| (QUOTE -4252)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-843)))) (|HasCategory| |#2| (QUOTE (-136))))) +((|HasCategory| |#2| (QUOTE (-843))) (-3309 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-843)))) (-3309 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-843)))) (-3309 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-843)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3309 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| (-799 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (-3309 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#2| (QUOTE -4252)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-843)))) (|HasCategory| |#2| (QUOTE (-136))))) (-675 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,{}var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,{}var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,{}var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2646,7 +2646,7 @@ NIL ((-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-789)))) (-679 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4244 . T) (-4255 . T) (-2341 . T)) +((-4244 . T) (-4255 . T) (-1996 . T)) NIL (-680 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,{}ms,{}number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,{}ms,{}number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,{}ms,{}number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,{}ms,{}number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) @@ -2760,15 +2760,15 @@ 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 -(-708 -1896) +(-708 -1346) ((|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 -(-709 P -1896) +(-709 P -1346) ((|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 -(-710 UP -1896) +(-710 UP -1346) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -2784,7 +2784,7 @@ 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."))) (((-4256 "*") . T)) NIL -(-714 R -1896) +(-714 R -1346) ((|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 @@ -2804,7 +2804,7 @@ 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 -(-719 -1896 |ExtF| |SUEx| |ExtP| |n|) +(-719 -1346 |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 @@ -2819,7 +2819,7 @@ NIL (-722 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4252 |has| |#1| (-6 -4252)) (-4249 . T) (-4248 . T) (-4251 . 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(QUOTE -37) (QUOTE (-525))))) (-2480 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-1090)))) (-2480 (|HasCategory| |#1| (LIST (QUOTE -924) (QUOTE (-525))))))) (-3309 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4252)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136))))) (-723 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -2827,14 +2827,14 @@ NIL (-724 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4250 |has| |#1| (-341)) (-4252 |has| |#1| (-6 -4252)) (-4249 . T) (-4248 . T) (-4251 . T)) -((|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (-3215 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4252)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (-3309 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4252)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136))))) (-725 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-726 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,{}v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,{}v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,{}mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular 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} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\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}{[4] \\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.}"))) -((-4255 . T) (-4254 . T) (-2341 . T)) +((-4255 . T) (-4254 . T) (-1996 . T)) NIL (-727 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) @@ -2888,23 +2888,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4248 . T) (-4249 . T) (-4251 . T)) NIL -(-740 -3215 R OS S) +(-740 -3309 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-741 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (-3215 (|HasCategory| (-930 |#1|) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3215 (|HasCategory| (-930 |#1|) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-985))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| (-930 |#1|) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-930 |#1|) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525))))) +((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (-3309 (|HasCategory| (-930 |#1|) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3309 (|HasCategory| (-930 |#1|) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-985))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| (-930 |#1|) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-930 |#1|) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525))))) (-742) ((|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 -(-743 R -1896 L) +(-743 R -1346 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-744 R -1896) +(-744 R -1346) ((|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 @@ -2912,7 +2912,7 @@ 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 -(-746 R -1896) +(-746 R -1346) ((|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 @@ -2920,11 +2920,11 @@ 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 -(-748 -1896 UP UPUP R) +(-748 -1346 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 -(-749 -1896 UP L LQ) +(-749 -1346 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 @@ -2932,38 +2932,38 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|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 -(-751 -1896 UP L LQ) +(-751 -1346 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-752 -1896 UP) +(-752 -1346 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 -(-753 -1896 L UP A LO) +(-753 -1346 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 -(-754 -1896 UP) +(-754 -1346 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-755 -1896 LO) +(-755 -1346 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 -(-756 -1896 LODO) +(-756 -1346 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) NIL NIL -(-757 -3815 S |f|) +(-757 -3339 S |f|) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4248 |has| |#2| (-976)) (-4249 |has| |#2| (-976)) (-4251 |has| |#2| (-6 -4251)) ((-4256 "*") |has| |#2| (-160)) (-4254 . 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((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4252 |has| |#1| (-6 -4252)) (-4249 . T) (-4248 . T) (-4251 . T)) -((|HasCategory| |#1| (QUOTE (-843))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-760 (-1090)) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| (-760 (-1090)) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| (-760 (-1090)) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| (-760 (-1090)) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| (-760 (-1090)) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-341))) (-3215 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4252)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-843))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-760 (-1090)) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| (-760 (-1090)) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| (-760 (-1090)) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| (-760 (-1090)) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| (-760 (-1090)) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-341))) (-3309 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4252)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136))))) (-759 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")) (|coerce| ((|#2| $) "\\spad{coerce(p)} views \\spad{p} as a valie in the partial differential ring.") (($ |#2|) "\\spad{coerce(r)} views \\spad{r} as a value in the ordinary differential ring."))) (((-4256 "*") |has| |#2| (-341)) (-4247 |has| |#2| (-341)) (-4252 |has| |#2| (-341)) (-4246 |has| |#2| (-341)) (-4251 . T) (-4249 . T) (-4248 . T)) @@ -3018,7 +3018,7 @@ NIL NIL (-772 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4254 . T) (-4244 . T) (-4255 . T) (-2341 . T)) +((-4254 . T) (-4244 . T) (-4255 . T) (-1996 . T)) NIL (-773) ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,{}timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,{}u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) @@ -3031,7 +3031,7 @@ NIL (-775 R) ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) ((-4251 |has| |#1| (-787))) -((|HasCategory| |#1| (QUOTE (-787))) (-3215 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-787)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-510))) (-3215 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-787))) (-3309 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-787)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-510))) (-3309 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) (-776 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) ((-4249 |has| |#1| (-160)) (-4248 |has| |#1| (-160)) (-4251 . T)) @@ -3059,12 +3059,12 @@ NIL (-782 R) ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4251 |has| |#1| (-787))) -((|HasCategory| |#1| (QUOTE (-787))) (-3215 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-787)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-510))) (-3215 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-787))) (-3309 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-787)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-510))) (-3309 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) (-783) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-784 -3815 S) +(-784 -3339 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3100,11 +3100,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) -(-793 R |sigma| -1880) +(-793 R |sigma| -3626) ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{} x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) ((-4248 . T) (-4249 . T) (-4251 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-341)))) -(-794 |x| R |sigma| -1880) +(-794 |x| R |sigma| -3626) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} returns \\spad{x} as a skew-polynomial."))) ((-4248 . T) (-4249 . T) (-4251 . T)) ((|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-341)))) @@ -3151,15 +3151,15 @@ NIL (-805 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| (-804 |#1|) (QUOTE (-843))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| (-804 |#1|) (QUOTE (-136))) (|HasCategory| (-804 |#1|) (QUOTE (-138))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-804 |#1|) (QUOTE (-952))) (|HasCategory| (-804 |#1|) (QUOTE (-762))) (-3215 (|HasCategory| (-804 |#1|) (QUOTE (-762))) (|HasCategory| (-804 |#1|) (QUOTE (-789)))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-804 |#1|) (QUOTE (-1066))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-804 |#1|) (QUOTE (-213))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -486) (QUOTE (-1090)) (LIST (QUOTE -804) (|devaluate| |#1|)))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -288) (LIST (QUOTE -804) (|devaluate| |#1|)))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -265) (LIST (QUOTE -804) (|devaluate| |#1|)) (LIST (QUOTE -804) (|devaluate| |#1|)))) (|HasCategory| (-804 |#1|) (QUOTE (-286))) (|HasCategory| (-804 |#1|) (QUOTE (-510))) (|HasCategory| (-804 |#1|) (QUOTE (-789))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-804 |#1|) (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-804 |#1|) (QUOTE (-843)))) (|HasCategory| (-804 |#1|) (QUOTE (-136))))) +((|HasCategory| (-804 |#1|) (QUOTE (-843))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| (-804 |#1|) (QUOTE (-136))) (|HasCategory| (-804 |#1|) (QUOTE (-138))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-804 |#1|) (QUOTE (-952))) (|HasCategory| (-804 |#1|) (QUOTE (-762))) (-3309 (|HasCategory| (-804 |#1|) (QUOTE (-762))) (|HasCategory| (-804 |#1|) (QUOTE (-789)))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-804 |#1|) (QUOTE (-1066))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-804 |#1|) (QUOTE (-213))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -486) (QUOTE (-1090)) (LIST (QUOTE -804) (|devaluate| |#1|)))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -288) (LIST (QUOTE -804) (|devaluate| |#1|)))) (|HasCategory| (-804 |#1|) (LIST (QUOTE -265) (LIST (QUOTE -804) (|devaluate| |#1|)) (LIST (QUOTE -804) (|devaluate| |#1|)))) (|HasCategory| (-804 |#1|) (QUOTE (-286))) (|HasCategory| (-804 |#1|) (QUOTE (-510))) (|HasCategory| (-804 |#1|) (QUOTE (-789))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-804 |#1|) (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-804 |#1|) (QUOTE (-843)))) (|HasCategory| (-804 |#1|) (QUOTE (-136))))) (-806 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#2| (QUOTE (-843))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-952))) (|HasCategory| |#2| (QUOTE (-762))) (-3215 (|HasCategory| |#2| (QUOTE (-762))) (|HasCategory| |#2| (QUOTE (-789)))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#2| (LIST (QUOTE -486) (QUOTE (-1090)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -265) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-789))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-843)))) (|HasCategory| |#2| (QUOTE (-136))))) +((|HasCategory| |#2| (QUOTE (-843))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-952))) (|HasCategory| |#2| (QUOTE (-762))) (-3309 (|HasCategory| |#2| (QUOTE (-762))) (|HasCategory| |#2| (QUOTE (-789)))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#2| (LIST (QUOTE -486) (QUOTE (-1090)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -265) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-789))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-843)))) (|HasCategory| |#2| (QUOTE (-136))))) (-807 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,{}t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))))) (-808) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3215,7 +3215,7 @@ NIL (-821 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,{}...,{}en],{} pat)} matches the pattern pat on the list of expressions \\spad{[e1,{}...,{}en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,{}...,{}en],{} pat)} tests if the list of expressions \\spad{[e1,{}...,{}en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr,{} pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-2823 (|HasCategory| |#2| (QUOTE (-976)))) (-2823 (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-1090)))))) (-12 (|HasCategory| |#2| (QUOTE (-976))) (-2823 (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-1090)))))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-1090))))) +((-12 (-2480 (|HasCategory| |#2| (QUOTE (-976)))) (-2480 (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-1090)))))) (-12 (|HasCategory| |#2| (QUOTE (-976))) (-2480 (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-1090)))))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-1090))))) (-822 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3224,7 +3224,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-824 R -1990) +(-824 R -1424) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3248,7 +3248,7 @@ 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 -(-830 UP -1896) +(-830 UP -1346) ((|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 @@ -3271,7 +3271,7 @@ NIL (-835 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|coerce| (((|Tree| |#1|) $) "\\spad{coerce(x)} \\undocumented")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-836 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL @@ -3287,7 +3287,7 @@ NIL (-839 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4251 . T)) -((-3215 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-789)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-789)))) +((-3309 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-789)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-789)))) (-840 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3308,7 +3308,7 @@ 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."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) ((|HasCategory| $ (QUOTE (-138))) (|HasCategory| $ (QUOTE (-136))) (|HasCategory| $ (QUOTE (-346)))) -(-845 R0 -1896 UP UPUP R) +(-845 R0 -1346 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 @@ -3336,7 +3336,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) NIL NIL -(-852 -1896) +(-852 -1346) ((|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 @@ -3352,11 +3352,11 @@ 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}."))) (((-4256 "*") . T)) NIL -(-856 -1896 P) +(-856 -1346 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-857 |xx| -1896) +(-857 |xx| -1346) ((|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 @@ -3380,7 +3380,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-863 R -1896) +(-863 R -1346) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3392,7 +3392,7 @@ 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 -(-866 S R -1896) +(-866 S R -1346) ((|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 @@ -3412,11 +3412,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -820) (|devaluate| |#1|)))) -(-871 R -1896 -1990) +(-871 R -1346 -1424) ((|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 -(-872 -1990) +(-872 -1424) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -3439,7 +3439,7 @@ NIL (-877 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4255 . T) (-4254 . T)) -((-3215 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3215 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-976))) (-12 (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-976)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3309 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-976))) (-12 (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-976)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-878 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL @@ -3464,7 +3464,7 @@ 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}."))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4252 |has| |#1| (-6 -4252)) (-4249 . T) (-4248 . T) (-4251 . T)) NIL -(-884 E V R P -1896) +(-884 E V R P -1346) ((|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 @@ -3475,8 +3475,8 @@ NIL (-886 R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,{}x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4252 |has| |#1| (-6 -4252)) (-4249 . T) (-4248 . T) (-4251 . T)) -((|HasCategory| |#1| (QUOTE (-843))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1090) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| (-1090) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| (-1090) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| (-1090) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| (-1090) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))) (-3215 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4252)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136))))) -(-887 E V R P -1896) +((|HasCategory| |#1| (QUOTE (-843))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1090) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| (-1090) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| (-1090) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| (-1090) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| (-1090) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))) (-3309 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4252)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136))))) +(-887 E V R P -1346) ((|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)}.")) (|coerce| (($ |#4|) "\\spad{coerce(p)} \\undocumented")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-429)))) @@ -3495,12 +3495,12 @@ NIL (-891 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4255 . T) (-4254 . T)) -((-3215 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3215 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3309 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-892) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-893 -1896) +(-893 -1346) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3515,11 +3515,11 @@ NIL (-896 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4252 |has| |#1| (-6 -4252)) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-126)))) (-3215 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4252))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-126)))) (-3309 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4252))) (-897 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,{}b)} \\undocumented"))) ((-4251 -12 (|has| |#2| (-450)) (|has| |#1| (-450)))) -((-3215 (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735)))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735))))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-12 (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#2| (QUOTE (-669))))) (-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-346)))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-12 (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#2| (QUOTE (-669)))) (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735))))) (-12 (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#2| (QUOTE (-669)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) +((-3309 (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735)))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735))))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-12 (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#2| (QUOTE (-669))))) (-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-346)))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-12 (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#2| (QUOTE (-669)))) (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735))))) (-12 (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#2| (QUOTE (-669)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-898) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3534,7 +3534,7 @@ NIL NIL (-901 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,{}q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) -((-4254 . T) (-4255 . T) (-2341 . T)) +((-4254 . T) (-4255 . T) (-1996 . T)) NIL (-902 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) @@ -3562,7 +3562,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-517)))) (-908 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4254 . T) (-2341 . T)) +((-4254 . T) (-1996 . T)) NIL (-909 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) @@ -3578,7 +3578,7 @@ NIL NIL (-912 R) ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,{}l,{}r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|convert| (($ (|List| |#1|)) "\\spad{convert(l)} takes a list of elements,{} \\spad{l},{} from the domain Ring and returns the form of point category.")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) -((-4255 . T) (-4254 . T) (-2341 . T)) +((-4255 . T) (-4254 . T) (-1996 . T)) NIL (-913 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3596,7 +3596,7 @@ 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 -(-917 K R UP -1896) +(-917 K R UP -1346) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -3626,7 +3626,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-843))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-952))) (|HasCategory| |#2| (QUOTE (-762))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1066)))) (-924 S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) -((-2341 . T) (-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) +((-1996 . T) (-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL (-925 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) @@ -3634,7 +3634,7 @@ NIL NIL (-926 S) ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,{}q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-4254 . T) (-4255 . T) (-2341 . T)) +((-4254 . T) (-4255 . T) (-1996 . T)) NIL (-927 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) @@ -3651,11 +3651,11 @@ NIL (-930 R) ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) ((-4247 |has| |#1| (-269)) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-341))) (-3215 (|HasCategory| |#1| (QUOTE (-269))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-269))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-985))) (|HasCategory| |#1| (QUOTE (-510))) (-3215 (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))))) +((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-341))) (-3309 (|HasCategory| |#1| (QUOTE (-269))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-269))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-985))) (|HasCategory| |#1| (QUOTE (-510))) (-3309 (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))))) (-931 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,{}y,{}...,{}z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-932 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3664,14 +3664,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-934 -1896 UP UPUP |radicnd| |n|) +(-934 -1346 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4247 |has| (-385 |#2|) (-341)) (-4252 |has| (-385 |#2|) (-341)) (-4246 |has| (-385 |#2|) (-341)) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| (-385 |#2|) (QUOTE (-136))) (|HasCategory| (-385 |#2|) (QUOTE (-138))) (|HasCategory| (-385 |#2|) (QUOTE (-327))) (-3215 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-3215 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-3215 (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-385 |#2|) (QUOTE (-327))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3215 (|HasCategory| (-385 |#2|) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341))))) +((|HasCategory| (-385 |#2|) (QUOTE (-136))) (|HasCategory| (-385 |#2|) (QUOTE (-138))) (|HasCategory| (-385 |#2|) (QUOTE (-327))) (-3309 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-3309 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-3309 (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-385 |#2|) (QUOTE (-327))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3309 (|HasCategory| (-385 |#2|) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341))))) (-935 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion.")) (|coerce| (((|Fraction| (|Integer|)) $) "\\spad{coerce(rx)} converts a radix expansion to a rational number."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| (-525) (QUOTE (-843))) (|HasCategory| (-525) (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-952))) (|HasCategory| (-525) (QUOTE (-762))) (-3215 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1066))) (|HasCategory| (-525) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1090)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-525) (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-843)))) (|HasCategory| (-525) (QUOTE (-136))))) +((|HasCategory| (-525) (QUOTE (-843))) (|HasCategory| (-525) (LIST (QUOTE -967) (QUOTE (-1090)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-952))) (|HasCategory| (-525) (QUOTE (-762))) (-3309 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1066))) (|HasCategory| (-525) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1090)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-525) (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-843)))) (|HasCategory| (-525) (QUOTE (-136))))) (-936) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,{}b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL @@ -3694,29 +3694,29 @@ NIL ((|HasAttribute| |#1| (QUOTE -4255)) (|HasCategory| |#2| (QUOTE (-1019)))) (-941 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) -((-2341 . T)) +((-1996 . T)) NIL (-942 S) -((|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)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\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}}"))) +((|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}}"))) NIL NIL (-943) -((|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)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\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}}"))) +((|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}}"))) ((-4247 . T) (-4252 . T) (-4246 . T) (-4249 . T) (-4248 . T) ((-4256 "*") . T) (-4251 . T)) NIL -(-944 R -1896) +(-944 R -1346) ((|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 -(-945 R -1896) +(-945 R -1346) ((|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 -(-946 -1896 UP) +(-946 -1346 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 -(-947 -1896 UP) +(-947 -1346 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 @@ -3747,8 +3747,8 @@ NIL (-954 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) ((-4247 . T) (-4252 . T) (-4246 . T) (-4249 . T) (-4248 . T) ((-4256 "*") . T) (-4251 . T)) -((-3215 (|HasCategory| (-385 (-525)) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-385 (-525)) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 (-525)) (LIST (QUOTE -967) (QUOTE (-525))))) -(-955 -1896 L) +((-3309 (|HasCategory| (-385 (-525)) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-385 (-525)) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 (-525)) (LIST (QUOTE -967) (QUOTE (-525))))) +(-955 -1346 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -3784,14 +3784,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-964 -1896 |Expon| |VarSet| |FPol| |LFPol|) +(-964 -1346 |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"))) (((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL (-965) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3160) (QUOTE (-1090))) (LIST (QUOTE |:|) (QUOTE -3978) (QUOTE (-51))))))) (-3215 (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (QUOTE (-1019))) (|HasCategory| (-51) (QUOTE (-1019)))) (-3215 (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-51) (QUOTE (-1019))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1019))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (QUOTE (-1019))) (|HasCategory| (-1090) (QUOTE (-789))) (|HasCategory| (-51) (QUOTE (-1019))) (-3215 (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3946) (QUOTE (-1090))) (LIST (QUOTE |:|) (QUOTE -2511) (QUOTE (-51))))))) (-3309 (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (QUOTE (-1019))) (|HasCategory| (-51) (QUOTE (-1019)))) (-3309 (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-51) (QUOTE (-1019))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1019))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (QUOTE (-1019))) (|HasCategory| (-1090) (QUOTE (-789))) (|HasCategory| (-51) (QUOTE (-1019))) (-3309 (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (LIST (QUOTE -566) (QUOTE (-797))))) (-966 A S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} transforms a into an element of \\%."))) NIL @@ -3836,7 +3836,7 @@ 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\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|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."))) ((-4251 . T)) NIL -(-977 |xx| -1896) +(-977 |xx| -1346) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -3846,12 +3846,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-286))) (|HasCategory| |#4| (QUOTE (-341))) (|HasCategory| |#4| (QUOTE (-517))) (|HasCategory| |#4| (QUOTE (-160)))) (-979 |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) -((-4254 . T) (-2341 . T) (-4249 . T) (-4248 . T)) +((-4254 . T) (-1996 . T) (-4249 . T) (-4248 . T)) NIL (-980 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|coerce| (((|Matrix| |#3|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{RectangularMatrix} to a matrix of type \\spad{Matrix}.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4254 . T) (-4249 . T) (-4248 . T)) -((-3215 (-12 (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1019))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -567) (QUOTE (-501)))) (-3215 (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (QUOTE (-341)))) (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (QUOTE (-1019))) (|HasCategory| |#3| (QUOTE (-286))) (|HasCategory| |#3| (QUOTE (-517))) (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (LIST (QUOTE -566) (QUOTE (-797)))) (-12 (|HasCategory| |#3| (QUOTE (-1019))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|))))) +((-3309 (-12 (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1019))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -567) (QUOTE (-501)))) (-3309 (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (QUOTE (-341)))) (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (QUOTE (-1019))) (|HasCategory| |#3| (QUOTE (-286))) (|HasCategory| |#3| (QUOTE (-517))) (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (LIST (QUOTE -566) (QUOTE (-797)))) (-12 (|HasCategory| |#3| (QUOTE (-1019))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|))))) (-981 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL @@ -3883,7 +3883,7 @@ NIL (-988) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,{}routineName,{}ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,{}s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,{}s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,{}s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,{}s,{}newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,{}s,{}newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,{}y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3160) (QUOTE (-1090))) (LIST (QUOTE |:|) (QUOTE -3978) (QUOTE (-51))))))) (-3215 (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (QUOTE (-1019))) (|HasCategory| (-51) (QUOTE (-1019)))) (-3215 (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-51) (QUOTE (-1019))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1019))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (QUOTE (-1019))) (|HasCategory| (-1090) (QUOTE (-789))) (|HasCategory| (-51) (QUOTE (-1019))) (-3215 (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3946) (QUOTE (-1090))) (LIST (QUOTE |:|) (QUOTE -2511) (QUOTE (-51))))))) (-3309 (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (QUOTE (-1019))) (|HasCategory| (-51) (QUOTE (-1019)))) (-3309 (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-51) (QUOTE (-1019))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1019))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (QUOTE (-1019))) (|HasCategory| (-1090) (QUOTE (-789))) (|HasCategory| (-51) (QUOTE (-1019))) (-3309 (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (LIST (QUOTE -566) (QUOTE (-797))))) (-989 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL @@ -3910,7 +3910,7 @@ NIL NIL (-995 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#4| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4255 . T) (-4254 . T) (-2341 . T)) +((-4255 . T) (-4254 . T) (-1996 . T)) NIL (-996 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\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}{[2] \\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.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) @@ -3920,11 +3920,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-998 |Base| R -1896) +(-998 |Base| R -1346) ((|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 -(-999 |Base| R -1896) +(-999 |Base| R -1346) ((|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 @@ -3939,7 +3939,7 @@ NIL (-1002 R UP M) ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) ((-4247 |has| |#1| (-341)) (-4252 |has| |#1| (-341)) (-4246 |has| |#1| (-341)) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327))) (-3215 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-327)))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090))))) (-3215 (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341)))) (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341))))) +((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327))) (-3309 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-327)))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090))))) (-3309 (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341)))) (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341))))) (-1003 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -3963,7 +3963,7 @@ NIL (-1008 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4252 |has| |#1| (-6 -4252)) (-4249 . T) (-4248 . T) (-4251 . 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A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -3982,7 +3982,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-1019)))) (-1013 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|convert| (($ |#1|) "\\spad{convert(i)} creates the segment \\spad{i..i}.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,{}j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\spad{hi}(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) -((-2341 . T)) +((-1996 . T)) NIL (-1014 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) @@ -3990,7 +3990,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (QUOTE (-1019)))) (-1015 S L) ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l),{} f(l+k),{} ...,{} f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l,{} l+k,{} ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,{}3,{}5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-2341 . T)) +((-1996 . T)) NIL (-1016 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) @@ -3998,7 +3998,7 @@ NIL NIL (-1017 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4244 . T) (-2341 . T)) +((-4244 . T) (-1996 . T)) NIL (-1018 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) @@ -4015,7 +4015,7 @@ NIL (-1021 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}"))) ((-4254 . T) (-4244 . T) (-4255 . T)) -((-3215 (-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-789))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-789))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-1022 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|convert| (($ |#5|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#4|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#3|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#2|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#1|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the \\spad{S}-expression \\spad{(a1,{}...,{}an)}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL @@ -4042,7 +4042,7 @@ NIL NIL (-1028 R E V P) ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,{}mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\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}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-4255 . T) (-4254 . T) (-2341 . T)) +((-4255 . T) (-4254 . T) (-1996 . T)) NIL (-1029) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,{}0,{}0] < [0,{}3,{}0] < [0,{}0,{}3] < [2,{}1,{}0] < [2,{}0,{}1] < [0,{}2,{}1] < [1,{}2,{}0] < [1,{}0,{}2] < [0,{}1,{}2] < [1,{}1,{}1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,{}0,{}3] < [0,{}1,{}2] < [0,{}2,{}1] < [0,{}3,{}0] < [1,{}0,{}2] < [1,{}1,{}1] < [1,{}2,{}0] < [2,{}0,{}1] < [2,{}1,{}0] < [3,{}0,{}0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,{}m,{}k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,{}1,{}...,{}(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,{}...,{}(m-1)} into {\\em 0,{}...,{}(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,{}m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,{}3)} is 10,{} since {\\em [0,{}0,{}3],{} [0,{}1,{}2],{} [0,{}2,{}1],{} [0,{}3,{}0],{} [1,{}0,{}2],{} [1,{}1,{}1],{} [1,{}2,{}0],{} [2,{}0,{}1],{} [2,{}1,{}0],{} [3,{}0,{}0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,{}lattP,{}constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,{}beta,{}C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,{}1,{}0)}. Also,{} {\\em new(1,{}1,{}0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,{}gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,{}...,{}n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,{}...,{}n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,{}beta,{}C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,{}beta,{}\\spad{pi})}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4059,12 +4059,12 @@ NIL (-1032 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. 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(QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-126))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-213))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-346))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-735))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-787))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-976))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-1019))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525)))))) (|HasCategory| (-525) (QUOTE (-789))) (-12 (|HasCategory| |#3| (QUOTE (-976))) (|HasCategory| |#3| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-213))) (|HasCategory| |#3| (QUOTE (-976)))) (-12 (|HasCategory| |#3| (QUOTE (-976))) (|HasCategory| |#3| (LIST (QUOTE -834) (QUOTE (-1090))))) (|HasCategory| |#3| (QUOTE (-669))) (-12 (|HasCategory| |#3| (QUOTE (-1019))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525))))) (-3309 (|HasCategory| |#3| (QUOTE (-976))) (-12 (|HasCategory| |#3| (QUOTE (-1019))) (|HasCategory| |#3| (LIST (QUOTE -967) (QUOTE (-525)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#3| (QUOTE (-1019)))) (|HasAttribute| |#3| (QUOTE -4251)) (|HasCategory| |#3| (QUOTE (-126))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1019))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -566) (QUOTE (-797))))) (-1033 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL ((|HasCategory| |#1| (QUOTE (-429)))) -(-1034 R -1896) +(-1034 R -1346) ((|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 @@ -4082,7 +4082,7 @@ NIL NIL (-1038 S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\spad{#s}}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4254 . T) (-4255 . T) (-2341 . T)) +((-4254 . T) (-4255 . T) (-1996 . T)) NIL (-1039 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) @@ -4090,7 +4090,7 @@ NIL ((|HasCategory| |#3| (QUOTE (-341))) (|HasAttribute| |#3| (QUOTE (-4256 "*"))) (|HasCategory| |#3| (QUOTE (-160)))) (-1040 |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) -((-2341 . T) (-4254 . T) (-4248 . T) (-4249 . T) (-4251 . T)) +((-1996 . T) (-4254 . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL (-1041 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,{}B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) @@ -4099,16 +4099,16 @@ NIL (-1042 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4252 |has| |#1| (-6 -4252)) (-4249 . T) (-4248 . T) (-4251 . T)) -((|HasCategory| |#1| (QUOTE (-843))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))) (-3215 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4252)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-843))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))) (-3309 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4252)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136))))) (-1043 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4249 . T) (-4248 . T) (-4251 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341)))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341)))) (-1044 R E V P) ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) -((-4255 . T) (-4254 . T) (-2341 . T)) +((-4255 . T) (-4254 . T) (-1996 . T)) NIL -(-1045 UP -1896) +(-1045 UP -1346) ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,{}g,{}h,{}i,{}k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,{}g,{}h,{}j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,{}g,{}h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,{}g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,{}g,{}h,{}i,{}j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,{}g,{}h,{}i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,{}g,{}h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,{}g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,{}f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) NIL NIL @@ -4155,18 +4155,18 @@ NIL (-1056 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| (-1055 |#1| |#2|) (LIST (QUOTE -288) (LIST (QUOTE -1055) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1019)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1019))) (-3215 (|HasCategory| (-1055 |#1| |#2|) (LIST (QUOTE -566) (QUOTE (-797)))) (-12 (|HasCategory| (-1055 |#1| |#2|) (LIST (QUOTE -288) (LIST (QUOTE -1055) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1019))))) (|HasCategory| (-1055 |#1| |#2|) (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| (-1055 |#1| |#2|) (LIST (QUOTE -288) (LIST (QUOTE -1055) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1019)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1019))) (-3309 (|HasCategory| (-1055 |#1| |#2|) (LIST (QUOTE -566) (QUOTE (-797)))) (-12 (|HasCategory| (-1055 |#1| |#2|) (LIST (QUOTE -288) (LIST (QUOTE -1055) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1019))))) (|HasCategory| (-1055 |#1| |#2|) (LIST (QUOTE -566) (QUOTE (-797))))) (-1057 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|coerce| (((|Matrix| |#2|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{SquareMatrix} to a matrix of type \\spadtype{Matrix}.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}."))) ((-4251 . T) (-4243 |has| |#2| (-6 (-4256 "*"))) (-4254 . T) (-4248 . T) (-4249 . T)) -((|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE (-4256 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-525)))) (-3215 (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-341))) (-3215 (|HasAttribute| |#2| (QUOTE (-4256 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#2| (QUOTE (-213)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-160)))) +((|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE (-4256 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-525)))) (-3309 (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-341))) (-3309 (|HasAttribute| |#2| (QUOTE (-4256 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasCategory| |#2| (QUOTE (-213)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-160)))) (-1058 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1059) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4255 . T) (-4254 . T) (-2341 . T)) +((-4255 . T) (-4254 . T) (-1996 . T)) NIL (-1060 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4179,19 +4179,19 @@ NIL (-1062 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,{}y,{}...,{}z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-1063 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL (-1064 S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) -((-2341 . T)) +((-1996 . T)) NIL (-1065 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4255 . T)) -((-12 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3160) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3978) (|devaluate| |#2|)))))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-789))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3946) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#2|)))))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-789))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797))))) (-1066) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4215,19 +4215,19 @@ NIL (-1071 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} converts a list \\spad{l} to a stream.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) ((-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-1072) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4255 . T) (-4254 . T) (-2341 . T)) +((-4255 . T) (-4254 . T) (-1996 . T)) NIL (-1073) NIL ((-4255 . T) (-4254 . T)) -((-3215 (-12 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1019))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1019))) (-12 (|HasCategory| (-135) (QUOTE (-1019))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1019))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1019))) (-12 (|HasCategory| (-135) (QUOTE (-1019))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-797))))) (-1074 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3160) (QUOTE (-1073))) (LIST (QUOTE |:|) (QUOTE -3978) (|devaluate| |#1|)))))) (-3215 (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-1019)))) (-3215 (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (QUOTE (-1019))) (|HasCategory| (-1073) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3946) (QUOTE (-1073))) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#1|)))))) (-3309 (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-1019)))) (-3309 (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (QUOTE (-1019))) (|HasCategory| (-1073) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (LIST (QUOTE -566) (QUOTE (-797))))) (-1075 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL @@ -4254,9 +4254,9 @@ NIL NIL (-1081 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4256 "*") -3215 (-2385 (|has| |#1| (-341)) (|has| (-1088 |#1| |#2| |#3|) (-762))) (|has| |#1| (-160)) (-2385 (|has| |#1| (-341)) (|has| (-1088 |#1| |#2| |#3|) (-843)))) (-4247 -3215 (-2385 (|has| |#1| (-341)) (|has| (-1088 |#1| |#2| |#3|) (-762))) (|has| |#1| (-517)) (-2385 (|has| |#1| (-341)) (|has| (-1088 |#1| |#2| |#3|) (-843)))) (-4252 |has| |#1| (-341)) (-4246 |has| |#1| (-341)) (-4248 . T) (-4249 . T) (-4251 . 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(-843)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (-3309 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4252)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-136))))) (-1087 |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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4252 |has| |#1| (-341)) (-4246 |has| |#1| (-341)) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-341))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3215 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -4044) (LIST (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3215 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-892))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2313) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (LIST (QUOTE -3122) (LIST (LIST (QUOTE -592) (QUOTE (-1090))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-341))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3309 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -1908) (LIST (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3309 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-892))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -3766) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (LIST (QUOTE -4104) (LIST (LIST (QUOTE -592) (QUOTE (-1090))) (|devaluate| |#1|))))))) (-1088 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-713)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-713)) (|devaluate| |#1|)))) (|HasCategory| (-713) (QUOTE (-1031))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasSignature| |#1| (LIST (QUOTE -4044) (LIST (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasCategory| |#1| (QUOTE (-341))) (-3215 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-892))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2313) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (LIST (QUOTE -3122) (LIST (LIST (QUOTE -592) (QUOTE (-1090))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-713)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-713)) (|devaluate| |#1|)))) (|HasCategory| (-713) (QUOTE (-1031))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasSignature| |#1| (LIST (QUOTE -1908) (LIST (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasCategory| |#1| (QUOTE (-341))) (-3309 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-892))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -3766) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (LIST (QUOTE -4104) (LIST (LIST (QUOTE -592) (QUOTE (-1090))) (|devaluate| |#1|))))))) (-1089) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4299,7 +4299,7 @@ NIL (-1092 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4252 |has| |#1| (-6 -4252)) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| (-903) (QUOTE (-126))) (|HasCategory| |#1| (QUOTE (-517)))) (-3215 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4252))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| (-903) (QUOTE (-126))) (|HasCategory| |#1| (QUOTE (-517)))) (-3309 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4252))) (-1093) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4331,7 +4331,7 @@ NIL (-1100 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) ((-4254 . T) (-4255 . T)) -((-12 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3160) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3978) (|devaluate| |#2|)))))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1019))) (-3215 (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3946) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#2|)))))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1019)))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1019))) (-3309 (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -566) (QUOTE (-797))))) (-1101 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) NIL @@ -4342,7 +4342,7 @@ NIL NIL (-1103 |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,{}t1,{}t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,{}y,{}...,{}z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,{}k,{}e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) -((-4255 . T) (-2341 . T)) +((-4255 . T) (-1996 . T)) NIL (-1104 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) @@ -4383,7 +4383,7 @@ NIL (-1113 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1,{} t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4255 . T) (-4254 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1019))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-1114 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4392,7 +4392,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1116 R -1896) +(-1116 R -1346) ((|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 @@ -4400,7 +4400,7 @@ 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 -(-1118 R -1896) +(-1118 R -1346) ((|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 -567) (LIST (QUOTE -826) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -820) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -820) (|devaluate| |#1|))))) @@ -4410,12 +4410,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-346)))) (-1120 R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4255 . T) (-4254 . T) (-2341 . T)) +((-4255 . T) (-4254 . T) (-1996 . T)) NIL (-1121 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4249 . T) (-4248 . T) (-4251 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341)))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341)))) (-1122 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,{}ll,{}b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,{}b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4428,13 +4428,13 @@ 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")) (|coerce| (($ (|PrimitiveArray| |#1|)) "\\spad{coerce(a)} makes a tuple from primitive array a"))) NIL ((|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) -(-1125 -1896) +(-1125 -1346) ((|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 (-1126) ((|constructor| (NIL "The fundamental Type."))) -((-2341 . T)) +((-1996 . T)) NIL (-1127 S) ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l,{} fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by \\spad{fn}.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a,{} b,{} fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a,{} b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,{}...,{}bm],{}[a1,{}...,{}an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < \\spad{ai}}\\space{2}for \\spad{c} not among the \\spad{ai}\\spad{'s} and \\spad{bj}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,{}d)} if neither is among the \\spad{ai}\\spad{'s},{}\\spad{bj}\\spad{'s}.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < \\spad{ai}\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b,{} c)} if neither is among the \\spad{ai}\\spad{'s}.}"))) @@ -4466,16 +4466,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-341)))) (-1134 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is 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)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) 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(QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3309 (-12 (|HasCategory| (-1164 |#1| |#2| |#3|) (QUOTE (-762))) (|HasCategory| |#1| (QUOTE (-341)))) (-12 (|HasCategory| (-1164 |#1| |#2| |#3|) (QUOTE (-843))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-160)))) (-12 (|HasCategory| (-1164 |#1| |#2| |#3|) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-1164 |#1| |#2| |#3|) (QUOTE (-843))) (|HasCategory| |#1| (QUOTE (-341)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-1164 |#1| |#2| |#3|) (QUOTE (-843))) (|HasCategory| |#1| (QUOTE (-341)))) (-12 (|HasCategory| (-1164 |#1| |#2| |#3|) (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-136))))) (-1137 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4511,7 +4511,7 @@ NIL (-1145 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} converts the variable \\spad{x} to a univariate polynomial."))) (((-4256 "*") |has| |#2| (-160)) (-4247 |has| |#2| (-517)) (-4250 |has| |#2| (-341)) (-4252 |has| |#2| (-6 -4252)) (-4249 . T) (-4248 . T) (-4251 . T)) -((|HasCategory| |#2| (QUOTE (-843))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3215 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (-3215 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-843)))) (-3215 (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-843)))) (-3215 (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-843)))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))) (-3215 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE -4252)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-843)))) (-3215 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-843)))) (|HasCategory| |#2| (QUOTE (-136))))) +((|HasCategory| |#2| (QUOTE (-843))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3309 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -820) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-357))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -820) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-525))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-357)))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -826) (QUOTE (-525)))))) (-12 (|HasCategory| (-1004) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (-3309 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-843)))) (-3309 (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-843)))) (-3309 (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-843)))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))) (-3309 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE -4252)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-843)))) (-3309 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-843)))) (|HasCategory| |#2| (QUOTE (-136))))) (-1146 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4527,7 +4527,7 @@ NIL (-1149 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1031))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4044) (LIST (|devaluate| |#2|) (QUOTE (-1090)))))) +((|HasCategory| |#2| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1031))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -1908) (LIST (|devaluate| |#2|) (QUOTE (-1090)))))) (-1150 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4248 . T) (-4249 . T) (-4251 . T)) @@ -4555,22 +4555,22 @@ NIL (-1156 |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)}."))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4252 |has| |#1| (-341)) (-4246 |has| |#1| (-341)) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-341))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3215 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -4044) (LIST (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3215 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-892))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2313) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (LIST (QUOTE -3122) (LIST (LIST (QUOTE -592) (QUOTE (-1090))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) +((|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-341))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3309 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -1908) (LIST (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3309 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-892))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -3766) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (LIST (QUOTE -4104) (LIST (LIST (QUOTE -592) (QUOTE (-1090))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-1157 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4252 |has| |#1| (-341)) (-4246 |has| |#1| (-341)) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-341))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3215 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -4044) (LIST (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3215 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-892))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2313) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (LIST (QUOTE -3122) (LIST (LIST (QUOTE -592) (QUOTE (-1090))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-341))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3309 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -1908) (LIST (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3309 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-892))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -3766) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (LIST (QUOTE -4104) (LIST (LIST (QUOTE -592) (QUOTE (-1090))) (|devaluate| |#1|))))))) (-1158 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))}."))) (((-4256 "*") |has| (-1157 |#2| |#3| |#4|) (-160)) (-4247 |has| (-1157 |#2| |#3| |#4|) (-517)) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| (-1157 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1157 |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1157 |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1157 |#2| |#3| |#4|) (QUOTE (-160))) (|HasCategory| (-1157 |#2| |#3| |#4|) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1157 |#2| |#3| |#4|) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-1157 |#2| |#3| |#4|) (QUOTE (-341))) (|HasCategory| (-1157 |#2| |#3| |#4|) (QUOTE (-429))) (-3215 (|HasCategory| (-1157 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1157 |#2| |#3| |#4|) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| (-1157 |#2| |#3| |#4|) (QUOTE (-517)))) +((|HasCategory| (-1157 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1157 |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1157 |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1157 |#2| |#3| |#4|) (QUOTE (-160))) (|HasCategory| (-1157 |#2| |#3| |#4|) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1157 |#2| |#3| |#4|) (LIST (QUOTE -967) (QUOTE (-525)))) (|HasCategory| (-1157 |#2| |#3| |#4|) (QUOTE (-341))) (|HasCategory| (-1157 |#2| |#3| |#4|) (QUOTE (-429))) (-3309 (|HasCategory| (-1157 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1157 |#2| |#3| |#4|) (LIST (QUOTE -967) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| (-1157 |#2| |#3| |#4|) (QUOTE (-517)))) (-1159 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL ((|HasAttribute| |#1| (QUOTE -4255))) (-1160 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-2341 . T)) +((-1996 . T)) NIL (-1161 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) @@ -4579,7 +4579,7 @@ NIL (-1162 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-525)))) (|HasCategory| |#2| (QUOTE (-892))) (|HasCategory| |#2| (QUOTE (-1112))) (|HasSignature| |#2| (LIST (QUOTE -3122) (LIST (LIST (QUOTE -592) (QUOTE (-1090))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2313) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1090))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-892))) (|HasCategory| |#2| (QUOTE (-1112))) (|HasSignature| |#2| (LIST (QUOTE -4104) (LIST (LIST (QUOTE -592) (QUOTE (-1090))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3766) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1090))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341)))) (-1163 |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."))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4248 . T) (-4249 . T) (-4251 . T)) @@ -4587,18 +4587,18 @@ NIL (-1164 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4256 "*") |has| |#1| (-160)) (-4247 |has| |#1| (-517)) (-4248 . T) (-4249 . T) (-4251 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3215 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-713)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-713)) (|devaluate| |#1|)))) (|HasCategory| (-713) (QUOTE (-1031))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasSignature| |#1| (LIST (QUOTE -4044) (LIST (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasCategory| |#1| (QUOTE (-341))) (-3215 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-892))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2313) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (LIST (QUOTE -3122) (LIST (LIST (QUOTE -592) (QUOTE (-1090))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3309 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -834) (QUOTE (-1090)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-713)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-713)) (|devaluate| |#1|)))) (|HasCategory| (-713) (QUOTE (-1031))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasSignature| |#1| (LIST (QUOTE -1908) (LIST (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasCategory| |#1| (QUOTE (-341))) (-3309 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-892))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -3766) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (LIST (QUOTE -4104) (LIST (LIST (QUOTE -592) (QUOTE (-1090))) (|devaluate| |#1|))))))) (-1165 |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 -(-1166 -1896 UP L UTS) +(-1166 -1346 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 (-517)))) (-1167) ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) -((-2341 . T)) +((-1996 . T)) NIL (-1168 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) @@ -4610,7 +4610,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-976))) (|HasCategory| |#2| (QUOTE (-669))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1170 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4255 . T) (-4254 . T) (-2341 . T)) +((-4255 . T) (-4254 . T) (-1996 . T)) NIL (-1171 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4619,7 +4619,7 @@ NIL (-1172 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4255 . T) (-4254 . T)) -((-3215 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3215 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3215 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-976))) (-12 (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-976)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) +((-3309 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3309 (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3309 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-976))) (-12 (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-976)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-797))))) (-1173) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -4652,7 +4652,7 @@ 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 -(-1181 K R UP -1896) +(-1181 K R UP -1346) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -4680,11 +4680,11 @@ 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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4247 |has| |#2| (-6 -4247)) (-4249 . T) (-4248 . T) (-4251 . T)) NIL -(-1188 S -1896) +(-1188 S -1346) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138)))) -(-1189 -1896) +(-1189 -1346) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4246 . T) (-4252 . T) (-4247 . T) ((-4256 "*") . T) (-4248 . T) (-4249 . T) (-4251 . T)) NIL @@ -4740,4 +4740,4 @@ NIL NIL NIL NIL -((-3 NIL 2238300 2238305 2238310 2238315) (-2 NIL 2238280 2238285 2238290 2238295) (-1 NIL 2238260 2238265 2238270 2238275) (0 NIL 2238240 2238245 2238250 2238255) (-1198 "ZMOD.spad" 2238049 2238062 2238178 2238235) (-1197 "ZLINDEP.spad" 2237093 2237104 2238039 2238044) (-1196 "ZDSOLVE.spad" 2226942 2226964 2237083 2237088) (-1195 "YSTREAM.spad" 2226435 2226446 2226932 2226937) (-1194 "XRPOLY.spad" 2225655 2225675 2226291 2226360) (-1193 "XPR.spad" 2223384 2223397 2225373 2225472) (-1192 "XPOLY.spad" 2222939 2222950 2223240 2223309) (-1191 "XPOLYC.spad" 2222256 2222272 2222865 2222934) (-1190 "XPBWPOLY.spad" 2220693 2220713 2222036 2222105) (-1189 "XF.spad" 2219154 2219169 2220595 2220688) (-1188 "XF.spad" 2217595 2217612 2219038 2219043) (-1187 "XFALG.spad" 2214619 2214635 2217521 2217590) (-1186 "XEXPPKG.spad" 2213870 2213896 2214609 2214614) (-1185 "XDPOLY.spad" 2213484 2213500 2213726 2213795) (-1184 "XALG.spad" 2213082 2213093 2213440 2213479) (-1183 "WUTSET.spad" 2208921 2208938 2212728 2212755) (-1182 "WP.spad" 2207935 2207979 2208779 2208846) (-1181 "WFFINTBS.spad" 2205498 2205520 2207925 2207930) (-1180 "WEIER.spad" 2203712 2203723 2205488 2205493) (-1179 "VSPACE.spad" 2203385 2203396 2203680 2203707) (-1178 "VSPACE.spad" 2203078 2203091 2203375 2203380) (-1177 "VOID.spad" 2202668 2202677 2203068 2203073) (-1176 "VIEW.spad" 2200290 2200299 2202658 2202663) (-1175 "VIEWDEF.spad" 2195487 2195496 2200280 2200285) (-1174 "VIEW3D.spad" 2179322 2179331 2195477 2195482) (-1173 "VIEW2D.spad" 2167059 2167068 2179312 2179317) (-1172 "VECTOR.spad" 2165736 2165747 2165987 2166014) (-1171 "VECTOR2.spad" 2164363 2164376 2165726 2165731) (-1170 "VECTCAT.spad" 2162251 2162262 2164319 2164358) (-1169 "VECTCAT.spad" 2159960 2159973 2162030 2162035) (-1168 "VARIABLE.spad" 2159740 2159755 2159950 2159955) (-1167 "UTYPE.spad" 2159374 2159383 2159720 2159735) (-1166 "UTSODETL.spad" 2158667 2158691 2159330 2159335) (-1165 "UTSODE.spad" 2156855 2156875 2158657 2158662) (-1164 "UTS.spad" 2151644 2151672 2155322 2155419) (-1163 "UTSCAT.spad" 2149095 2149111 2151542 2151639) (-1162 "UTSCAT.spad" 2146190 2146208 2148639 2148644) (-1161 "UTS2.spad" 2145783 2145818 2146180 2146185) (-1160 "URAGG.spad" 2140405 2140416 2145763 2145778) (-1159 "URAGG.spad" 2135001 2135014 2140361 2140366) (-1158 "UPXSSING.spad" 2132647 2132673 2134085 2134218) (-1157 "UPXS.spad" 2129674 2129702 2130779 2130928) (-1156 "UPXSCONS.spad" 2127431 2127451 2127806 2127955) (-1155 "UPXSCCA.spad" 2125889 2125909 2127277 2127426) (-1154 "UPXSCCA.spad" 2124489 2124511 2125879 2125884) (-1153 "UPXSCAT.spad" 2123070 2123086 2124335 2124484) (-1152 "UPXS2.spad" 2122611 2122664 2123060 2123065) (-1151 "UPSQFREE.spad" 2121023 2121037 2122601 2122606) (-1150 "UPSCAT.spad" 2118616 2118640 2120921 2121018) (-1149 "UPSCAT.spad" 2115915 2115941 2118222 2118227) (-1148 "UPOLYC.spad" 2110893 2110904 2115757 2115910) (-1147 "UPOLYC.spad" 2105763 2105776 2110629 2110634) (-1146 "UPOLYC2.spad" 2105232 2105251 2105753 2105758) (-1145 "UP.spad" 2102277 2102292 2102785 2102938) (-1144 "UPMP.spad" 2101167 2101180 2102267 2102272) (-1143 "UPDIVP.spad" 2100730 2100744 2101157 2101162) (-1142 "UPDECOMP.spad" 2098967 2098981 2100720 2100725) (-1141 "UPCDEN.spad" 2098174 2098190 2098957 2098962) (-1140 "UP2.spad" 2097536 2097557 2098164 2098169) (-1139 "UNISEG.spad" 2096889 2096900 2097455 2097460) (-1138 "UNISEG2.spad" 2096382 2096395 2096845 2096850) (-1137 "UNIFACT.spad" 2095483 2095495 2096372 2096377) (-1136 "ULS.spad" 2086042 2086070 2087135 2087564) (-1135 "ULSCONS.spad" 2080085 2080105 2080457 2080606) (-1134 "ULSCCAT.spad" 2077682 2077702 2079905 2080080) (-1133 "ULSCCAT.spad" 2075413 2075435 2077638 2077643) (-1132 "ULSCAT.spad" 2073629 2073645 2075259 2075408) (-1131 "ULS2.spad" 2073141 2073194 2073619 2073624) (-1130 "UFD.spad" 2072206 2072215 2073067 2073136) (-1129 "UFD.spad" 2071333 2071344 2072196 2072201) (-1128 "UDVO.spad" 2070180 2070189 2071323 2071328) (-1127 "UDPO.spad" 2067607 2067618 2070136 2070141) (-1126 "TYPE.spad" 2067529 2067538 2067587 2067602) (-1125 "TWOFACT.spad" 2066179 2066194 2067519 2067524) (-1124 "TUPLE.spad" 2065565 2065576 2066078 2066083) (-1123 "TUBETOOL.spad" 2062402 2062411 2065555 2065560) (-1122 "TUBE.spad" 2061043 2061060 2062392 2062397) (-1121 "TS.spad" 2059632 2059648 2060608 2060705) (-1120 "TSETCAT.spad" 2046747 2046764 2059588 2059627) (-1119 "TSETCAT.spad" 2033860 2033879 2046703 2046708) (-1118 "TRMANIP.spad" 2028226 2028243 2033566 2033571) (-1117 "TRIMAT.spad" 2027185 2027210 2028216 2028221) (-1116 "TRIGMNIP.spad" 2025702 2025719 2027175 2027180) (-1115 "TRIGCAT.spad" 2025214 2025223 2025692 2025697) (-1114 "TRIGCAT.spad" 2024724 2024735 2025204 2025209) (-1113 "TREE.spad" 2023295 2023306 2024331 2024358) (-1112 "TRANFUN.spad" 2023126 2023135 2023285 2023290) (-1111 "TRANFUN.spad" 2022955 2022966 2023116 2023121) (-1110 "TOPSP.spad" 2022629 2022638 2022945 2022950) (-1109 "TOOLSIGN.spad" 2022292 2022303 2022619 2022624) (-1108 "TEXTFILE.spad" 2020849 2020858 2022282 2022287) (-1107 "TEX.spad" 2017866 2017875 2020839 2020844) (-1106 "TEX1.spad" 2017422 2017433 2017856 2017861) (-1105 "TEMUTL.spad" 2016977 2016986 2017412 2017417) (-1104 "TBCMPPK.spad" 2015070 2015093 2016967 2016972) (-1103 "TBAGG.spad" 2014094 2014117 2015038 2015065) (-1102 "TBAGG.spad" 2013138 2013163 2014084 2014089) (-1101 "TANEXP.spad" 2012514 2012525 2013128 2013133) (-1100 "TABLE.spad" 2010925 2010948 2011195 2011222) (-1099 "TABLEAU.spad" 2010406 2010417 2010915 2010920) (-1098 "TABLBUMP.spad" 2007189 2007200 2010396 2010401) (-1097 "SYSTEM.spad" 2006463 2006472 2007179 2007184) (-1096 "SYSSOLP.spad" 2003936 2003947 2006453 2006458) (-1095 "SYNTAX.spad" 2000128 2000137 2003926 2003931) (-1094 "SYMTAB.spad" 1998184 1998193 2000118 2000123) (-1093 "SYMS.spad" 1994169 1994178 1998174 1998179) (-1092 "SYMPOLY.spad" 1993179 1993190 1993261 1993388) (-1091 "SYMFUNC.spad" 1992654 1992665 1993169 1993174) (-1090 "SYMBOL.spad" 1989990 1989999 1992644 1992649) (-1089 "SWITCH.spad" 1986747 1986756 1989980 1989985) (-1088 "SUTS.spad" 1983646 1983674 1985214 1985311) (-1087 "SUPXS.spad" 1980660 1980688 1981778 1981927) (-1086 "SUP.spad" 1977432 1977443 1978213 1978366) (-1085 "SUPFRACF.spad" 1976537 1976555 1977422 1977427) (-1084 "SUP2.spad" 1975927 1975940 1976527 1976532) (-1083 "SUMRF.spad" 1974893 1974904 1975917 1975922) (-1082 "SUMFS.spad" 1974526 1974543 1974883 1974888) (-1081 "SULS.spad" 1965072 1965100 1966178 1966607) (-1080 "SUCH.spad" 1964752 1964767 1965062 1965067) (-1079 "SUBSPACE.spad" 1956759 1956774 1964742 1964747) (-1078 "SUBRESP.spad" 1955919 1955933 1956715 1956720) (-1077 "STTF.spad" 1952018 1952034 1955909 1955914) (-1076 "STTFNC.spad" 1948486 1948502 1952008 1952013) (-1075 "STTAYLOR.spad" 1940884 1940895 1948367 1948372) (-1074 "STRTBL.spad" 1939389 1939406 1939538 1939565) (-1073 "STRING.spad" 1938798 1938807 1938812 1938839) (-1072 "STRICAT.spad" 1938574 1938583 1938754 1938793) (-1071 "STREAM.spad" 1935342 1935353 1938099 1938114) (-1070 "STREAM3.spad" 1934887 1934902 1935332 1935337) (-1069 "STREAM2.spad" 1933955 1933968 1934877 1934882) (-1068 "STREAM1.spad" 1933659 1933670 1933945 1933950) (-1067 "STINPROD.spad" 1932565 1932581 1933649 1933654) (-1066 "STEP.spad" 1931766 1931775 1932555 1932560) (-1065 "STBL.spad" 1930292 1930320 1930459 1930474) (-1064 "STAGG.spad" 1929357 1929368 1930272 1930287) (-1063 "STAGG.spad" 1928430 1928443 1929347 1929352) (-1062 "STACK.spad" 1927781 1927792 1928037 1928064) (-1061 "SREGSET.spad" 1925485 1925502 1927427 1927454) (-1060 "SRDCMPK.spad" 1924030 1924050 1925475 1925480) (-1059 "SRAGG.spad" 1919115 1919124 1923986 1924025) (-1058 "SRAGG.spad" 1914232 1914243 1919105 1919110) (-1057 "SQMATRIX.spad" 1911858 1911876 1912766 1912853) (-1056 "SPLTREE.spad" 1906410 1906423 1911294 1911321) (-1055 "SPLNODE.spad" 1902998 1903011 1906400 1906405) (-1054 "SPFCAT.spad" 1901775 1901784 1902988 1902993) (-1053 "SPECOUT.spad" 1900325 1900334 1901765 1901770) (-1052 "spad-parser.spad" 1899790 1899799 1900315 1900320) (-1051 "SPACEC.spad" 1883803 1883814 1899780 1899785) (-1050 "SPACE3.spad" 1883579 1883590 1883793 1883798) (-1049 "SORTPAK.spad" 1883124 1883137 1883535 1883540) (-1048 "SOLVETRA.spad" 1880881 1880892 1883114 1883119) (-1047 "SOLVESER.spad" 1879401 1879412 1880871 1880876) (-1046 "SOLVERAD.spad" 1875411 1875422 1879391 1879396) (-1045 "SOLVEFOR.spad" 1873831 1873849 1875401 1875406) (-1044 "SNTSCAT.spad" 1873419 1873436 1873787 1873826) (-1043 "SMTS.spad" 1871679 1871705 1872984 1873081) (-1042 "SMP.spad" 1869121 1869141 1869511 1869638) (-1041 "SMITH.spad" 1867964 1867989 1869111 1869116) (-1040 "SMATCAT.spad" 1866062 1866092 1867896 1867959) (-1039 "SMATCAT.spad" 1864104 1864136 1865940 1865945) (-1038 "SKAGG.spad" 1863053 1863064 1864060 1864099) (-1037 "SINT.spad" 1861361 1861370 1862919 1863048) (-1036 "SIMPAN.spad" 1861089 1861098 1861351 1861356) (-1035 "SIGNRF.spad" 1860197 1860208 1861079 1861084) (-1034 "SIGNEF.spad" 1859466 1859483 1860187 1860192) (-1033 "SHP.spad" 1857384 1857399 1859422 1859427) (-1032 "SHDP.spad" 1848774 1848801 1849283 1849412) (-1031 "SGROUP.spad" 1848240 1848249 1848764 1848769) (-1030 "SGROUP.spad" 1847704 1847715 1848230 1848235) (-1029 "SGCF.spad" 1840585 1840594 1847694 1847699) (-1028 "SFRTCAT.spad" 1839501 1839518 1840541 1840580) (-1027 "SFRGCD.spad" 1838564 1838584 1839491 1839496) (-1026 "SFQCMPK.spad" 1833201 1833221 1838554 1838559) (-1025 "SFORT.spad" 1832636 1832650 1833191 1833196) (-1024 "SEXOF.spad" 1832479 1832519 1832626 1832631) (-1023 "SEX.spad" 1832371 1832380 1832469 1832474) (-1022 "SEXCAT.spad" 1829475 1829515 1832361 1832366) (-1021 "SET.spad" 1827775 1827786 1828896 1828935) (-1020 "SETMN.spad" 1826209 1826226 1827765 1827770) (-1019 "SETCAT.spad" 1825694 1825703 1826199 1826204) (-1018 "SETCAT.spad" 1825177 1825188 1825684 1825689) (-1017 "SETAGG.spad" 1821700 1821711 1825145 1825172) (-1016 "SETAGG.spad" 1818243 1818256 1821690 1821695) (-1015 "SEGXCAT.spad" 1817355 1817368 1818223 1818238) (-1014 "SEG.spad" 1817168 1817179 1817274 1817279) (-1013 "SEGCAT.spad" 1815987 1815998 1817148 1817163) (-1012 "SEGBIND.spad" 1815059 1815070 1815942 1815947) (-1011 "SEGBIND2.spad" 1814755 1814768 1815049 1815054) (-1010 "SEG2.spad" 1814180 1814193 1814711 1814716) (-1009 "SDVAR.spad" 1813456 1813467 1814170 1814175) (-1008 "SDPOL.spad" 1810849 1810860 1811140 1811267) (-1007 "SCPKG.spad" 1808928 1808939 1810839 1810844) (-1006 "SCOPE.spad" 1808073 1808082 1808918 1808923) (-1005 "SCACHE.spad" 1806755 1806766 1808063 1808068) (-1004 "SAOS.spad" 1806627 1806636 1806745 1806750) (-1003 "SAERFFC.spad" 1806340 1806360 1806617 1806622) (-1002 "SAE.spad" 1804518 1804534 1805129 1805264) (-1001 "SAEFACT.spad" 1804219 1804239 1804508 1804513) (-1000 "RURPK.spad" 1801860 1801876 1804209 1804214) (-999 "RULESET.spad" 1801302 1801325 1801850 1801855) (-998 "RULE.spad" 1799507 1799530 1801292 1801297) (-997 "RULECOLD.spad" 1799360 1799372 1799497 1799502) (-996 "RSETGCD.spad" 1795739 1795758 1799350 1799355) (-995 "RSETCAT.spad" 1785512 1785528 1795695 1795734) (-994 "RSETCAT.spad" 1775317 1775335 1785502 1785507) (-993 "RSDCMPK.spad" 1773770 1773789 1775307 1775312) (-992 "RRCC.spad" 1772155 1772184 1773760 1773765) (-991 "RRCC.spad" 1770538 1770569 1772145 1772150) (-990 "RPOLCAT.spad" 1749899 1749913 1770406 1770533) (-989 "RPOLCAT.spad" 1728975 1728991 1749484 1749489) (-988 "ROUTINE.spad" 1724839 1724847 1727622 1727649) (-987 "ROMAN.spad" 1724072 1724080 1724705 1724834) (-986 "ROIRC.spad" 1723153 1723184 1724062 1724067) (-985 "RNS.spad" 1722057 1722065 1723055 1723148) (-984 "RNS.spad" 1721047 1721057 1722047 1722052) (-983 "RNG.spad" 1720783 1720791 1721037 1721042) (-982 "RMODULE.spad" 1720422 1720432 1720773 1720778) (-981 "RMCAT2.spad" 1719831 1719887 1720412 1720417) (-980 "RMATRIX.spad" 1718511 1718529 1718998 1719037) (-979 "RMATCAT.spad" 1714033 1714063 1718455 1718506) (-978 "RMATCAT.spad" 1709457 1709489 1713881 1713886) (-977 "RINTERP.spad" 1709346 1709365 1709447 1709452) (-976 "RING.spad" 1708704 1708712 1709326 1709341) (-975 "RING.spad" 1708070 1708080 1708694 1708699) (-974 "RIDIST.spad" 1707455 1707463 1708060 1708065) (-973 "RGCHAIN.spad" 1706035 1706050 1706940 1706967) (-972 "RF.spad" 1703650 1703660 1706025 1706030) (-971 "RFFACTOR.spad" 1703113 1703123 1703640 1703645) (-970 "RFFACT.spad" 1702849 1702860 1703103 1703108) (-969 "RFDIST.spad" 1701838 1701846 1702839 1702844) (-968 "RETSOL.spad" 1701256 1701268 1701828 1701833) (-967 "RETRACT.spad" 1700606 1700616 1701246 1701251) (-966 "RETRACT.spad" 1699954 1699966 1700596 1700601) (-965 "RESULT.spad" 1698015 1698023 1698601 1698628) (-964 "RESRING.spad" 1697363 1697409 1697953 1698010) (-963 "RESLATC.spad" 1696688 1696698 1697353 1697358) (-962 "REPSQ.spad" 1696418 1696428 1696678 1696683) (-961 "REP.spad" 1693971 1693979 1696408 1696413) (-960 "REPDB.spad" 1693677 1693687 1693961 1693966) (-959 "REP2.spad" 1683250 1683260 1693519 1693524) (-958 "REP1.spad" 1677241 1677251 1683200 1683205) (-957 "REGSET.spad" 1675039 1675055 1676887 1676914) (-956 "REF.spad" 1674369 1674379 1674994 1674999) (-955 "REDORDER.spad" 1673546 1673562 1674359 1674364) (-954 "RECLOS.spad" 1672336 1672355 1673039 1673132) (-953 "REALSOLV.spad" 1671469 1671477 1672326 1672331) (-952 "REAL.spad" 1671342 1671350 1671459 1671464) (-951 "REAL0Q.spad" 1668625 1668639 1671332 1671337) (-950 "REAL0.spad" 1665454 1665468 1668615 1668620) (-949 "RDIV.spad" 1665106 1665130 1665444 1665449) (-948 "RDIST.spad" 1664670 1664680 1665096 1665101) (-947 "RDETRS.spad" 1663467 1663484 1664660 1664665) (-946 "RDETR.spad" 1661575 1661592 1663457 1663462) (-945 "RDEEFS.spad" 1660649 1660665 1661565 1661570) (-944 "RDEEF.spad" 1659646 1659662 1660639 1660644) (-943 "RCFIELD.spad" 1656830 1656838 1659548 1659641) (-942 "RCFIELD.spad" 1654100 1654110 1656820 1656825) (-941 "RCAGG.spad" 1652003 1652013 1654080 1654095) (-940 "RCAGG.spad" 1649843 1649855 1651922 1651927) (-939 "RATRET.spad" 1649204 1649214 1649833 1649838) (-938 "RATFACT.spad" 1648897 1648908 1649194 1649199) (-937 "RANDSRC.spad" 1648217 1648225 1648887 1648892) (-936 "RADUTIL.spad" 1647972 1647980 1648207 1648212) (-935 "RADIX.spad" 1644765 1644778 1646442 1646535) (-934 "RADFF.spad" 1643182 1643218 1643300 1643456) (-933 "RADCAT.spad" 1642776 1642784 1643172 1643177) (-932 "RADCAT.spad" 1642368 1642378 1642766 1642771) (-931 "QUEUE.spad" 1641711 1641721 1641975 1642002) (-930 "QUAT.spad" 1640297 1640307 1640639 1640704) (-929 "QUATCT2.spad" 1639916 1639934 1640287 1640292) (-928 "QUATCAT.spad" 1638081 1638091 1639846 1639911) (-927 "QUATCAT.spad" 1635998 1636010 1637765 1637770) (-926 "QUAGG.spad" 1634812 1634822 1635954 1635993) (-925 "QFORM.spad" 1634275 1634289 1634802 1634807) (-924 "QFCAT.spad" 1632966 1632976 1634165 1634270) (-923 "QFCAT.spad" 1631263 1631275 1632464 1632469) (-922 "QFCAT2.spad" 1630954 1630970 1631253 1631258) (-921 "QEQUAT.spad" 1630511 1630519 1630944 1630949) (-920 "QCMPACK.spad" 1625258 1625277 1630501 1630506) (-919 "QALGSET.spad" 1621333 1621365 1625172 1625177) (-918 "QALGSET2.spad" 1619329 1619347 1621323 1621328) (-917 "PWFFINTB.spad" 1616639 1616660 1619319 1619324) (-916 "PUSHVAR.spad" 1615968 1615987 1616629 1616634) (-915 "PTRANFN.spad" 1612094 1612104 1615958 1615963) (-914 "PTPACK.spad" 1609182 1609192 1612084 1612089) (-913 "PTFUNC2.spad" 1609003 1609017 1609172 1609177) (-912 "PTCAT.spad" 1608085 1608095 1608959 1608998) (-911 "PSQFR.spad" 1607392 1607416 1608075 1608080) (-910 "PSEUDLIN.spad" 1606250 1606260 1607382 1607387) (-909 "PSETPK.spad" 1591683 1591699 1606128 1606133) (-908 "PSETCAT.spad" 1585591 1585614 1591651 1591678) (-907 "PSETCAT.spad" 1579485 1579510 1585547 1585552) (-906 "PSCURVE.spad" 1578468 1578476 1579475 1579480) (-905 "PSCAT.spad" 1577235 1577264 1578366 1578463) (-904 "PSCAT.spad" 1576092 1576123 1577225 1577230) (-903 "PRTITION.spad" 1574935 1574943 1576082 1576087) (-902 "PRS.spad" 1564497 1564514 1574891 1574896) (-901 "PRQAGG.spad" 1563916 1563926 1564453 1564492) (-900 "PROPLOG.spad" 1563319 1563327 1563906 1563911) (-899 "PROPFRML.spad" 1561184 1561195 1563255 1563260) (-898 "PROPERTY.spad" 1560678 1560686 1561174 1561179) (-897 "PRODUCT.spad" 1558358 1558370 1558644 1558699) (-896 "PR.spad" 1556747 1556759 1557452 1557579) (-895 "PRINT.spad" 1556499 1556507 1556737 1556742) (-894 "PRIMES.spad" 1554750 1554760 1556489 1556494) (-893 "PRIMELT.spad" 1552731 1552745 1554740 1554745) (-892 "PRIMCAT.spad" 1552354 1552362 1552721 1552726) (-891 "PRIMARR.spad" 1551359 1551369 1551537 1551564) (-890 "PRIMARR2.spad" 1550082 1550094 1551349 1551354) (-889 "PREASSOC.spad" 1549454 1549466 1550072 1550077) (-888 "PPCURVE.spad" 1548591 1548599 1549444 1549449) (-887 "POLYROOT.spad" 1547363 1547385 1548547 1548552) (-886 "POLY.spad" 1544663 1544673 1545180 1545307) (-885 "POLYLIFT.spad" 1543924 1543947 1544653 1544658) (-884 "POLYCATQ.spad" 1542026 1542048 1543914 1543919) (-883 "POLYCAT.spad" 1535432 1535453 1541894 1542021) (-882 "POLYCAT.spad" 1528140 1528163 1534604 1534609) (-881 "POLY2UP.spad" 1527588 1527602 1528130 1528135) (-880 "POLY2.spad" 1527183 1527195 1527578 1527583) (-879 "POLUTIL.spad" 1526124 1526153 1527139 1527144) (-878 "POLTOPOL.spad" 1524872 1524887 1526114 1526119) (-877 "POINT.spad" 1523713 1523723 1523800 1523827) (-876 "PNTHEORY.spad" 1520379 1520387 1523703 1523708) (-875 "PMTOOLS.spad" 1519136 1519150 1520369 1520374) (-874 "PMSYM.spad" 1518681 1518691 1519126 1519131) (-873 "PMQFCAT.spad" 1518268 1518282 1518671 1518676) (-872 "PMPRED.spad" 1517737 1517751 1518258 1518263) (-871 "PMPREDFS.spad" 1517181 1517203 1517727 1517732) (-870 "PMPLCAT.spad" 1516251 1516269 1517113 1517118) (-869 "PMLSAGG.spad" 1515832 1515846 1516241 1516246) (-868 "PMKERNEL.spad" 1515399 1515411 1515822 1515827) (-867 "PMINS.spad" 1514975 1514985 1515389 1515394) (-866 "PMFS.spad" 1514548 1514566 1514965 1514970) (-865 "PMDOWN.spad" 1513834 1513848 1514538 1514543) (-864 "PMASS.spad" 1512846 1512854 1513824 1513829) (-863 "PMASSFS.spad" 1511815 1511831 1512836 1512841) (-862 "PLOTTOOL.spad" 1511595 1511603 1511805 1511810) (-861 "PLOT.spad" 1506426 1506434 1511585 1511590) (-860 "PLOT3D.spad" 1502846 1502854 1506416 1506421) (-859 "PLOT1.spad" 1501987 1501997 1502836 1502841) (-858 "PLEQN.spad" 1489203 1489230 1501977 1501982) (-857 "PINTERP.spad" 1488819 1488838 1489193 1489198) (-856 "PINTERPA.spad" 1488601 1488617 1488809 1488814) (-855 "PI.spad" 1488208 1488216 1488575 1488596) (-854 "PID.spad" 1487164 1487172 1488134 1488203) (-853 "PICOERCE.spad" 1486821 1486831 1487154 1487159) (-852 "PGROEB.spad" 1485418 1485432 1486811 1486816) (-851 "PGE.spad" 1476671 1476679 1485408 1485413) (-850 "PGCD.spad" 1475553 1475570 1476661 1476666) (-849 "PFRPAC.spad" 1474696 1474706 1475543 1475548) (-848 "PFR.spad" 1471353 1471363 1474598 1474691) (-847 "PFOTOOLS.spad" 1470611 1470627 1471343 1471348) (-846 "PFOQ.spad" 1469981 1469999 1470601 1470606) (-845 "PFO.spad" 1469400 1469427 1469971 1469976) (-844 "PF.spad" 1468974 1468986 1469205 1469298) (-843 "PFECAT.spad" 1466640 1466648 1468900 1468969) (-842 "PFECAT.spad" 1464334 1464344 1466596 1466601) (-841 "PFBRU.spad" 1462204 1462216 1464324 1464329) (-840 "PFBR.spad" 1459742 1459765 1462194 1462199) (-839 "PERM.spad" 1455423 1455433 1459572 1459587) (-838 "PERMGRP.spad" 1450159 1450169 1455413 1455418) (-837 "PERMCAT.spad" 1448711 1448721 1450139 1450154) (-836 "PERMAN.spad" 1447243 1447257 1448701 1448706) (-835 "PENDTREE.spad" 1446516 1446526 1446872 1446877) (-834 "PDRING.spad" 1445007 1445017 1446496 1446511) (-833 "PDRING.spad" 1443506 1443518 1444997 1445002) (-832 "PDEPROB.spad" 1442463 1442471 1443496 1443501) (-831 "PDEPACK.spad" 1436465 1436473 1442453 1442458) (-830 "PDECOMP.spad" 1435927 1435944 1436455 1436460) (-829 "PDECAT.spad" 1434281 1434289 1435917 1435922) (-828 "PCOMP.spad" 1434132 1434145 1434271 1434276) (-827 "PBWLB.spad" 1432714 1432731 1434122 1434127) (-826 "PATTERN.spad" 1427145 1427155 1432704 1432709) (-825 "PATTERN2.spad" 1426881 1426893 1427135 1427140) (-824 "PATTERN1.spad" 1425183 1425199 1426871 1426876) (-823 "PATRES.spad" 1422730 1422742 1425173 1425178) (-822 "PATRES2.spad" 1422392 1422406 1422720 1422725) (-821 "PATMATCH.spad" 1420554 1420585 1422105 1422110) (-820 "PATMAB.spad" 1419979 1419989 1420544 1420549) (-819 "PATLRES.spad" 1419063 1419077 1419969 1419974) (-818 "PATAB.spad" 1418827 1418837 1419053 1419058) (-817 "PARTPERM.spad" 1416189 1416197 1418817 1418822) (-816 "PARSURF.spad" 1415617 1415645 1416179 1416184) (-815 "PARSU2.spad" 1415412 1415428 1415607 1415612) (-814 "script-parser.spad" 1414932 1414940 1415402 1415407) (-813 "PARSCURV.spad" 1414360 1414388 1414922 1414927) (-812 "PARSC2.spad" 1414149 1414165 1414350 1414355) (-811 "PARPCURV.spad" 1413607 1413635 1414139 1414144) (-810 "PARPC2.spad" 1413396 1413412 1413597 1413602) (-809 "PAN2EXPR.spad" 1412808 1412816 1413386 1413391) (-808 "PALETTE.spad" 1411778 1411786 1412798 1412803) (-807 "PAIR.spad" 1410761 1410774 1411366 1411371) (-806 "PADICRC.spad" 1408094 1408112 1409269 1409362) (-805 "PADICRAT.spad" 1406112 1406124 1406333 1406426) (-804 "PADIC.spad" 1405807 1405819 1406038 1406107) (-803 "PADICCT.spad" 1404348 1404360 1405733 1405802) (-802 "PADEPAC.spad" 1403027 1403046 1404338 1404343) (-801 "PADE.spad" 1401767 1401783 1403017 1403022) (-800 "OWP.spad" 1400751 1400781 1401625 1401692) (-799 "OVAR.spad" 1400532 1400555 1400741 1400746) (-798 "OUT.spad" 1399616 1399624 1400522 1400527) (-797 "OUTFORM.spad" 1389030 1389038 1399606 1399611) (-796 "OSI.spad" 1388505 1388513 1389020 1389025) (-795 "ORTHPOL.spad" 1386966 1386976 1388422 1388427) (-794 "OREUP.spad" 1386326 1386354 1386648 1386687) (-793 "ORESUP.spad" 1385627 1385651 1386008 1386047) (-792 "OREPCTO.spad" 1383446 1383458 1385547 1385552) (-791 "OREPCAT.spad" 1377503 1377513 1383402 1383441) (-790 "OREPCAT.spad" 1371450 1371462 1377351 1377356) (-789 "ORDSET.spad" 1370616 1370624 1371440 1371445) (-788 "ORDSET.spad" 1369780 1369790 1370606 1370611) (-787 "ORDRING.spad" 1369170 1369178 1369760 1369775) (-786 "ORDRING.spad" 1368568 1368578 1369160 1369165) (-785 "ORDMON.spad" 1368423 1368431 1368558 1368563) (-784 "ORDFUNS.spad" 1367549 1367565 1368413 1368418) (-783 "ORDFIN.spad" 1367483 1367491 1367539 1367544) (-782 "ORDCOMP.spad" 1365951 1365961 1367033 1367062) (-781 "ORDCOMP2.spad" 1365236 1365248 1365941 1365946) (-780 "OPTPROB.spad" 1363816 1363824 1365226 1365231) (-779 "OPTPACK.spad" 1356201 1356209 1363806 1363811) (-778 "OPTCAT.spad" 1353876 1353884 1356191 1356196) (-777 "OPQUERY.spad" 1353425 1353433 1353866 1353871) (-776 "OP.spad" 1353167 1353177 1353247 1353314) (-775 "ONECOMP.spad" 1351915 1351925 1352717 1352746) (-774 "ONECOMP2.spad" 1351333 1351345 1351905 1351910) (-773 "OMSERVER.spad" 1350335 1350343 1351323 1351328) (-772 "OMSAGG.spad" 1350111 1350121 1350279 1350330) (-771 "OMPKG.spad" 1348723 1348731 1350101 1350106) (-770 "OM.spad" 1347688 1347696 1348713 1348718) (-769 "OMLO.spad" 1347113 1347125 1347574 1347613) (-768 "OMEXPR.spad" 1346947 1346957 1347103 1347108) (-767 "OMERR.spad" 1346490 1346498 1346937 1346942) (-766 "OMERRK.spad" 1345524 1345532 1346480 1346485) (-765 "OMENC.spad" 1344868 1344876 1345514 1345519) (-764 "OMDEV.spad" 1339157 1339165 1344858 1344863) (-763 "OMCONN.spad" 1338566 1338574 1339147 1339152) (-762 "OINTDOM.spad" 1338329 1338337 1338492 1338561) (-761 "OFMONOID.spad" 1334516 1334526 1338319 1338324) (-760 "ODVAR.spad" 1333777 1333787 1334506 1334511) (-759 "ODR.spad" 1333225 1333251 1333589 1333738) (-758 "ODPOL.spad" 1330574 1330584 1330914 1331041) (-757 "ODP.spad" 1322100 1322120 1322473 1322602) (-756 "ODETOOLS.spad" 1320683 1320702 1322090 1322095) (-755 "ODESYS.spad" 1318333 1318350 1320673 1320678) (-754 "ODERTRIC.spad" 1314274 1314291 1318290 1318295) (-753 "ODERED.spad" 1313661 1313685 1314264 1314269) (-752 "ODERAT.spad" 1311212 1311229 1313651 1313656) (-751 "ODEPRRIC.spad" 1308103 1308125 1311202 1311207) (-750 "ODEPROB.spad" 1307302 1307310 1308093 1308098) (-749 "ODEPRIM.spad" 1304576 1304598 1307292 1307297) (-748 "ODEPAL.spad" 1303952 1303976 1304566 1304571) (-747 "ODEPACK.spad" 1290554 1290562 1303942 1303947) (-746 "ODEINT.spad" 1289985 1290001 1290544 1290549) (-745 "ODEIFTBL.spad" 1287380 1287388 1289975 1289980) (-744 "ODEEF.spad" 1282747 1282763 1287370 1287375) (-743 "ODECONST.spad" 1282266 1282284 1282737 1282742) (-742 "ODECAT.spad" 1280862 1280870 1282256 1282261) (-741 "OCT.spad" 1279009 1279019 1279725 1279764) (-740 "OCTCT2.spad" 1278653 1278674 1278999 1279004) (-739 "OC.spad" 1276427 1276437 1278609 1278648) (-738 "OC.spad" 1273927 1273939 1276111 1276116) (-737 "OCAMON.spad" 1273775 1273783 1273917 1273922) (-736 "OASGP.spad" 1273590 1273598 1273765 1273770) (-735 "OAMONS.spad" 1273110 1273118 1273580 1273585) (-734 "OAMON.spad" 1272971 1272979 1273100 1273105) (-733 "OAGROUP.spad" 1272833 1272841 1272961 1272966) (-732 "NUMTUBE.spad" 1272420 1272436 1272823 1272828) (-731 "NUMQUAD.spad" 1260282 1260290 1272410 1272415) (-730 "NUMODE.spad" 1251418 1251426 1260272 1260277) (-729 "NUMINT.spad" 1248976 1248984 1251408 1251413) (-728 "NUMFMT.spad" 1247816 1247824 1248966 1248971) (-727 "NUMERIC.spad" 1239889 1239899 1247622 1247627) (-726 "NTSCAT.spad" 1238379 1238395 1239845 1239884) (-725 "NTPOLFN.spad" 1237924 1237934 1238296 1238301) (-724 "NSUP.spad" 1230937 1230947 1235477 1235630) (-723 "NSUP2.spad" 1230329 1230341 1230927 1230932) (-722 "NSMP.spad" 1226528 1226547 1226836 1226963) (-721 "NREP.spad" 1224900 1224914 1226518 1226523) (-720 "NPCOEF.spad" 1224146 1224166 1224890 1224895) (-719 "NORMRETR.spad" 1223744 1223783 1224136 1224141) (-718 "NORMPK.spad" 1221646 1221665 1223734 1223739) (-717 "NORMMA.spad" 1221334 1221360 1221636 1221641) 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1126437) (-678 "MRING.spad" 1123246 1123258 1125983 1126050) (-677 "MRF2.spad" 1122814 1122828 1123236 1123241) (-676 "MRATFAC.spad" 1122360 1122377 1122804 1122809) (-675 "MPRFF.spad" 1120390 1120409 1122350 1122355) (-674 "MPOLY.spad" 1117828 1117843 1118187 1118314) (-673 "MPCPF.spad" 1117092 1117111 1117818 1117823) (-672 "MPC3.spad" 1116907 1116947 1117082 1117087) (-671 "MPC2.spad" 1116549 1116582 1116897 1116902) (-670 "MONOTOOL.spad" 1114884 1114901 1116539 1116544) (-669 "MONOID.spad" 1114058 1114066 1114874 1114879) (-668 "MONOID.spad" 1113230 1113240 1114048 1114053) (-667 "MONOGEN.spad" 1111976 1111989 1113090 1113225) (-666 "MONOGEN.spad" 1110744 1110759 1111860 1111865) (-665 "MONADWU.spad" 1108758 1108766 1110734 1110739) (-664 "MONADWU.spad" 1106770 1106780 1108748 1108753) (-663 "MONAD.spad" 1105914 1105922 1106760 1106765) (-662 "MONAD.spad" 1105056 1105066 1105904 1105909) (-661 "MOEBIUS.spad" 1103742 1103756 1105036 1105051) (-660 "MODULE.spad" 1103612 1103622 1103710 1103737) (-659 "MODULE.spad" 1103502 1103514 1103602 1103607) (-658 "MODRING.spad" 1102833 1102872 1103482 1103497) (-657 "MODOP.spad" 1101492 1101504 1102655 1102722) (-656 "MODMONOM.spad" 1101024 1101042 1101482 1101487) (-655 "MODMON.spad" 1097729 1097745 1098505 1098658) (-654 "MODFIELD.spad" 1097087 1097126 1097631 1097724) (-653 "MMLFORM.spad" 1095947 1095955 1097077 1097082) (-652 "MMAP.spad" 1095687 1095721 1095937 1095942) (-651 "MLO.spad" 1094114 1094124 1095643 1095682) (-650 "MLIFT.spad" 1092686 1092703 1094104 1094109) (-649 "MKUCFUNC.spad" 1092219 1092237 1092676 1092681) (-648 "MKRECORD.spad" 1091821 1091834 1092209 1092214) (-647 "MKFUNC.spad" 1091202 1091212 1091811 1091816) (-646 "MKFLCFN.spad" 1090158 1090168 1091192 1091197) (-645 "MKCHSET.spad" 1089934 1089944 1090148 1090153) (-644 "MKBCFUNC.spad" 1089419 1089437 1089924 1089929) (-643 "MINT.spad" 1088858 1088866 1089321 1089414) (-642 "MHROWRED.spad" 1087359 1087369 1088848 1088853) (-641 "MFLOAT.spad" 1085804 1085812 1087249 1087354) (-640 "MFINFACT.spad" 1085204 1085226 1085794 1085799) (-639 "MESH.spad" 1082936 1082944 1085194 1085199) (-638 "MDDFACT.spad" 1081129 1081139 1082926 1082931) (-637 "MDAGG.spad" 1080404 1080414 1081097 1081124) (-636 "MCMPLX.spad" 1076384 1076392 1076998 1077199) (-635 "MCDEN.spad" 1075592 1075604 1076374 1076379) (-634 "MCALCFN.spad" 1072694 1072720 1075582 1075587) (-633 "MATSTOR.spad" 1069970 1069980 1072684 1072689) (-632 "MATRIX.spad" 1068674 1068684 1069158 1069185) (-631 "MATLIN.spad" 1066000 1066024 1068558 1068563) (-630 "MATCAT.spad" 1057573 1057595 1065956 1065995) (-629 "MATCAT.spad" 1049030 1049054 1057415 1057420) (-628 "MATCAT2.spad" 1048298 1048346 1049020 1049025) (-627 "MAPPKG3.spad" 1047197 1047211 1048288 1048293) (-626 "MAPPKG2.spad" 1046531 1046543 1047187 1047192) (-625 "MAPPKG1.spad" 1045349 1045359 1046521 1046526) (-624 "MAPHACK3.spad" 1045157 1045171 1045339 1045344) (-623 "MAPHACK2.spad" 1044922 1044934 1045147 1045152) (-622 "MAPHACK1.spad" 1044552 1044562 1044912 1044917) (-621 "MAGMA.spad" 1042342 1042359 1044542 1044547) (-620 "M3D.spad" 1040040 1040050 1041722 1041727) (-619 "LZSTAGG.spad" 1037258 1037268 1040020 1040035) (-618 "LZSTAGG.spad" 1034484 1034496 1037248 1037253) (-617 "LWORD.spad" 1031189 1031206 1034474 1034479) (-616 "LSQM.spad" 1029417 1029431 1029815 1029866) (-615 "LSPP.spad" 1028950 1028967 1029407 1029412) (-614 "LSMP.spad" 1027790 1027818 1028940 1028945) (-613 "LSMP1.spad" 1025594 1025608 1027780 1027785) (-612 "LSAGG.spad" 1025251 1025261 1025550 1025589) (-611 "LSAGG.spad" 1024940 1024952 1025241 1025246) (-610 "LPOLY.spad" 1023894 1023913 1024796 1024865) (-609 "LPEFRAC.spad" 1023151 1023161 1023884 1023889) (-608 "LO.spad" 1022552 1022566 1023085 1023112) (-607 "LOGIC.spad" 1022154 1022162 1022542 1022547) (-606 "LOGIC.spad" 1021754 1021764 1022144 1022149) (-605 "LODOOPS.spad" 1020672 1020684 1021744 1021749) (-604 "LODO.spad" 1020058 1020074 1020354 1020393) (-603 "LODOF.spad" 1019102 1019119 1020015 1020020) (-602 "LODOCAT.spad" 1017760 1017770 1019058 1019097) (-601 "LODOCAT.spad" 1016416 1016428 1017716 1017721) (-600 "LODO2.spad" 1015691 1015703 1016098 1016137) (-599 "LODO1.spad" 1015093 1015103 1015373 1015412) (-598 "LODEEF.spad" 1013865 1013883 1015083 1015088) (-597 "LNAGG.spad" 1009657 1009667 1013845 1013860) (-596 "LNAGG.spad" 1005423 1005435 1009613 1009618) (-595 "LMOPS.spad" 1002159 1002176 1005413 1005418) (-594 "LMODULE.spad" 1001801 1001811 1002149 1002154) (-593 "LMDICT.spad" 1001084 1001094 1001352 1001379) (-592 "LIST.spad" 998802 998812 1000231 1000258) (-591 "LIST3.spad" 998093 998107 998792 998797) (-590 "LIST2.spad" 996733 996745 998083 998088) (-589 "LIST2MAP.spad" 993610 993622 996723 996728) (-588 "LINEXP.spad" 993042 993052 993590 993605) (-587 "LINDEP.spad" 991819 991831 992954 992959) (-586 "LIMITRF.spad" 989733 989743 991809 991814) (-585 "LIMITPS.spad" 988616 988629 989723 989728) (-584 "LIE.spad" 986630 986642 987906 988051) (-583 "LIECAT.spad" 986106 986116 986556 986625) (-582 "LIECAT.spad" 985610 985622 986062 986067) (-581 "LIB.spad" 983658 983666 984269 984284) (-580 "LGROBP.spad" 981011 981030 983648 983653) (-579 "LF.spad" 979930 979946 981001 981006) (-578 "LFCAT.spad" 978949 978957 979920 979925) (-577 "LEXTRIPK.spad" 974452 974467 978939 978944) (-576 "LEXP.spad" 972455 972482 974432 974447) (-575 "LEADCDET.spad" 970839 970856 972445 972450) (-574 "LAZM3PK.spad" 969543 969565 970829 970834) (-573 "LAUPOL.spad" 968234 968247 969138 969207) (-572 "LAPLACE.spad" 967807 967823 968224 968229) (-571 "LA.spad" 967247 967261 967729 967768) (-570 "LALG.spad" 967023 967033 967227 967242) (-569 "LALG.spad" 966807 966819 967013 967018) (-568 "KOVACIC.spad" 965520 965537 966797 966802) (-567 "KONVERT.spad" 965242 965252 965510 965515) (-566 "KOERCE.spad" 964979 964989 965232 965237) (-565 "KERNEL.spad" 963514 963524 964763 964768) (-564 "KERNEL2.spad" 963217 963229 963504 963509) (-563 "KDAGG.spad" 962308 962330 963185 963212) (-562 "KDAGG.spad" 961419 961443 962298 962303) (-561 "KAFILE.spad" 960382 960398 960617 960644) (-560 "JORDAN.spad" 958209 958221 959672 959817) (-559 "JAVACODE.spad" 957975 957983 958199 958204) (-558 "IXAGG.spad" 956088 956112 957955 957970) (-557 "IXAGG.spad" 954066 954092 955935 955940) (-556 "IVECTOR.spad" 952839 952854 952994 953021) (-555 "ITUPLE.spad" 951984 951994 952829 952834) (-554 "ITRIGMNP.spad" 950795 950814 951974 951979) (-553 "ITFUN3.spad" 950289 950303 950785 950790) (-552 "ITFUN2.spad" 950019 950031 950279 950284) (-551 "ITAYLOR.spad" 947811 947826 949855 949980) (-550 "ISUPS.spad" 940222 940237 946785 946882) (-549 "ISUMP.spad" 939719 939735 940212 940217) (-548 "ISTRING.spad" 938722 938735 938888 938915) (-547 "IRURPK.spad" 937435 937454 938712 938717) (-546 "IRSN.spad" 935395 935403 937425 937430) (-545 "IRRF2F.spad" 933870 933880 935351 935356) (-544 "IRREDFFX.spad" 933471 933482 933860 933865) (-543 "IROOT.spad" 931802 931812 933461 933466) (-542 "IR.spad" 929592 929606 931658 931685) (-541 "IR2.spad" 928612 928628 929582 929587) (-540 "IR2F.spad" 927812 927828 928602 928607) (-539 "IPRNTPK.spad" 927572 927580 927802 927807) (-538 "IPF.spad" 927137 927149 927377 927470) (-537 "IPADIC.spad" 926898 926924 927063 927132) (-536 "INVLAPLA.spad" 926543 926559 926888 926893) (-535 "INTTR.spad" 919789 919806 926533 926538) (-534 "INTTOOLS.spad" 917501 917517 919364 919369) (-533 "INTSLPE.spad" 916807 916815 917491 917496) (-532 "INTRVL.spad" 916373 916383 916721 916802) (-531 "INTRF.spad" 914737 914751 916363 916368) (-530 "INTRET.spad" 914169 914179 914727 914732) (-529 "INTRAT.spad" 912844 912861 914159 914164) (-528 "INTPM.spad" 911207 911223 912487 912492) (-527 "INTPAF.spad" 908975 908993 911139 911144) (-526 "INTPACK.spad" 899285 899293 908965 908970) (-525 "INT.spad" 898646 898654 899139 899280) (-524 "INTHERTR.spad" 897912 897929 898636 898641) (-523 "INTHERAL.spad" 897578 897602 897902 897907) (-522 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839164 839169) (-481 "IDPC.spad" 837828 837840 838884 838889) (-480 "IDPAM.spad" 837573 837585 837818 837823) (-479 "IDPAG.spad" 837320 837332 837563 837568) (-478 "IDECOMP.spad" 834557 834575 837310 837315) (-477 "IDEAL.spad" 829480 829519 834492 834497) (-476 "ICDEN.spad" 828631 828647 829470 829475) (-475 "ICARD.spad" 827820 827828 828621 828626) (-474 "IBPTOOLS.spad" 826413 826430 827810 827815) (-473 "IBITS.spad" 825612 825625 826049 826076) (-472 "IBATOOL.spad" 822487 822506 825602 825607) (-471 "IBACHIN.spad" 820974 820989 822477 822482) (-470 "IARRAY2.spad" 819962 819988 820581 820608) (-469 "IARRAY1.spad" 819007 819022 819145 819172) (-468 "IAN.spad" 817222 817230 818825 818918) (-467 "IALGFACT.spad" 816823 816856 817212 817217) (-466 "HYPCAT.spad" 816247 816255 816813 816818) (-465 "HYPCAT.spad" 815669 815679 816237 816242) (-464 "HOAGG.spad" 812927 812937 815649 815664) (-463 "HOAGG.spad" 809970 809982 812694 812699) (-462 "HEXADEC.spad" 807842 807850 808440 808533) (-461 "HEUGCD.spad" 806857 806868 807832 807837) (-460 "HELLFDIV.spad" 806447 806471 806847 806852) (-459 "HEAP.spad" 805839 805849 806054 806081) (-458 "HDP.spad" 797361 797377 797738 797867) (-457 "HDMP.spad" 794540 794555 795158 795285) (-456 "HB.spad" 792777 792785 794530 794535) (-455 "HASHTBL.spad" 791247 791278 791458 791485) (-454 "HACKPI.spad" 790730 790738 791149 791242) (-453 "GTSET.spad" 789669 789685 790376 790403) (-452 "GSTBL.spad" 788188 788223 788362 788377) (-451 "GSERIES.spad" 785355 785382 786320 786469) (-450 "GROUP.spad" 784529 784537 785335 785350) (-449 "GROUP.spad" 783711 783721 784519 784524) (-448 "GROEBSOL.spad" 782199 782220 783701 783706) (-447 "GRMOD.spad" 780770 780782 782189 782194) (-446 "GRMOD.spad" 779339 779353 780760 780765) (-445 "GRIMAGE.spad" 771944 771952 779329 779334) (-444 "GRDEF.spad" 770323 770331 771934 771939) (-443 "GRAY.spad" 768782 768790 770313 770318) (-442 "GRALG.spad" 767829 767841 768772 768777) (-441 "GRALG.spad" 766874 766888 767819 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82644) (-70 "ASP33.spad" 81510 81523 81940 81945) (-69 "ASP31.spad" 80650 80663 81500 81505) (-68 "ASP30.spad" 79542 79555 80640 80645) (-67 "ASP29.spad" 79008 79021 79532 79537) (-66 "ASP28.spad" 70281 70294 78998 79003) (-65 "ASP27.spad" 69178 69191 70271 70276) (-64 "ASP24.spad" 68265 68278 69168 69173) (-63 "ASP20.spad" 67481 67494 68255 68260) (-62 "ASP1.spad" 66862 66875 67471 67476) (-61 "ASP19.spad" 61548 61561 66852 66857) (-60 "ASP12.spad" 60962 60975 61538 61543) (-59 "ASP10.spad" 60233 60246 60952 60957) (-58 "ARRAY2.spad" 59593 59602 59840 59867) (-57 "ARRAY1.spad" 58428 58437 58776 58803) (-56 "ARRAY12.spad" 57097 57108 58418 58423) (-55 "ARR2CAT.spad" 52747 52768 57053 57092) (-54 "ARR2CAT.spad" 48429 48452 52737 52742) (-53 "APPRULE.spad" 47673 47695 48419 48424) (-52 "APPLYORE.spad" 47288 47301 47663 47668) (-51 "ANY.spad" 45630 45637 47278 47283) (-50 "ANY1.spad" 44701 44710 45620 45625) (-49 "ANTISYM.spad" 43140 43156 44681 44696) (-48 "ANON.spad" 42837 42844 43130 43135) (-47 "AN.spad" 41140 41147 42655 42748) (-46 "AMR.spad" 39319 39330 41038 41135) (-45 "AMR.spad" 37335 37348 39056 39061) (-44 "ALIST.spad" 34747 34768 35097 35124) (-43 "ALGSC.spad" 33870 33896 34619 34672) (-42 "ALGPKG.spad" 29579 29590 33826 33831) (-41 "ALGMFACT.spad" 28768 28782 29569 29574) (-40 "ALGMANIP.spad" 26189 26204 28566 28571) (-39 "ALGFF.spad" 24507 24534 24724 24880) (-38 "ALGFACT.spad" 23628 23638 24497 24502) (-37 "ALGEBRA.spad" 23359 23368 23584 23623) (-36 "ALGEBRA.spad" 23122 23133 23349 23354) (-35 "ALAGG.spad" 22620 22641 23078 23117) (-34 "AHYP.spad" 22001 22008 22610 22615) (-33 "AGG.spad" 20300 20307 21981 21996) (-32 "AGG.spad" 18573 18582 20256 20261) (-31 "AF.spad" 16999 17014 18509 18514) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2238294 2238299 2238304 2238309) (-2 NIL 2238274 2238279 2238284 2238289) (-1 NIL 2238254 2238259 2238264 2238269) (0 NIL 2238234 2238239 2238244 2238249) (-1198 "ZMOD.spad" 2238043 2238056 2238172 2238229) (-1197 "ZLINDEP.spad" 2237087 2237098 2238033 2238038) (-1196 "ZDSOLVE.spad" 2226936 2226958 2237077 2237082) (-1195 "YSTREAM.spad" 2226429 2226440 2226926 2226931) (-1194 "XRPOLY.spad" 2225649 2225669 2226285 2226354) (-1193 "XPR.spad" 2223378 2223391 2225367 2225466) (-1192 "XPOLY.spad" 2222933 2222944 2223234 2223303) (-1191 "XPOLYC.spad" 2222250 2222266 2222859 2222928) (-1190 "XPBWPOLY.spad" 2220687 2220707 2222030 2222099) (-1189 "XF.spad" 2219148 2219163 2220589 2220682) (-1188 "XF.spad" 2217589 2217606 2219032 2219037) (-1187 "XFALG.spad" 2214613 2214629 2217515 2217584) (-1186 "XEXPPKG.spad" 2213864 2213890 2214603 2214608) (-1185 "XDPOLY.spad" 2213478 2213494 2213720 2213789) (-1184 "XALG.spad" 2213076 2213087 2213434 2213473) (-1183 "WUTSET.spad" 2208915 2208932 2212722 2212749) (-1182 "WP.spad" 2207929 2207973 2208773 2208840) (-1181 "WFFINTBS.spad" 2205492 2205514 2207919 2207924) (-1180 "WEIER.spad" 2203706 2203717 2205482 2205487) (-1179 "VSPACE.spad" 2203379 2203390 2203674 2203701) (-1178 "VSPACE.spad" 2203072 2203085 2203369 2203374) (-1177 "VOID.spad" 2202662 2202671 2203062 2203067) (-1176 "VIEW.spad" 2200284 2200293 2202652 2202657) (-1175 "VIEWDEF.spad" 2195481 2195490 2200274 2200279) (-1174 "VIEW3D.spad" 2179316 2179325 2195471 2195476) (-1173 "VIEW2D.spad" 2167053 2167062 2179306 2179311) (-1172 "VECTOR.spad" 2165730 2165741 2165981 2166008) (-1171 "VECTOR2.spad" 2164357 2164370 2165720 2165725) (-1170 "VECTCAT.spad" 2162245 2162256 2164313 2164352) (-1169 "VECTCAT.spad" 2159954 2159967 2162024 2162029) (-1168 "VARIABLE.spad" 2159734 2159749 2159944 2159949) (-1167 "UTYPE.spad" 2159368 2159377 2159714 2159729) (-1166 "UTSODETL.spad" 2158661 2158685 2159324 2159329) (-1165 "UTSODE.spad" 2156849 2156869 2158651 2158656) (-1164 "UTS.spad" 2151638 2151666 2155316 2155413) (-1163 "UTSCAT.spad" 2149089 2149105 2151536 2151633) (-1162 "UTSCAT.spad" 2146184 2146202 2148633 2148638) (-1161 "UTS2.spad" 2145777 2145812 2146174 2146179) (-1160 "URAGG.spad" 2140399 2140410 2145757 2145772) (-1159 "URAGG.spad" 2134995 2135008 2140355 2140360) (-1158 "UPXSSING.spad" 2132641 2132667 2134079 2134212) (-1157 "UPXS.spad" 2129668 2129696 2130773 2130922) (-1156 "UPXSCONS.spad" 2127425 2127445 2127800 2127949) (-1155 "UPXSCCA.spad" 2125883 2125903 2127271 2127420) (-1154 "UPXSCCA.spad" 2124483 2124505 2125873 2125878) (-1153 "UPXSCAT.spad" 2123064 2123080 2124329 2124478) (-1152 "UPXS2.spad" 2122605 2122658 2123054 2123059) (-1151 "UPSQFREE.spad" 2121017 2121031 2122595 2122600) (-1150 "UPSCAT.spad" 2118610 2118634 2120915 2121012) (-1149 "UPSCAT.spad" 2115909 2115935 2118216 2118221) (-1148 "UPOLYC.spad" 2110887 2110898 2115751 2115904) (-1147 "UPOLYC.spad" 2105757 2105770 2110623 2110628) (-1146 "UPOLYC2.spad" 2105226 2105245 2105747 2105752) (-1145 "UP.spad" 2102271 2102286 2102779 2102932) (-1144 "UPMP.spad" 2101161 2101174 2102261 2102266) (-1143 "UPDIVP.spad" 2100724 2100738 2101151 2101156) (-1142 "UPDECOMP.spad" 2098961 2098975 2100714 2100719) (-1141 "UPCDEN.spad" 2098168 2098184 2098951 2098956) (-1140 "UP2.spad" 2097530 2097551 2098158 2098163) (-1139 "UNISEG.spad" 2096883 2096894 2097449 2097454) (-1138 "UNISEG2.spad" 2096376 2096389 2096839 2096844) (-1137 "UNIFACT.spad" 2095477 2095489 2096366 2096371) (-1136 "ULS.spad" 2086036 2086064 2087129 2087558) (-1135 "ULSCONS.spad" 2080079 2080099 2080451 2080600) (-1134 "ULSCCAT.spad" 2077676 2077696 2079899 2080074) (-1133 "ULSCCAT.spad" 2075407 2075429 2077632 2077637) (-1132 "ULSCAT.spad" 2073623 2073639 2075253 2075402) (-1131 "ULS2.spad" 2073135 2073188 2073613 2073618) (-1130 "UFD.spad" 2072200 2072209 2073061 2073130) (-1129 "UFD.spad" 2071327 2071338 2072190 2072195) (-1128 "UDVO.spad" 2070174 2070183 2071317 2071322) (-1127 "UDPO.spad" 2067601 2067612 2070130 2070135) (-1126 "TYPE.spad" 2067523 2067532 2067581 2067596) (-1125 "TWOFACT.spad" 2066173 2066188 2067513 2067518) (-1124 "TUPLE.spad" 2065559 2065570 2066072 2066077) (-1123 "TUBETOOL.spad" 2062396 2062405 2065549 2065554) (-1122 "TUBE.spad" 2061037 2061054 2062386 2062391) (-1121 "TS.spad" 2059626 2059642 2060602 2060699) (-1120 "TSETCAT.spad" 2046741 2046758 2059582 2059621) (-1119 "TSETCAT.spad" 2033854 2033873 2046697 2046702) (-1118 "TRMANIP.spad" 2028220 2028237 2033560 2033565) (-1117 "TRIMAT.spad" 2027179 2027204 2028210 2028215) (-1116 "TRIGMNIP.spad" 2025696 2025713 2027169 2027174) (-1115 "TRIGCAT.spad" 2025208 2025217 2025686 2025691) (-1114 "TRIGCAT.spad" 2024718 2024729 2025198 2025203) (-1113 "TREE.spad" 2023289 2023300 2024325 2024352) (-1112 "TRANFUN.spad" 2023120 2023129 2023279 2023284) (-1111 "TRANFUN.spad" 2022949 2022960 2023110 2023115) (-1110 "TOPSP.spad" 2022623 2022632 2022939 2022944) (-1109 "TOOLSIGN.spad" 2022286 2022297 2022613 2022618) (-1108 "TEXTFILE.spad" 2020843 2020852 2022276 2022281) (-1107 "TEX.spad" 2017860 2017869 2020833 2020838) (-1106 "TEX1.spad" 2017416 2017427 2017850 2017855) (-1105 "TEMUTL.spad" 2016971 2016980 2017406 2017411) (-1104 "TBCMPPK.spad" 2015064 2015087 2016961 2016966) (-1103 "TBAGG.spad" 2014088 2014111 2015032 2015059) (-1102 "TBAGG.spad" 2013132 2013157 2014078 2014083) (-1101 "TANEXP.spad" 2012508 2012519 2013122 2013127) (-1100 "TABLE.spad" 2010919 2010942 2011189 2011216) (-1099 "TABLEAU.spad" 2010400 2010411 2010909 2010914) (-1098 "TABLBUMP.spad" 2007183 2007194 2010390 2010395) (-1097 "SYSTEM.spad" 2006457 2006466 2007173 2007178) (-1096 "SYSSOLP.spad" 2003930 2003941 2006447 2006452) (-1095 "SYNTAX.spad" 2000122 2000131 2003920 2003925) (-1094 "SYMTAB.spad" 1998178 1998187 2000112 2000117) (-1093 "SYMS.spad" 1994163 1994172 1998168 1998173) (-1092 "SYMPOLY.spad" 1993173 1993184 1993255 1993382) (-1091 "SYMFUNC.spad" 1992648 1992659 1993163 1993168) (-1090 "SYMBOL.spad" 1989984 1989993 1992638 1992643) (-1089 "SWITCH.spad" 1986741 1986750 1989974 1989979) (-1088 "SUTS.spad" 1983640 1983668 1985208 1985305) (-1087 "SUPXS.spad" 1980654 1980682 1981772 1981921) (-1086 "SUP.spad" 1977426 1977437 1978207 1978360) (-1085 "SUPFRACF.spad" 1976531 1976549 1977416 1977421) (-1084 "SUP2.spad" 1975921 1975934 1976521 1976526) (-1083 "SUMRF.spad" 1974887 1974898 1975911 1975916) (-1082 "SUMFS.spad" 1974520 1974537 1974877 1974882) (-1081 "SULS.spad" 1965066 1965094 1966172 1966601) (-1080 "SUCH.spad" 1964746 1964761 1965056 1965061) (-1079 "SUBSPACE.spad" 1956753 1956768 1964736 1964741) (-1078 "SUBRESP.spad" 1955913 1955927 1956709 1956714) (-1077 "STTF.spad" 1952012 1952028 1955903 1955908) (-1076 "STTFNC.spad" 1948480 1948496 1952002 1952007) (-1075 "STTAYLOR.spad" 1940878 1940889 1948361 1948366) (-1074 "STRTBL.spad" 1939383 1939400 1939532 1939559) (-1073 "STRING.spad" 1938792 1938801 1938806 1938833) (-1072 "STRICAT.spad" 1938568 1938577 1938748 1938787) (-1071 "STREAM.spad" 1935336 1935347 1938093 1938108) (-1070 "STREAM3.spad" 1934881 1934896 1935326 1935331) (-1069 "STREAM2.spad" 1933949 1933962 1934871 1934876) (-1068 "STREAM1.spad" 1933653 1933664 1933939 1933944) (-1067 "STINPROD.spad" 1932559 1932575 1933643 1933648) (-1066 "STEP.spad" 1931760 1931769 1932549 1932554) (-1065 "STBL.spad" 1930286 1930314 1930453 1930468) (-1064 "STAGG.spad" 1929351 1929362 1930266 1930281) (-1063 "STAGG.spad" 1928424 1928437 1929341 1929346) (-1062 "STACK.spad" 1927775 1927786 1928031 1928058) (-1061 "SREGSET.spad" 1925479 1925496 1927421 1927448) (-1060 "SRDCMPK.spad" 1924024 1924044 1925469 1925474) (-1059 "SRAGG.spad" 1919109 1919118 1923980 1924019) (-1058 "SRAGG.spad" 1914226 1914237 1919099 1919104) (-1057 "SQMATRIX.spad" 1911852 1911870 1912760 1912847) (-1056 "SPLTREE.spad" 1906404 1906417 1911288 1911315) (-1055 "SPLNODE.spad" 1902992 1903005 1906394 1906399) (-1054 "SPFCAT.spad" 1901769 1901778 1902982 1902987) (-1053 "SPECOUT.spad" 1900319 1900328 1901759 1901764) (-1052 "spad-parser.spad" 1899784 1899793 1900309 1900314) (-1051 "SPACEC.spad" 1883797 1883808 1899774 1899779) (-1050 "SPACE3.spad" 1883573 1883584 1883787 1883792) (-1049 "SORTPAK.spad" 1883118 1883131 1883529 1883534) (-1048 "SOLVETRA.spad" 1880875 1880886 1883108 1883113) (-1047 "SOLVESER.spad" 1879395 1879406 1880865 1880870) (-1046 "SOLVERAD.spad" 1875405 1875416 1879385 1879390) (-1045 "SOLVEFOR.spad" 1873825 1873843 1875395 1875400) (-1044 "SNTSCAT.spad" 1873413 1873430 1873781 1873820) (-1043 "SMTS.spad" 1871673 1871699 1872978 1873075) (-1042 "SMP.spad" 1869115 1869135 1869505 1869632) (-1041 "SMITH.spad" 1867958 1867983 1869105 1869110) (-1040 "SMATCAT.spad" 1866056 1866086 1867890 1867953) (-1039 "SMATCAT.spad" 1864098 1864130 1865934 1865939) (-1038 "SKAGG.spad" 1863047 1863058 1864054 1864093) (-1037 "SINT.spad" 1861355 1861364 1862913 1863042) (-1036 "SIMPAN.spad" 1861083 1861092 1861345 1861350) (-1035 "SIGNRF.spad" 1860191 1860202 1861073 1861078) (-1034 "SIGNEF.spad" 1859460 1859477 1860181 1860186) (-1033 "SHP.spad" 1857378 1857393 1859416 1859421) (-1032 "SHDP.spad" 1848768 1848795 1849277 1849406) (-1031 "SGROUP.spad" 1848234 1848243 1848758 1848763) (-1030 "SGROUP.spad" 1847698 1847709 1848224 1848229) (-1029 "SGCF.spad" 1840579 1840588 1847688 1847693) (-1028 "SFRTCAT.spad" 1839495 1839512 1840535 1840574) (-1027 "SFRGCD.spad" 1838558 1838578 1839485 1839490) (-1026 "SFQCMPK.spad" 1833195 1833215 1838548 1838553) (-1025 "SFORT.spad" 1832630 1832644 1833185 1833190) (-1024 "SEXOF.spad" 1832473 1832513 1832620 1832625) (-1023 "SEX.spad" 1832365 1832374 1832463 1832468) (-1022 "SEXCAT.spad" 1829469 1829509 1832355 1832360) (-1021 "SET.spad" 1827769 1827780 1828890 1828929) (-1020 "SETMN.spad" 1826203 1826220 1827759 1827764) (-1019 "SETCAT.spad" 1825688 1825697 1826193 1826198) (-1018 "SETCAT.spad" 1825171 1825182 1825678 1825683) (-1017 "SETAGG.spad" 1821694 1821705 1825139 1825166) (-1016 "SETAGG.spad" 1818237 1818250 1821684 1821689) (-1015 "SEGXCAT.spad" 1817349 1817362 1818217 1818232) (-1014 "SEG.spad" 1817162 1817173 1817268 1817273) (-1013 "SEGCAT.spad" 1815981 1815992 1817142 1817157) (-1012 "SEGBIND.spad" 1815053 1815064 1815936 1815941) (-1011 "SEGBIND2.spad" 1814749 1814762 1815043 1815048) (-1010 "SEG2.spad" 1814174 1814187 1814705 1814710) (-1009 "SDVAR.spad" 1813450 1813461 1814164 1814169) (-1008 "SDPOL.spad" 1810843 1810854 1811134 1811261) (-1007 "SCPKG.spad" 1808922 1808933 1810833 1810838) (-1006 "SCOPE.spad" 1808067 1808076 1808912 1808917) (-1005 "SCACHE.spad" 1806749 1806760 1808057 1808062) (-1004 "SAOS.spad" 1806621 1806630 1806739 1806744) (-1003 "SAERFFC.spad" 1806334 1806354 1806611 1806616) (-1002 "SAE.spad" 1804512 1804528 1805123 1805258) (-1001 "SAEFACT.spad" 1804213 1804233 1804502 1804507) (-1000 "RURPK.spad" 1801854 1801870 1804203 1804208) (-999 "RULESET.spad" 1801296 1801319 1801844 1801849) (-998 "RULE.spad" 1799501 1799524 1801286 1801291) (-997 "RULECOLD.spad" 1799354 1799366 1799491 1799496) (-996 "RSETGCD.spad" 1795733 1795752 1799344 1799349) (-995 "RSETCAT.spad" 1785506 1785522 1795689 1795728) (-994 "RSETCAT.spad" 1775311 1775329 1785496 1785501) (-993 "RSDCMPK.spad" 1773764 1773783 1775301 1775306) (-992 "RRCC.spad" 1772149 1772178 1773754 1773759) (-991 "RRCC.spad" 1770532 1770563 1772139 1772144) (-990 "RPOLCAT.spad" 1749893 1749907 1770400 1770527) (-989 "RPOLCAT.spad" 1728969 1728985 1749478 1749483) (-988 "ROUTINE.spad" 1724833 1724841 1727616 1727643) (-987 "ROMAN.spad" 1724066 1724074 1724699 1724828) (-986 "ROIRC.spad" 1723147 1723178 1724056 1724061) (-985 "RNS.spad" 1722051 1722059 1723049 1723142) (-984 "RNS.spad" 1721041 1721051 1722041 1722046) (-983 "RNG.spad" 1720777 1720785 1721031 1721036) (-982 "RMODULE.spad" 1720416 1720426 1720767 1720772) (-981 "RMCAT2.spad" 1719825 1719881 1720406 1720411) (-980 "RMATRIX.spad" 1718505 1718523 1718992 1719031) (-979 "RMATCAT.spad" 1714027 1714057 1718449 1718500) (-978 "RMATCAT.spad" 1709451 1709483 1713875 1713880) (-977 "RINTERP.spad" 1709340 1709359 1709441 1709446) (-976 "RING.spad" 1708698 1708706 1709320 1709335) (-975 "RING.spad" 1708064 1708074 1708688 1708693) (-974 "RIDIST.spad" 1707449 1707457 1708054 1708059) (-973 "RGCHAIN.spad" 1706029 1706044 1706934 1706961) (-972 "RF.spad" 1703644 1703654 1706019 1706024) (-971 "RFFACTOR.spad" 1703107 1703117 1703634 1703639) (-970 "RFFACT.spad" 1702843 1702854 1703097 1703102) (-969 "RFDIST.spad" 1701832 1701840 1702833 1702838) (-968 "RETSOL.spad" 1701250 1701262 1701822 1701827) (-967 "RETRACT.spad" 1700600 1700610 1701240 1701245) (-966 "RETRACT.spad" 1699948 1699960 1700590 1700595) (-965 "RESULT.spad" 1698009 1698017 1698595 1698622) (-964 "RESRING.spad" 1697357 1697403 1697947 1698004) (-963 "RESLATC.spad" 1696682 1696692 1697347 1697352) (-962 "REPSQ.spad" 1696412 1696422 1696672 1696677) (-961 "REP.spad" 1693965 1693973 1696402 1696407) (-960 "REPDB.spad" 1693671 1693681 1693955 1693960) (-959 "REP2.spad" 1683244 1683254 1693513 1693518) (-958 "REP1.spad" 1677235 1677245 1683194 1683199) (-957 "REGSET.spad" 1675033 1675049 1676881 1676908) (-956 "REF.spad" 1674363 1674373 1674988 1674993) (-955 "REDORDER.spad" 1673540 1673556 1674353 1674358) (-954 "RECLOS.spad" 1672330 1672349 1673033 1673126) (-953 "REALSOLV.spad" 1671463 1671471 1672320 1672325) (-952 "REAL.spad" 1671336 1671344 1671453 1671458) (-951 "REAL0Q.spad" 1668619 1668633 1671326 1671331) (-950 "REAL0.spad" 1665448 1665462 1668609 1668614) (-949 "RDIV.spad" 1665100 1665124 1665438 1665443) (-948 "RDIST.spad" 1664664 1664674 1665090 1665095) (-947 "RDETRS.spad" 1663461 1663478 1664654 1664659) (-946 "RDETR.spad" 1661569 1661586 1663451 1663456) (-945 "RDEEFS.spad" 1660643 1660659 1661559 1661564) (-944 "RDEEF.spad" 1659640 1659656 1660633 1660638) (-943 "RCFIELD.spad" 1656827 1656835 1659542 1659635) (-942 "RCFIELD.spad" 1654100 1654110 1656817 1656822) (-941 "RCAGG.spad" 1652003 1652013 1654080 1654095) (-940 "RCAGG.spad" 1649843 1649855 1651922 1651927) (-939 "RATRET.spad" 1649204 1649214 1649833 1649838) (-938 "RATFACT.spad" 1648897 1648908 1649194 1649199) (-937 "RANDSRC.spad" 1648217 1648225 1648887 1648892) (-936 "RADUTIL.spad" 1647972 1647980 1648207 1648212) (-935 "RADIX.spad" 1644765 1644778 1646442 1646535) (-934 "RADFF.spad" 1643182 1643218 1643300 1643456) (-933 "RADCAT.spad" 1642776 1642784 1643172 1643177) (-932 "RADCAT.spad" 1642368 1642378 1642766 1642771) (-931 "QUEUE.spad" 1641711 1641721 1641975 1642002) (-930 "QUAT.spad" 1640297 1640307 1640639 1640704) (-929 "QUATCT2.spad" 1639916 1639934 1640287 1640292) (-928 "QUATCAT.spad" 1638081 1638091 1639846 1639911) (-927 "QUATCAT.spad" 1635998 1636010 1637765 1637770) (-926 "QUAGG.spad" 1634812 1634822 1635954 1635993) (-925 "QFORM.spad" 1634275 1634289 1634802 1634807) (-924 "QFCAT.spad" 1632966 1632976 1634165 1634270) (-923 "QFCAT.spad" 1631263 1631275 1632464 1632469) (-922 "QFCAT2.spad" 1630954 1630970 1631253 1631258) (-921 "QEQUAT.spad" 1630511 1630519 1630944 1630949) (-920 "QCMPACK.spad" 1625258 1625277 1630501 1630506) (-919 "QALGSET.spad" 1621333 1621365 1625172 1625177) (-918 "QALGSET2.spad" 1619329 1619347 1621323 1621328) (-917 "PWFFINTB.spad" 1616639 1616660 1619319 1619324) (-916 "PUSHVAR.spad" 1615968 1615987 1616629 1616634) (-915 "PTRANFN.spad" 1612094 1612104 1615958 1615963) (-914 "PTPACK.spad" 1609182 1609192 1612084 1612089) (-913 "PTFUNC2.spad" 1609003 1609017 1609172 1609177) (-912 "PTCAT.spad" 1608085 1608095 1608959 1608998) (-911 "PSQFR.spad" 1607392 1607416 1608075 1608080) (-910 "PSEUDLIN.spad" 1606250 1606260 1607382 1607387) (-909 "PSETPK.spad" 1591683 1591699 1606128 1606133) (-908 "PSETCAT.spad" 1585591 1585614 1591651 1591678) (-907 "PSETCAT.spad" 1579485 1579510 1585547 1585552) (-906 "PSCURVE.spad" 1578468 1578476 1579475 1579480) (-905 "PSCAT.spad" 1577235 1577264 1578366 1578463) (-904 "PSCAT.spad" 1576092 1576123 1577225 1577230) (-903 "PRTITION.spad" 1574935 1574943 1576082 1576087) (-902 "PRS.spad" 1564497 1564514 1574891 1574896) (-901 "PRQAGG.spad" 1563916 1563926 1564453 1564492) (-900 "PROPLOG.spad" 1563319 1563327 1563906 1563911) (-899 "PROPFRML.spad" 1561184 1561195 1563255 1563260) (-898 "PROPERTY.spad" 1560678 1560686 1561174 1561179) (-897 "PRODUCT.spad" 1558358 1558370 1558644 1558699) (-896 "PR.spad" 1556747 1556759 1557452 1557579) (-895 "PRINT.spad" 1556499 1556507 1556737 1556742) (-894 "PRIMES.spad" 1554750 1554760 1556489 1556494) (-893 "PRIMELT.spad" 1552731 1552745 1554740 1554745) (-892 "PRIMCAT.spad" 1552354 1552362 1552721 1552726) (-891 "PRIMARR.spad" 1551359 1551369 1551537 1551564) (-890 "PRIMARR2.spad" 1550082 1550094 1551349 1551354) (-889 "PREASSOC.spad" 1549454 1549466 1550072 1550077) (-888 "PPCURVE.spad" 1548591 1548599 1549444 1549449) (-887 "POLYROOT.spad" 1547363 1547385 1548547 1548552) (-886 "POLY.spad" 1544663 1544673 1545180 1545307) (-885 "POLYLIFT.spad" 1543924 1543947 1544653 1544658) (-884 "POLYCATQ.spad" 1542026 1542048 1543914 1543919) (-883 "POLYCAT.spad" 1535432 1535453 1541894 1542021) (-882 "POLYCAT.spad" 1528140 1528163 1534604 1534609) (-881 "POLY2UP.spad" 1527588 1527602 1528130 1528135) (-880 "POLY2.spad" 1527183 1527195 1527578 1527583) (-879 "POLUTIL.spad" 1526124 1526153 1527139 1527144) (-878 "POLTOPOL.spad" 1524872 1524887 1526114 1526119) (-877 "POINT.spad" 1523713 1523723 1523800 1523827) (-876 "PNTHEORY.spad" 1520379 1520387 1523703 1523708) (-875 "PMTOOLS.spad" 1519136 1519150 1520369 1520374) (-874 "PMSYM.spad" 1518681 1518691 1519126 1519131) (-873 "PMQFCAT.spad" 1518268 1518282 1518671 1518676) (-872 "PMPRED.spad" 1517737 1517751 1518258 1518263) (-871 "PMPREDFS.spad" 1517181 1517203 1517727 1517732) (-870 "PMPLCAT.spad" 1516251 1516269 1517113 1517118) (-869 "PMLSAGG.spad" 1515832 1515846 1516241 1516246) (-868 "PMKERNEL.spad" 1515399 1515411 1515822 1515827) (-867 "PMINS.spad" 1514975 1514985 1515389 1515394) (-866 "PMFS.spad" 1514548 1514566 1514965 1514970) (-865 "PMDOWN.spad" 1513834 1513848 1514538 1514543) (-864 "PMASS.spad" 1512846 1512854 1513824 1513829) (-863 "PMASSFS.spad" 1511815 1511831 1512836 1512841) (-862 "PLOTTOOL.spad" 1511595 1511603 1511805 1511810) (-861 "PLOT.spad" 1506426 1506434 1511585 1511590) (-860 "PLOT3D.spad" 1502846 1502854 1506416 1506421) (-859 "PLOT1.spad" 1501987 1501997 1502836 1502841) (-858 "PLEQN.spad" 1489203 1489230 1501977 1501982) (-857 "PINTERP.spad" 1488819 1488838 1489193 1489198) (-856 "PINTERPA.spad" 1488601 1488617 1488809 1488814) (-855 "PI.spad" 1488208 1488216 1488575 1488596) (-854 "PID.spad" 1487164 1487172 1488134 1488203) (-853 "PICOERCE.spad" 1486821 1486831 1487154 1487159) (-852 "PGROEB.spad" 1485418 1485432 1486811 1486816) (-851 "PGE.spad" 1476671 1476679 1485408 1485413) (-850 "PGCD.spad" 1475553 1475570 1476661 1476666) (-849 "PFRPAC.spad" 1474696 1474706 1475543 1475548) (-848 "PFR.spad" 1471353 1471363 1474598 1474691) (-847 "PFOTOOLS.spad" 1470611 1470627 1471343 1471348) (-846 "PFOQ.spad" 1469981 1469999 1470601 1470606) (-845 "PFO.spad" 1469400 1469427 1469971 1469976) (-844 "PF.spad" 1468974 1468986 1469205 1469298) (-843 "PFECAT.spad" 1466640 1466648 1468900 1468969) (-842 "PFECAT.spad" 1464334 1464344 1466596 1466601) (-841 "PFBRU.spad" 1462204 1462216 1464324 1464329) (-840 "PFBR.spad" 1459742 1459765 1462194 1462199) (-839 "PERM.spad" 1455423 1455433 1459572 1459587) (-838 "PERMGRP.spad" 1450159 1450169 1455413 1455418) (-837 "PERMCAT.spad" 1448711 1448721 1450139 1450154) (-836 "PERMAN.spad" 1447243 1447257 1448701 1448706) (-835 "PENDTREE.spad" 1446516 1446526 1446872 1446877) (-834 "PDRING.spad" 1445007 1445017 1446496 1446511) (-833 "PDRING.spad" 1443506 1443518 1444997 1445002) (-832 "PDEPROB.spad" 1442463 1442471 1443496 1443501) (-831 "PDEPACK.spad" 1436465 1436473 1442453 1442458) (-830 "PDECOMP.spad" 1435927 1435944 1436455 1436460) (-829 "PDECAT.spad" 1434281 1434289 1435917 1435922) (-828 "PCOMP.spad" 1434132 1434145 1434271 1434276) (-827 "PBWLB.spad" 1432714 1432731 1434122 1434127) (-826 "PATTERN.spad" 1427145 1427155 1432704 1432709) (-825 "PATTERN2.spad" 1426881 1426893 1427135 1427140) (-824 "PATTERN1.spad" 1425183 1425199 1426871 1426876) (-823 "PATRES.spad" 1422730 1422742 1425173 1425178) (-822 "PATRES2.spad" 1422392 1422406 1422720 1422725) (-821 "PATMATCH.spad" 1420554 1420585 1422105 1422110) (-820 "PATMAB.spad" 1419979 1419989 1420544 1420549) (-819 "PATLRES.spad" 1419063 1419077 1419969 1419974) (-818 "PATAB.spad" 1418827 1418837 1419053 1419058) (-817 "PARTPERM.spad" 1416189 1416197 1418817 1418822) (-816 "PARSURF.spad" 1415617 1415645 1416179 1416184) (-815 "PARSU2.spad" 1415412 1415428 1415607 1415612) (-814 "script-parser.spad" 1414932 1414940 1415402 1415407) (-813 "PARSCURV.spad" 1414360 1414388 1414922 1414927) (-812 "PARSC2.spad" 1414149 1414165 1414350 1414355) (-811 "PARPCURV.spad" 1413607 1413635 1414139 1414144) (-810 "PARPC2.spad" 1413396 1413412 1413597 1413602) (-809 "PAN2EXPR.spad" 1412808 1412816 1413386 1413391) (-808 "PALETTE.spad" 1411778 1411786 1412798 1412803) (-807 "PAIR.spad" 1410761 1410774 1411366 1411371) (-806 "PADICRC.spad" 1408094 1408112 1409269 1409362) (-805 "PADICRAT.spad" 1406112 1406124 1406333 1406426) (-804 "PADIC.spad" 1405807 1405819 1406038 1406107) (-803 "PADICCT.spad" 1404348 1404360 1405733 1405802) (-802 "PADEPAC.spad" 1403027 1403046 1404338 1404343) (-801 "PADE.spad" 1401767 1401783 1403017 1403022) (-800 "OWP.spad" 1400751 1400781 1401625 1401692) (-799 "OVAR.spad" 1400532 1400555 1400741 1400746) (-798 "OUT.spad" 1399616 1399624 1400522 1400527) (-797 "OUTFORM.spad" 1389030 1389038 1399606 1399611) (-796 "OSI.spad" 1388505 1388513 1389020 1389025) (-795 "ORTHPOL.spad" 1386966 1386976 1388422 1388427) (-794 "OREUP.spad" 1386326 1386354 1386648 1386687) (-793 "ORESUP.spad" 1385627 1385651 1386008 1386047) (-792 "OREPCTO.spad" 1383446 1383458 1385547 1385552) (-791 "OREPCAT.spad" 1377503 1377513 1383402 1383441) (-790 "OREPCAT.spad" 1371450 1371462 1377351 1377356) (-789 "ORDSET.spad" 1370616 1370624 1371440 1371445) (-788 "ORDSET.spad" 1369780 1369790 1370606 1370611) (-787 "ORDRING.spad" 1369170 1369178 1369760 1369775) (-786 "ORDRING.spad" 1368568 1368578 1369160 1369165) (-785 "ORDMON.spad" 1368423 1368431 1368558 1368563) (-784 "ORDFUNS.spad" 1367549 1367565 1368413 1368418) (-783 "ORDFIN.spad" 1367483 1367491 1367539 1367544) (-782 "ORDCOMP.spad" 1365951 1365961 1367033 1367062) (-781 "ORDCOMP2.spad" 1365236 1365248 1365941 1365946) (-780 "OPTPROB.spad" 1363816 1363824 1365226 1365231) (-779 "OPTPACK.spad" 1356201 1356209 1363806 1363811) (-778 "OPTCAT.spad" 1353876 1353884 1356191 1356196) (-777 "OPQUERY.spad" 1353425 1353433 1353866 1353871) (-776 "OP.spad" 1353167 1353177 1353247 1353314) (-775 "ONECOMP.spad" 1351915 1351925 1352717 1352746) (-774 "ONECOMP2.spad" 1351333 1351345 1351905 1351910) (-773 "OMSERVER.spad" 1350335 1350343 1351323 1351328) (-772 "OMSAGG.spad" 1350111 1350121 1350279 1350330) (-771 "OMPKG.spad" 1348723 1348731 1350101 1350106) (-770 "OM.spad" 1347688 1347696 1348713 1348718) (-769 "OMLO.spad" 1347113 1347125 1347574 1347613) (-768 "OMEXPR.spad" 1346947 1346957 1347103 1347108) (-767 "OMERR.spad" 1346490 1346498 1346937 1346942) (-766 "OMERRK.spad" 1345524 1345532 1346480 1346485) (-765 "OMENC.spad" 1344868 1344876 1345514 1345519) (-764 "OMDEV.spad" 1339157 1339165 1344858 1344863) (-763 "OMCONN.spad" 1338566 1338574 1339147 1339152) (-762 "OINTDOM.spad" 1338329 1338337 1338492 1338561) (-761 "OFMONOID.spad" 1334516 1334526 1338319 1338324) (-760 "ODVAR.spad" 1333777 1333787 1334506 1334511) (-759 "ODR.spad" 1333225 1333251 1333589 1333738) (-758 "ODPOL.spad" 1330574 1330584 1330914 1331041) (-757 "ODP.spad" 1322100 1322120 1322473 1322602) (-756 "ODETOOLS.spad" 1320683 1320702 1322090 1322095) (-755 "ODESYS.spad" 1318333 1318350 1320673 1320678) (-754 "ODERTRIC.spad" 1314274 1314291 1318290 1318295) (-753 "ODERED.spad" 1313661 1313685 1314264 1314269) (-752 "ODERAT.spad" 1311212 1311229 1313651 1313656) (-751 "ODEPRRIC.spad" 1308103 1308125 1311202 1311207) (-750 "ODEPROB.spad" 1307302 1307310 1308093 1308098) (-749 "ODEPRIM.spad" 1304576 1304598 1307292 1307297) (-748 "ODEPAL.spad" 1303952 1303976 1304566 1304571) (-747 "ODEPACK.spad" 1290554 1290562 1303942 1303947) (-746 "ODEINT.spad" 1289985 1290001 1290544 1290549) (-745 "ODEIFTBL.spad" 1287380 1287388 1289975 1289980) (-744 "ODEEF.spad" 1282747 1282763 1287370 1287375) (-743 "ODECONST.spad" 1282266 1282284 1282737 1282742) (-742 "ODECAT.spad" 1280862 1280870 1282256 1282261) (-741 "OCT.spad" 1279009 1279019 1279725 1279764) (-740 "OCTCT2.spad" 1278653 1278674 1278999 1279004) (-739 "OC.spad" 1276427 1276437 1278609 1278648) (-738 "OC.spad" 1273927 1273939 1276111 1276116) (-737 "OCAMON.spad" 1273775 1273783 1273917 1273922) (-736 "OASGP.spad" 1273590 1273598 1273765 1273770) (-735 "OAMONS.spad" 1273110 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1126437) (-678 "MRING.spad" 1123246 1123258 1125983 1126050) (-677 "MRF2.spad" 1122814 1122828 1123236 1123241) (-676 "MRATFAC.spad" 1122360 1122377 1122804 1122809) (-675 "MPRFF.spad" 1120390 1120409 1122350 1122355) (-674 "MPOLY.spad" 1117828 1117843 1118187 1118314) (-673 "MPCPF.spad" 1117092 1117111 1117818 1117823) (-672 "MPC3.spad" 1116907 1116947 1117082 1117087) (-671 "MPC2.spad" 1116549 1116582 1116897 1116902) (-670 "MONOTOOL.spad" 1114884 1114901 1116539 1116544) (-669 "MONOID.spad" 1114058 1114066 1114874 1114879) (-668 "MONOID.spad" 1113230 1113240 1114048 1114053) (-667 "MONOGEN.spad" 1111976 1111989 1113090 1113225) (-666 "MONOGEN.spad" 1110744 1110759 1111860 1111865) (-665 "MONADWU.spad" 1108758 1108766 1110734 1110739) (-664 "MONADWU.spad" 1106770 1106780 1108748 1108753) (-663 "MONAD.spad" 1105914 1105922 1106760 1106765) (-662 "MONAD.spad" 1105056 1105066 1105904 1105909) (-661 "MOEBIUS.spad" 1103742 1103756 1105036 1105051) (-660 "MODULE.spad" 1103612 1103622 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(-622 "MAPHACK1.spad" 1044552 1044562 1044912 1044917) (-621 "MAGMA.spad" 1042342 1042359 1044542 1044547) (-620 "M3D.spad" 1040040 1040050 1041722 1041727) (-619 "LZSTAGG.spad" 1037258 1037268 1040020 1040035) (-618 "LZSTAGG.spad" 1034484 1034496 1037248 1037253) (-617 "LWORD.spad" 1031189 1031206 1034474 1034479) (-616 "LSQM.spad" 1029417 1029431 1029815 1029866) (-615 "LSPP.spad" 1028950 1028967 1029407 1029412) (-614 "LSMP.spad" 1027790 1027818 1028940 1028945) (-613 "LSMP1.spad" 1025594 1025608 1027780 1027785) (-612 "LSAGG.spad" 1025251 1025261 1025550 1025589) (-611 "LSAGG.spad" 1024940 1024952 1025241 1025246) (-610 "LPOLY.spad" 1023894 1023913 1024796 1024865) (-609 "LPEFRAC.spad" 1023151 1023161 1023884 1023889) (-608 "LO.spad" 1022552 1022566 1023085 1023112) (-607 "LOGIC.spad" 1022154 1022162 1022542 1022547) (-606 "LOGIC.spad" 1021754 1021764 1022144 1022149) (-605 "LODOOPS.spad" 1020672 1020684 1021744 1021749) (-604 "LODO.spad" 1020058 1020074 1020354 1020393) (-603 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(-420 "GALFACTU.spad" 727174 727193 728999 729004) (-419 "GALFACT.spad" 717307 717318 727164 727169) (-418 "FVFUN.spad" 714320 714328 717287 717302) (-417 "FVC.spad" 713362 713370 714300 714315) (-416 "FUNCTION.spad" 713211 713223 713352 713357) (-415 "FT.spad" 711423 711431 713201 713206) (-414 "FTEM.spad" 710586 710594 711413 711418) (-413 "FSUPFACT.spad" 709487 709506 710523 710528) (-412 "FST.spad" 707573 707581 709477 709482) (-411 "FSRED.spad" 707051 707067 707563 707568) (-410 "FSPRMELT.spad" 705875 705891 707008 707013) (-409 "FSPECF.spad" 703952 703968 705865 705870) (-408 "FS.spad" 698003 698013 703716 703947) (-407 "FS.spad" 691845 691857 697560 697565) (-406 "FSINT.spad" 691503 691519 691835 691840) (-405 "FSERIES.spad" 690690 690702 691323 691422) (-404 "FSCINT.spad" 690003 690019 690680 690685) (-403 "FSAGG.spad" 689108 689118 689947 689998) (-402 "FSAGG.spad" 688187 688199 689028 689033) (-401 "FSAGG2.spad" 686886 686902 688177 688182) (-400 "FS2UPS.spad" 681275 681309 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"FEXPR.spad" 510384 510430 518431 518470) (-316 "FEVALAB.spad" 510090 510100 510374 510379) (-315 "FEVALAB.spad" 509581 509593 509867 509872) (-314 "FDIV.spad" 509023 509047 509571 509576) (-313 "FDIVCAT.spad" 507065 507089 509013 509018) (-312 "FDIVCAT.spad" 505105 505131 507055 507060) (-311 "FDIV2.spad" 504759 504799 505095 505100) (-310 "FCPAK1.spad" 503312 503320 504749 504754) (-309 "FCOMP.spad" 502691 502701 503302 503307) (-308 "FC.spad" 492516 492524 502681 502686) (-307 "FAXF.spad" 485451 485465 492418 492511) (-306 "FAXF.spad" 478438 478454 485407 485412) (-305 "FARRAY.spad" 476584 476594 477621 477648) (-304 "FAMR.spad" 474704 474716 476482 476579) (-303 "FAMR.spad" 472808 472822 474588 474593) (-302 "FAMONOID.spad" 472458 472468 472762 472767) (-301 "FAMONC.spad" 470680 470692 472448 472453) (-300 "FAGROUP.spad" 470286 470296 470576 470603) (-299 "FACUTIL.spad" 468482 468499 470276 470281) (-298 "FACTFUNC.spad" 467658 467668 468472 468477) (-297 "EXPUPXS.spad" 464491 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(-276 "ES1.spad" 411741 411757 412165 412170) (-275 "ERROR.spad" 409062 409070 411731 411736) (-274 "EQTBL.spad" 407534 407556 407743 407770) (-273 "EQ.spad" 402418 402428 405217 405326) (-272 "EQ2.spad" 402134 402146 402408 402413) (-271 "EP.spad" 398448 398458 402124 402129) (-270 "ENV.spad" 397150 397158 398438 398443) (-269 "ENTIRER.spad" 396818 396826 397094 397145) (-268 "EMR.spad" 396019 396060 396744 396813) (-267 "ELTAGG.spad" 394259 394278 396009 396014) (-266 "ELTAGG.spad" 392463 392484 394215 394220) (-265 "ELTAB.spad" 391910 391928 392453 392458) (-264 "ELFUTS.spad" 391289 391308 391900 391905) (-263 "ELEMFUN.spad" 390978 390986 391279 391284) (-262 "ELEMFUN.spad" 390665 390675 390968 390973) (-261 "ELAGG.spad" 388596 388606 390633 390660) (-260 "ELAGG.spad" 386476 386488 388515 388520) (-259 "ELABEXPR.spad" 385407 385415 386466 386471) (-258 "EFUPXS.spad" 382183 382213 385363 385368) (-257 "EFULS.spad" 379019 379042 382139 382144) (-256 "EFSTRUC.spad" 376974 376990 379009 379014) (-255 "EF.spad" 371740 371756 376964 376969) (-254 "EAB.spad" 370016 370024 371730 371735) (-253 "E04UCFA.spad" 369552 369560 370006 370011) (-252 "E04NAFA.spad" 369129 369137 369542 369547) (-251 "E04MBFA.spad" 368709 368717 369119 369124) (-250 "E04JAFA.spad" 368245 368253 368699 368704) (-249 "E04GCFA.spad" 367781 367789 368235 368240) (-248 "E04FDFA.spad" 367317 367325 367771 367776) (-247 "E04DGFA.spad" 366853 366861 367307 367312) (-246 "E04AGNT.spad" 362695 362703 366843 366848) (-245 "DVARCAT.spad" 359380 359390 362685 362690) (-244 "DVARCAT.spad" 356063 356075 359370 359375) (-243 "DSMP.spad" 353497 353511 353802 353929) (-242 "DROPT.spad" 347442 347450 353487 353492) (-241 "DROPT1.spad" 347105 347115 347432 347437) (-240 "DROPT0.spad" 341932 341940 347095 347100) (-239 "DRAWPT.spad" 340087 340095 341922 341927) (-238 "DRAW.spad" 332687 332700 340077 340082) (-237 "DRAWHACK.spad" 331995 332005 332677 332682) (-236 "DRAWCX.spad" 329437 329445 331985 331990) (-235 "DRAWCURV.spad" 328974 328989 329427 329432) (-234 "DRAWCFUN.spad" 318146 318154 328964 328969) (-233 "DQAGG.spad" 316302 316312 318102 318141) (-232 "DPOLCAT.spad" 311643 311659 316170 316297) (-231 "DPOLCAT.spad" 307070 307088 311599 311604) (-230 "DPMO.spad" 301057 301073 301195 301491) (-229 "DPMM.spad" 295057 295075 295182 295478) (-228 "DOMAIN.spad" 294328 294336 295047 295052) (-227 "DMP.spad" 291553 291568 292125 292252) (-226 "DLP.spad" 290901 290911 291543 291548) (-225 "DLIST.spad" 289313 289323 290084 290111) (-224 "DLAGG.spad" 287714 287724 289293 289308) (-223 "DIVRING.spad" 287161 287169 287658 287709) (-222 "DIVRING.spad" 286652 286662 287151 287156) (-221 "DISPLAY.spad" 284832 284840 286642 286647) (-220 "DIRPROD.spad" 276091 276107 276731 276860) (-219 "DIRPROD2.spad" 274899 274917 276081 276086) (-218 "DIRPCAT.spad" 273831 273847 274753 274894) (-217 "DIRPCAT.spad" 272503 272521 273427 273432) (-216 "DIOSP.spad" 271328 271336 272493 272498) (-215 "DIOPS.spad" 270300 270310 271296 271323) (-214 "DIOPS.spad" 269258 269270 270256 270261) (-213 "DIFRING.spad" 268550 268558 269238 269253) (-212 "DIFRING.spad" 267850 267860 268540 268545) (-211 "DIFEXT.spad" 267009 267019 267830 267845) (-210 "DIFEXT.spad" 266085 266097 266908 266913) (-209 "DIAGG.spad" 265703 265713 266053 266080) (-208 "DIAGG.spad" 265341 265353 265693 265698) (-207 "DHMATRIX.spad" 263645 263655 264798 264825) (-206 "DFSFUN.spad" 257053 257061 263635 263640) (-205 "DFLOAT.spad" 253576 253584 256943 257048) (-204 "DFINTTLS.spad" 251785 251801 253566 253571) (-203 "DERHAM.spad" 249695 249727 251765 251780) (-202 "DEQUEUE.spad" 249013 249023 249302 249329) (-201 "DEGRED.spad" 248628 248642 249003 249008) (-200 "DEFINTRF.spad" 246153 246163 248618 248623) (-199 "DEFINTEF.spad" 244649 244665 246143 246148) (-198 "DECIMAL.spad" 242533 242541 243119 243212) (-197 "DDFACT.spad" 240332 240349 242523 242528) (-196 "DBLRESP.spad" 239930 239954 240322 240327) (-195 "DBASE.spad" 238502 238512 239920 239925) (-194 "D03FAFA.spad" 238330 238338 238492 238497) (-193 "D03EEFA.spad" 238150 238158 238320 238325) (-192 "D03AGNT.spad" 237230 237238 238140 238145) (-191 "D02EJFA.spad" 236692 236700 237220 237225) (-190 "D02CJFA.spad" 236170 236178 236682 236687) (-189 "D02BHFA.spad" 235660 235668 236160 236165) (-188 "D02BBFA.spad" 235150 235158 235650 235655) (-187 "D02AGNT.spad" 229954 229962 235140 235145) (-186 "D01WGTS.spad" 228273 228281 229944 229949) (-185 "D01TRNS.spad" 228250 228258 228263 228268) (-184 "D01GBFA.spad" 227772 227780 228240 228245) (-183 "D01FCFA.spad" 227294 227302 227762 227767) (-182 "D01ASFA.spad" 226762 226770 227284 227289) (-181 "D01AQFA.spad" 226208 226216 226752 226757) (-180 "D01APFA.spad" 225632 225640 226198 226203) (-179 "D01ANFA.spad" 225126 225134 225622 225627) (-178 "D01AMFA.spad" 224636 224644 225116 225121) (-177 "D01ALFA.spad" 224176 224184 224626 224631) (-176 "D01AKFA.spad" 223702 223710 224166 224171) (-175 "D01AJFA.spad" 223225 223233 223692 223697) (-174 "D01AGNT.spad" 219284 219292 223215 223220) (-173 "CYCLOTOM.spad" 218790 218798 219274 219279) (-172 "CYCLES.spad" 215622 215630 218780 218785) (-171 "CVMP.spad" 215039 215049 215612 215617) (-170 "CTRIGMNP.spad" 213529 213545 215029 215034) (-169 "CTORCALL.spad" 213117 213125 213519 213524) (-168 "CSTTOOLS.spad" 212360 212373 213107 213112) (-167 "CRFP.spad" 206064 206077 212350 212355) (-166 "CRAPACK.spad" 205107 205117 206054 206059) (-165 "CPMATCH.spad" 204607 204622 205032 205037) (-164 "CPIMA.spad" 204312 204331 204597 204602) (-163 "COORDSYS.spad" 199205 199215 204302 204307) (-162 "CONTOUR.spad" 198607 198615 199195 199200) (-161 "CONTFRAC.spad" 194219 194229 198509 198602) (-160 "COMRING.spad" 193893 193901 194157 194214) (-159 "COMPPROP.spad" 193407 193415 193883 193888) (-158 "COMPLPAT.spad" 193174 193189 193397 193402) (-157 "COMPLEX.spad" 187207 187217 187451 187712) (-156 "COMPLEX2.spad" 186920 186932 187197 187202) (-155 "COMPFACT.spad" 186522 186536 186910 186915) (-154 "COMPCAT.spad" 184578 184588 186244 186517) (-153 "COMPCAT.spad" 182341 182353 184009 184014) (-152 "COMMUPC.spad" 182087 182105 182331 182336) (-151 "COMMONOP.spad" 181620 181628 182077 182082) (-150 "COMM.spad" 181429 181437 181610 181615) (-149 "COMBOPC.spad" 180334 180342 181419 181424) (-148 "COMBINAT.spad" 179079 179089 180324 180329) (-147 "COMBF.spad" 176447 176463 179069 179074) (-146 "COLOR.spad" 175284 175292 176437 176442) (-145 "CMPLXRT.spad" 174993 175010 175274 175279) (-144 "CLIP.spad" 171085 171093 174983 174988) (-143 "CLIF.spad" 169724 169740 171041 171080) (-142 "CLAGG.spad" 166199 166209 169704 169719) (-141 "CLAGG.spad" 162555 162567 166062 166067) (-140 "CINTSLPE.spad" 161880 161893 162545 162550) (-139 "CHVAR.spad" 159958 159980 161870 161875) (-138 "CHARZ.spad" 159873 159881 159938 159953) (-137 "CHARPOL.spad" 159381 159391 159863 159868) (-136 "CHARNZ.spad" 159134 159142 159361 159376) (-135 "CHAR.spad" 157002 157010 159124 159129) (-134 "CFCAT.spad" 156318 156326 156992 156997) (-133 "CDEN.spad" 155476 155490 156308 156313) (-132 "CCLASS.spad" 153625 153633 154887 154926) (-131 "CATEGORY.spad" 153404 153412 153615 153620) (-130 "CARTEN.spad" 148507 148531 153394 153399) (-129 "CARTEN2.spad" 147893 147920 148497 148502) (-128 "CARD.spad" 145182 145190 147867 147888) (-127 "CACHSET.spad" 144804 144812 145172 145177) (-126 "CABMON.spad" 144357 144365 144794 144799) (-125 "BYTE.spad" 143751 143759 144347 144352) (-124 "BYTEARY.spad" 142826 142834 142920 142947) (-123 "BTREE.spad" 141895 141905 142433 142460) (-122 "BTOURN.spad" 140898 140908 141502 141529) (-121 "BTCAT.spad" 140274 140284 140854 140893) (-120 "BTCAT.spad" 139682 139694 140264 140269) (-119 "BTAGG.spad" 138698 138706 139638 139677) (-118 "BTAGG.spad" 137746 137756 138688 138693) (-117 "BSTREE.spad" 136481 136491 137353 137380) (-116 "BRILL.spad" 134676 134687 136471 136476) (-115 "BRAGG.spad" 133590 133600 134656 134671) (-114 "BRAGG.spad" 132478 132490 133546 133551) (-113 "BPADICRT.spad" 130462 130474 130717 130810) (-112 "BPADIC.spad" 130126 130138 130388 130457) (-111 "BOUNDZRO.spad" 129782 129799 130116 130121) (-110 "BOP.spad" 125246 125254 129772 129777) (-109 "BOP1.spad" 122632 122642 125202 125207) (-108 "BOOLEAN.spad" 121895 121903 122622 122627) (-107 "BMODULE.spad" 121607 121619 121863 121890) (-106 "BITS.spad" 121026 121034 121243 121270) (-105 "BINFILE.spad" 120369 120377 121016 121021) (-104 "BINDING.spad" 119788 119796 120359 120364) (-103 "BINARY.spad" 117681 117689 118258 118351) (-102 "BGAGG.spad" 116866 116876 117649 117676) (-101 "BGAGG.spad" 116071 116083 116856 116861) (-100 "BFUNCT.spad" 115635 115643 116051 116066) (-99 "BEZOUT.spad" 114770 114796 115585 115590) (-98 "BBTREE.spad" 111590 111599 114377 114404) (-97 "BASTYPE.spad" 111263 111270 111580 111585) (-96 "BASTYPE.spad" 110934 110943 111253 111258) (-95 "BALFACT.spad" 110374 110386 110924 110929) (-94 "AUTOMOR.spad" 109821 109830 110354 110369) (-93 "ATTREG.spad" 106540 106547 109573 109816) (-92 "ATTRBUT.spad" 102563 102570 106520 106535) (-91 "ATRIG.spad" 102033 102040 102553 102558) (-90 "ATRIG.spad" 101501 101510 102023 102028) (-89 "ASTACK.spad" 100834 100843 101108 101135) (-88 "ASSOCEQ.spad" 99634 99645 100790 100795) (-87 "ASP9.spad" 98715 98728 99624 99629) (-86 "ASP8.spad" 97758 97771 98705 98710) (-85 "ASP80.spad" 97080 97093 97748 97753) (-84 "ASP7.spad" 96240 96253 97070 97075) (-83 "ASP78.spad" 95691 95704 96230 96235) (-82 "ASP77.spad" 95060 95073 95681 95686) (-81 "ASP74.spad" 94152 94165 95050 95055) (-80 "ASP73.spad" 93423 93436 94142 94147) (-79 "ASP6.spad" 92055 92068 93413 93418) (-78 "ASP55.spad" 90564 90577 92045 92050) (-77 "ASP50.spad" 88381 88394 90554 90559) (-76 "ASP4.spad" 87676 87689 88371 88376) (-75 "ASP49.spad" 86675 86688 87666 87671) (-74 "ASP42.spad" 85082 85121 86665 86670) (-73 "ASP41.spad" 83661 83700 85072 85077) (-72 "ASP35.spad" 82649 82662 83651 83656) (-71 "ASP34.spad" 81950 81963 82639 82644) (-70 "ASP33.spad" 81510 81523 81940 81945) (-69 "ASP31.spad" 80650 80663 81500 81505) (-68 "ASP30.spad" 79542 79555 80640 80645) (-67 "ASP29.spad" 79008 79021 79532 79537) (-66 "ASP28.spad" 70281 70294 78998 79003) (-65 "ASP27.spad" 69178 69191 70271 70276) (-64 "ASP24.spad" 68265 68278 69168 69173) (-63 "ASP20.spad" 67481 67494 68255 68260) (-62 "ASP1.spad" 66862 66875 67471 67476) (-61 "ASP19.spad" 61548 61561 66852 66857) (-60 "ASP12.spad" 60962 60975 61538 61543) (-59 "ASP10.spad" 60233 60246 60952 60957) (-58 "ARRAY2.spad" 59593 59602 59840 59867) (-57 "ARRAY1.spad" 58428 58437 58776 58803) (-56 "ARRAY12.spad" 57097 57108 58418 58423) (-55 "ARR2CAT.spad" 52747 52768 57053 57092) (-54 "ARR2CAT.spad" 48429 48452 52737 52742) (-53 "APPRULE.spad" 47673 47695 48419 48424) (-52 "APPLYORE.spad" 47288 47301 47663 47668) (-51 "ANY.spad" 45630 45637 47278 47283) (-50 "ANY1.spad" 44701 44710 45620 45625) (-49 "ANTISYM.spad" 43140 43156 44681 44696) (-48 "ANON.spad" 42837 42844 43130 43135) (-47 "AN.spad" 41140 41147 42655 42748) (-46 "AMR.spad" 39319 39330 41038 41135) (-45 "AMR.spad" 37335 37348 39056 39061) (-44 "ALIST.spad" 34747 34768 35097 35124) (-43 "ALGSC.spad" 33870 33896 34619 34672) (-42 "ALGPKG.spad" 29579 29590 33826 33831) (-41 "ALGMFACT.spad" 28768 28782 29569 29574) (-40 "ALGMANIP.spad" 26189 26204 28566 28571) (-39 "ALGFF.spad" 24507 24534 24724 24880) (-38 "ALGFACT.spad" 23628 23638 24497 24502) (-37 "ALGEBRA.spad" 23359 23368 23584 23623) (-36 "ALGEBRA.spad" 23122 23133 23349 23354) (-35 "ALAGG.spad" 22620 22641 23078 23117) (-34 "AHYP.spad" 22001 22008 22610 22615) (-33 "AGG.spad" 20300 20307 21981 21996) (-32 "AGG.spad" 18573 18582 20256 20261) (-31 "AF.spad" 16999 17014 18509 18514) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-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 092e9cdf..086bea99 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,14 +1,14 @@ -(142797 . 3419278785) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) ((#0=(-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) #0#) |has| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (-288 (-2 (|:| -3160 |#1|) (|:| -3978 |#2|))))) +(142797 . 3420122817) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) ((#0=(-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) #0#) |has| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (-288 (-2 (|:| -3946 |#1|) (|:| -2511 |#2|))))) (((|#2| |#2|) . T)) ((((-525)) . T)) -((($ $) -3215 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843))) ((|#2| |#2|) . T) ((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525))))) +((($ $) -3309 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843))) ((|#2| |#2|) . T) ((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2|) . T)) -((($) -3215 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843))) ((|#2|) . T) (((-385 (-525))) |has| |#2| (-37 (-385 (-525))))) +((($) -3309 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843))) ((|#2|) . T) (((-385 (-525))) |has| |#2| (-37 (-385 (-525))))) (|has| |#1| (-843)) ((((-797)) . T)) ((((-797)) . T)) @@ -23,28 +23,28 @@ ((((-205)) . T) (((-797)) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) (((|#1|) . T)) -(-3215 (|has| |#1| (-21)) (|has| |#1| (-787))) -((($ $) . 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T)) @@ -54,10 +54,10 @@ (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-517)) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-517))) ((($) . T)) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-789)) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-789)) (|has| |#1| (-1019)))) ((((-501)) |has| |#1| (-567 (-501)))) ((($) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T)) ((($) . T)) @@ -66,59 +66,59 @@ ((((-797)) . T)) ((((-797)) . T)) ((((-385 (-525))) . T) (($) . T)) -((((-385 (-525))) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (((-1164 |#1| |#2| |#3|)) |has| |#1| (-341)) (($) . T) ((|#1|) . T)) +((((-385 (-525))) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (((-1164 |#1| |#2| |#3|)) |has| |#1| (-341)) (($) . T) ((|#1|) . T)) ((((-797)) . 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T)) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-327))) -(-3215 (|has| |#4| (-735)) (|has| |#4| (-787))) -(-3215 (|has| |#4| (-735)) (|has| |#4| (-787))) -(-3215 (|has| |#3| (-735)) (|has| |#3| (-787))) -(-3215 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3309 (|has| |#4| (-735)) (|has| |#4| (-787))) +(-3309 (|has| |#4| (-735)) (|has| |#4| (-787))) +(-3309 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-3309 (|has| |#3| (-735)) (|has| |#3| (-787))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-1019)) @@ -132,21 +132,21 @@ ((((-525)) . T)) ((((-525)) . T)) (((|#1|) . T)) -(-3215 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(-3309 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) (((|#1| (-713)) . T)) (|has| |#2| (-735)) -(-3215 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3309 (|has| |#2| (-735)) (|has| |#2| (-787))) (|has| |#2| (-787)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) ((((-1073) |#1|) . 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T)) (((|#1|) . T)) ((((-385 (-525))) |has| |#1| (-967 (-385 (-525)))) (((-525)) |has| |#1| (-967 (-525))) ((|#1|) . T)) (((|#1|) . T) (((-525)) |has| |#1| (-588 (-525)))) -(((|#2|) . T) (((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -3160 (-1073)) (|:| -3978 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -3946 (-1073)) (|:| -2511 |#1|))) . T)) (|has| |#1| (-517)) (|has| |#1| (-517)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) -(-3215 (|has| |#1| (-789)) (|has| |#1| (-1019))) +(-3309 (|has| |#1| (-789)) (|has| |#1| (-1019))) (((|#1|) . T)) (|has| |#1| (-517)) (|has| |#1| (-517)) @@ -218,11 +218,11 @@ (((|#2|) . T) (($) . T) (((-385 (-525))) . T)) (-12 (|has| |#1| (-1019)) (|has| |#2| (-1019))) ((($) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . 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T) (((-205)) . T) (((-357)) . T) (((-826 (-357))) . T)) ((((-797)) . T)) -(-3215 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-834 (-1090))) (|has| |#1| (-976))) +(-3309 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-834 (-1090))) (|has| |#1| (-976))) (((|#1|) |has| |#1| (-160))) (((|#1| $) |has| |#1| (-265 |#1| |#1|))) ((((-797)) . T)) @@ -256,15 +256,15 @@ (|has| |#1| (-789)) (|has| |#1| (-1019)) (((|#1|) . T)) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-789)) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-789)) (|has| |#1| (-1019)))) ((((-501)) |has| |#1| (-567 (-501)))) ((((-125)) . 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T)) (((|#1| (-903)) . T)) (((#0=(-804 |#1|) $) |has| #0# (-265 #0# #0#))) @@ -273,7 +273,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1066)) -((((-2 (|:| -3160 (-1073)) (|:| -3978 |#1|))) . T)) +((((-2 (|:| -3946 (-1073)) (|:| -2511 |#1|))) . T)) (|has| (-1158 |#1| |#2| |#3| |#4|) (-136)) (|has| (-1158 |#1| |#2| |#3| |#4|) (-138)) (|has| |#1| (-136)) @@ -290,20 +290,20 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-976))) ((((-797)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) ((#0=(-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) #0#) |has| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (-288 (-2 (|:| -3160 |#1|) (|:| -3978 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) ((#0=(-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) #0#) |has| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (-288 (-2 (|:| -3946 |#1|) (|:| -2511 |#2|))))) (((|#1|) . 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T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($ $) -3309 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) ((($) . T)) ((($) . T)) ((($) . T)) -((($) -3215 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3309 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-797)) . T)) ((((-797)) . T)) (|has| (-1157 |#2| |#3| |#4|) (-138)) @@ -314,16 +314,16 @@ ((((-797)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3215 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-834 (-1090))) (|has| |#1| (-976))) +(-3309 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-834 (-1090))) (|has| |#1| (-976))) (((|#1|) . T)) ((((-525) |#1|) . 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T)) @@ -550,12 +550,12 @@ (((|#1| (-713) (-1004)) . T)) ((((-385 (-525))) |has| |#2| (-341)) (($) . T)) (((|#1| (-497 (-1009 (-1090))) (-1009 (-1090))) . T)) -(-3215 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) -(-3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) +(-3309 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) +(-3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) (((|#1|) . T)) -(-3215 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(-3309 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) (|has| |#2| (-735)) -(-3215 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3309 (|has| |#2| (-735)) (|has| |#2| (-787))) (|has| |#1| (-346)) (|has| |#1| (-346)) (|has| |#1| (-346)) @@ -588,63 +588,63 @@ (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1019)))) (((|#2|) . 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T)) ((((-525) (-125)) . T)) ((((-797)) . T)) @@ -660,22 +660,22 @@ (|has| |#1| (-1019)) (((|#2|) . T)) ((((-501)) |has| |#2| (-567 (-501))) (((-826 (-357))) |has| |#2| (-567 (-826 (-357)))) (((-826 (-525))) |has| |#2| (-567 (-826 (-525))))) -(((|#4|) -3215 (|has| |#4| (-160)) (|has| |#4| (-341)))) -(((|#3|) -3215 (|has| |#3| (-160)) (|has| |#3| (-341)))) +(((|#4|) -3309 (|has| |#4| (-160)) (|has| |#4| (-341)))) +(((|#3|) -3309 (|has| |#3| (-160)) (|has| |#3| (-341)))) ((((-797)) . T)) (((|#1|) . T)) -(-3215 (|has| |#2| (-429)) (|has| |#2| (-843))) -(-3215 (|has| |#1| (-429)) (|has| |#1| (-843))) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-843))) +(-3309 (|has| |#2| (-429)) (|has| |#2| (-843))) +(-3309 (|has| |#1| (-429)) (|has| |#1| (-843))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-843))) ((($ $) . T) ((#0=(-1090) $) |has| |#1| (-213)) ((#0# |#1|) |has| |#1| (-213)) ((#1=(-760 (-1090)) |#1|) . T) ((#1# $) . 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T)) (|has| (-385 |#2|) (-138)) (|has| (-385 |#2|) (-136)) @@ -688,22 +688,22 @@ (|has| |#1| (-517)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) ((((-797)) . T)) -((((-2 (|:| -3160 (-1073)) (|:| -3978 |#1|))) . T)) +((((-2 (|:| -3946 (-1073)) (|:| -2511 |#1|))) . T)) (|has| |#1| (-37 (-385 (-525)))) -((((-366) (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|))) . T)) +((((-366) (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|))) . T)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#2| (-1066)) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-517))) (((|#1|) . T)) ((((-366) (-1073)) . T)) (|has| |#1| (-517)) ((((-112 |#1|)) . T)) ((((-125)) . T)) ((((-525) |#1|) . T)) -(-3215 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) +(-3309 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) (((|#2|) . T)) ((((-797)) . T)) ((((-761 |#1|)) . T)) @@ -716,7 +716,7 @@ (((|#1|) |has| |#1| (-160))) ((((-797)) . T)) ((((-501)) |has| |#1| (-567 (-501)))) -(-3215 (|has| |#1| (-789)) (|has| |#1| (-1019))) +(-3309 (|has| |#1| (-789)) (|has| |#1| (-1019))) (((|#2|) |has| |#2| (-288 |#2|))) (((#0=(-525) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -726,7 +726,7 @@ (((#0=(-525) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) ((($) . T) (((-525)) . T) (((-385 (-525))) . T)) (|has| |#2| (-346)) -(-3215 (|has| |#1| (-789)) (|has| |#1| (-1019))) +(-3309 (|has| |#1| (-789)) (|has| |#1| (-1019))) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) @@ -737,9 +737,9 @@ ((((-1088 |#1| |#2| |#3|) $) -12 (|has| (-1088 |#1| |#2| |#3|) (-265 (-1088 |#1| |#2| |#3|) (-1088 |#1| |#2| |#3|))) (|has| |#1| (-341))) (($ $) . T)) ((((-797)) . T)) ((((-797)) . T)) -((($) . T) (((-385 (-525))) -3215 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) . T) (((-385 (-525))) -3309 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) ((((-501)) |has| |#1| (-567 (-501)))) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) ((($ $) . T)) ((($ $) . T)) ((((-797)) . T)) @@ -749,12 +749,12 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -3215 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3309 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-385 (-525))) . 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T) (((-385 (-525))) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) +((($) . T) (((-385 (-525))) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) (|has| |#1| (-770)) ((((-385 (-525))) |has| |#1| (-967 (-385 (-525)))) (((-525)) |has| |#1| (-967 (-525))) ((|#1|) . T)) (|has| |#1| (-1019)) @@ -819,8 +819,8 @@ (((|#3|) |has| |#3| (-1019))) (|has| |#3| (-346)) (((|#1|) . T) (((-797)) . T)) -((((-385 (-525))) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3215 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1164 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) -(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3215 (|has| |#1| (-341)) (|has| |#1| (-517)))) +((((-385 (-525))) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3309 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1164 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) +(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3309 (|has| |#1| (-341)) (|has| |#1| (-517)))) ((((-797)) . T)) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2|) . T)) @@ -830,30 +830,30 @@ (((|#1|) . T)) (((|#1|) |has| |#1| (-160))) ((((-385 (-525))) . T) (((-525)) . T)) -((($ $) -3215 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) -((($) -3215 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($ $) -3309 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($) -3309 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019)))) ((((-135)) . T)) (((|#1|) . T)) ((((-135)) . T)) -((($) -3215 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) ((|#2|) -3215 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-976)))) +((($) -3309 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) ((|#2|) -3309 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-976)))) ((((-135)) . T)) (((|#1| |#2| |#3|) . T)) -(-3215 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-976))) +(-3309 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-976))) (|has| $ (-138)) (|has| $ (-138)) (|has| |#1| (-1019)) ((((-797)) . T)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-976)) (|has| |#1| (-1031))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-976)) (|has| |#1| (-1031))) ((($ $) |has| |#1| (-265 $ $)) ((|#1| $) |has| |#1| (-265 |#1| |#1|))) (((|#1| (-385 (-525))) . T)) (((|#1|) . T)) ((((-1090)) . T)) (|has| |#1| (-517)) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-517)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) @@ -864,7 +864,7 @@ (|has| |#1| (-138)) (|has| |#1| (-136)) (|has| |#4| (-787)) -(((|#2| (-220 (-1696 |#1|) (-713)) (-799 |#1|)) . T)) +(((|#2| (-220 (-4140 |#1|) (-713)) (-799 |#1|)) . T)) (|has| |#3| (-787)) (((|#1| (-497 |#3|) |#3|) . T)) (|has| |#1| (-138)) @@ -878,21 +878,21 @@ (|has| |#1| (-136)) ((((-385 (-525))) |has| |#2| (-341)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) -(-3215 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843))) -(-3215 (|has| |#1| (-327)) (|has| |#1| (-346))) +(-3309 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843))) +(-3309 (|has| |#1| (-327)) (|has| |#1| (-346))) ((((-1057 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-160)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-213)) (|has| |#2| (-976))) -(((|#2|) . T) (((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) -(-3215 (|has| |#3| (-735)) (|has| |#3| (-787))) -(-3215 (|has| |#3| (-735)) (|has| |#3| (-787))) +(((|#2|) . T) (((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) +(-3309 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-3309 (|has| |#3| (-735)) (|has| |#3| (-787))) ((((-797)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) . T) (($) . T)) ((((-641)) . T)) -(-3215 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(-3309 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) (|has| |#1| (-517)) (((|#1|) . T)) (((|#1|) . T)) @@ -914,10 +914,10 @@ (((|#1| (-385 (-525))) . T)) (((|#3|) . T) (((-565 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) ((($ $) . T) ((|#2| $) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((#0=(-1088 |#1| |#2| |#3|) #0#) -12 (|has| (-1088 |#1| |#2| |#3|) (-288 (-1088 |#1| |#2| |#3|))) (|has| |#1| (-341))) (((-1090) #0#) -12 (|has| (-1088 |#1| |#2| |#3|) (-486 (-1090) (-1088 |#1| |#2| |#3|))) (|has| |#1| (-341)))) @@ -925,8 +925,8 @@ ((((-797)) . T)) ((((-797)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) (((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) |has| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (-288 (-2 (|:| -3160 |#1|) (|:| -3978 |#2|))))) -(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019))) (((-2 (|:| -3160 (-1073)) (|:| -3978 |#1|))) |has| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (-288 (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) (((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) |has| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (-288 (-2 (|:| -3946 |#1|) (|:| -2511 |#2|))))) +(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019))) (((-2 (|:| -3946 (-1073)) (|:| -2511 |#1|))) |has| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (-288 (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|))))) ((((-797)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -937,10 +937,10 @@ ((($ $) . T) ((#0=(-799 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-770)) (|has| |#1| (-1019)) -(((|#2| |#2|) -3215 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-976))) (($ $) |has| |#2| (-160))) -(((|#2|) -3215 (|has| |#2| (-160)) (|has| |#2| (-341)))) -((((-525) (-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -3215 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-976))) (($) |has| |#2| (-160))) +(((|#2| |#2|) -3309 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-976))) (($ $) |has| |#2| (-160))) +(((|#2|) -3309 (|has| |#2| (-160)) (|has| |#2| (-341)))) +((((-525) (-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -3309 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-976))) (($) |has| |#2| (-160))) ((((-713)) . T)) ((((-525)) . T)) (|has| |#1| (-517)) @@ -953,29 +953,29 @@ ((((-112 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-138)) -(-3215 (|has| |#1| (-160)) (|has| |#1| (-517))) -(-3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3215 (|has| |#1| (-160)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-160)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-160)) (|has| |#1| (-517))) ((((-826 (-525))) . T) (((-826 (-357))) . T) (((-501)) . T) (((-1090)) . T)) ((((-797)) . T)) -(-3215 (|has| |#1| (-789)) (|has| |#1| (-1019))) +(-3309 (|has| |#1| (-789)) (|has| |#1| (-1019))) ((($) . T)) ((((-797)) . 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T)) -(-3215 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976)) (|has| |#2| (-1019))) +(-3309 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976)) (|has| |#2| (-1019))) (-12 (|has| |#3| (-213)) (|has| |#3| (-976))) (|has| |#2| (-1066)) -(((#0=(-51)) . T) (((-2 (|:| -3160 (-1090)) (|:| -3978 #0#))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -3946 (-1090)) (|:| -2511 #0#))) . T)) (((|#1| |#2|) . T)) -(-3215 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-976))) +(-3309 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-976))) (((|#1| (-525) (-1004)) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) (((|#1| (-385 (-525)) (-1004)) . T)) -((($) -3215 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327)) (|has| |#1| (-517))) (((-385 (-525))) -3215 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) -3309 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327)) (|has| |#1| (-517))) (((-385 (-525))) -3309 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) ((((-525) |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) @@ -983,37 +983,37 @@ (-12 (|has| |#1| (-346)) (|has| |#2| (-346))) ((((-797)) . T)) ((((-1090) |#1|) |has| |#1| (-486 (-1090) |#1|)) ((|#1| |#1|) |has| |#1| (-288 |#1|))) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-346))) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-346))) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-346))) (((|#1|) . 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T)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3215 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3309 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843)))) ((($) . T)) ((((-797)) . T)) (((|#1|) . T)) ((((-804 |#1|)) . T) (($) . T) (((-385 (-525))) . T)) ((((-797)) . T)) -(((|#3| |#3|) -3215 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-976))) (($ $) |has| |#3| (-160))) +(((|#3| |#3|) -3309 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-976))) (($ $) |has| |#3| (-160))) (|has| |#1| (-952)) ((((-797)) . T)) -(((|#3|) -3215 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-976))) (($) |has| |#3| (-160))) +(((|#3|) -3309 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-976))) (($) |has| |#3| (-160))) ((((-525) (-108)) . T)) (((|#1|) |has| |#1| (-288 |#1|))) (|has| |#1| (-346)) @@ -1021,31 +1021,31 @@ (|has| |#1| (-346)) ((((-1090) $) |has| |#1| (-486 (-1090) $)) (($ $) |has| |#1| (-288 $)) ((|#1| |#1|) |has| |#1| (-288 |#1|)) (((-1090) |#1|) |has| |#1| (-486 (-1090) |#1|))) ((((-1090)) |has| |#1| (-834 (-1090)))) -(-3215 (-12 (|has| |#1| (-213)) (|has| |#1| (-341))) (|has| |#1| (-327))) +(-3309 (-12 (|has| |#1| (-213)) (|has| |#1| (-341))) (|has| |#1| (-327))) ((((-366) (-1037)) . T)) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-366) |#1|) . T)) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-1019)) ((((-797)) . T)) ((((-797)) . T)) ((((-844 |#1|)) . T)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3215 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843)))) -((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) -3215 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3309 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843)))) +((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) -3309 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843)))) (((|#1| |#2|) . T)) ((($) . T)) (((|#1| |#1|) . T)) (((#0=(-804 |#1|)) |has| #0# (-288 #0#))) (((|#1| |#2|) . T)) -(-3215 (|has| |#2| (-735)) (|has| |#2| (-787))) -(-3215 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3309 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3309 (|has| |#2| (-735)) (|has| |#2| (-787))) (-12 (|has| |#1| (-735)) (|has| |#2| (-735))) (((|#1|) . T)) (-12 (|has| |#1| (-735)) (|has| |#2| (-735))) -(-3215 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(-3309 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) (|has| |#1| (-1112)) (((#0=(-525) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) ((((-385 (-525))) . T) (($) . T)) @@ -1056,8 +1056,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-385 (-525)) #0#) . T)) (|has| |#1| (-341)) ((((-525)) . T) (((-385 (-525))) . T) (($) . T)) -((($ $) . T) ((#0=(-385 (-525)) #0#) -3215 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1| |#1|) . T)) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +((($ $) . T) ((#0=(-385 (-525)) #0#) -3309 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1| |#1|) . T)) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) (((|#1|) . T) (($) . T) (((-385 (-525))) . T)) ((((-797)) . T)) ((((-797)) . T)) @@ -1072,14 +1072,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-787)) (|has| |#1| (-787)) -((($) . T) (((-385 (-525))) -3215 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) -(-3215 (|has| |#1| (-160)) (|has| |#1| (-517))) -(((#0=(-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) #0#) |has| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (-288 (-2 (|:| -3160 (-1090)) (|:| -3978 (-51)))))) +((($) . T) (((-385 (-525))) -3309 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +(-3309 (|has| |#1| (-160)) (|has| |#1| (-517))) +(((#0=(-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) #0#) |has| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (-288 (-2 (|:| -3946 (-1090)) (|:| -2511 (-51)))))) ((($) . T)) (|has| |#2| (-789)) ((($) . T)) (((|#2|) |has| |#2| (-1019))) -((((-797)) -3215 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-566 (-797))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976)) (|has| |#2| (-1019))) (((-1172 |#2|)) . T)) +((((-797)) -3309 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-566 (-797))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976)) (|has| |#2| (-1019))) (((-1172 |#2|)) . T)) (|has| |#1| (-789)) (|has| |#1| (-789)) ((((-1073) (-51)) . T)) @@ -1087,10 +1087,10 @@ ((((-797)) . T)) ((((-525)) |has| #0=(-385 |#2|) (-588 (-525))) ((#0#) . T)) ((((-525) (-135)) . T)) -((((-525) (-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T) ((|#1| |#2|) . T)) +((((-525) (-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T) ((|#1| |#2|) . T)) ((((-385 (-525))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) ((((-797)) . T)) ((((-844 |#1|)) . T)) (|has| |#1| (-341)) @@ -1115,31 +1115,31 @@ ((($) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-160))) -((((-525) (-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T) ((|#1| |#2|) . T)) +((((-525) (-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) (((|#3|) . T)) (((|#1|) |has| |#1| (-160))) -((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) -3215 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843)))) -((($) -3215 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) -3309 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843)))) +((($) -3309 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1|) . T)) (((|#1|) . T)) ((((-501)) |has| |#1| (-567 (-501))) (((-826 (-357))) |has| |#1| (-567 (-826 (-357)))) (((-826 (-525))) |has| |#1| (-567 (-826 (-525))))) ((((-797)) . T)) -(((|#2|) . T) (((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) (|has| |#2| (-787)) (-12 (|has| |#2| (-213)) (|has| |#2| (-976))) (|has| |#1| (-517)) (|has| |#1| (-1066)) ((((-1073) |#1|) . T)) -(-3215 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) -(((#0=(-385 (-525)) #0#) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($ $) -3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1| |#1|) . T)) +(-3309 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(((#0=(-385 (-525)) #0#) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($ $) -3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1| |#1|) . T)) ((((-385 (-525))) |has| |#1| (-967 (-525))) (((-525)) |has| |#1| (-967 (-525))) (((-1090)) |has| |#1| (-967 (-1090))) ((|#1|) . T)) ((((-525) |#2|) . T)) ((((-385 (-525))) |has| |#1| (-967 (-385 (-525)))) (((-525)) |has| |#1| (-967 (-525))) ((|#1|) . T)) ((((-525)) |has| |#1| (-820 (-525))) (((-357)) |has| |#1| (-820 (-357)))) -((((-385 (-525))) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1|) . T)) +((((-385 (-525))) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1|) . T)) (((|#1|) . T)) ((((-592 |#4|)) . T) (((-797)) . T)) ((((-501)) |has| |#4| (-567 (-501)))) @@ -1152,17 +1152,17 @@ (((|#1|) . T)) (((|#2|) . T)) ((((-1090)) |has| (-385 |#2|) (-834 (-1090)))) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) ((#0=(-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) #0#) |has| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (-288 (-2 (|:| -3160 |#1|) (|:| -3978 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) ((#0=(-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) #0#) |has| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (-288 (-2 (|:| -3946 |#1|) (|:| -2511 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-797)) -3215 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-566 (-797))) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-976)) (|has| |#3| (-1019))) (((-1172 |#3|)) . T)) +((((-797)) -3309 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-566 (-797))) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-976)) (|has| |#3| (-1019))) (((-1172 |#3|)) . T)) ((((-525) |#2|) . T)) -(-3215 (|has| |#1| (-789)) (|has| |#1| (-1019))) -(((|#2| |#2|) -3215 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-976))) (($ $) |has| |#2| (-160))) +(-3309 (|has| |#1| (-789)) (|has| |#1| (-1019))) +(((|#2| |#2|) -3309 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-976))) (($ $) |has| |#2| (-160))) ((((-797)) . T)) ((((-797)) . T)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T) ((|#2|) . T)) ((((-797)) . T)) ((((-797)) . T)) ((((-1073) (-1090) (-525) (-205) (-797)) . T)) @@ -1197,8 +1197,8 @@ (|has| |#1| (-37 (-385 (-525)))) ((((-797)) . T)) ((((-501)) |has| |#1| (-567 (-501)))) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) -(((|#2|) -3215 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-976))) (($) |has| |#2| (-160))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +(((|#2|) -3309 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-976))) (($) |has| |#2| (-160))) (|has| $ (-138)) ((((-385 |#2|)) . T)) ((((-385 (-525))) |has| #0=(-385 |#2|) (-967 (-385 (-525)))) (((-525)) |has| #0# (-967 (-525))) ((#0#) . T)) @@ -1209,11 +1209,11 @@ (((|#3|) |has| |#3| (-160))) (|has| |#1| (-138)) (|has| |#1| (-136)) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) (((|#1|) . T)) (((|#2|) . T)) @@ -1244,7 +1244,7 @@ ((((-930 |#1|)) . T) ((|#1|) . T)) ((((-797)) . T)) ((((-797)) . T)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) ((((-385 (-525))) . T) (((-385 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1086 |#1|)) . T)) ((((-525)) . T) (($) . T) (((-385 (-525))) . T)) @@ -1252,9 +1252,9 @@ (|has| |#1| (-789)) (((|#2|) . T)) ((((-525)) . T) (($) . T) (((-385 (-525))) . T)) -((((-2 (|:| -3160 (-1073)) (|:| -3978 |#1|))) . T)) +((((-2 (|:| -3946 (-1073)) (|:| -2511 |#1|))) . T)) ((((-525) |#2|) . T)) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) (((|#2|) . T)) ((((-525) |#3|) . T)) (((|#2|) . T)) @@ -1269,7 +1269,7 @@ (((|#3|) -12 (|has| |#3| (-288 |#3|)) (|has| |#3| (-1019)))) (((|#2|) . T)) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) ((#0=(-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) #0#) |has| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (-288 (-2 (|:| -3160 |#1|) (|:| -3978 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) ((#0=(-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) #0#) |has| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (-288 (-2 (|:| -3946 |#1|) (|:| -2511 |#2|))))) (((|#2| |#2|) . T)) (|has| |#2| (-341)) (((|#2|) . T) (((-525)) |has| |#2| (-967 (-525))) (((-385 (-525))) |has| |#2| (-967 (-385 (-525))))) @@ -1299,19 +1299,19 @@ (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) (((|#1| |#2|) . T)) ((((-525) (-135)) . T)) -(((#0=(-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) #0#) |has| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (-288 (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019)))) -((($) -3215 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +(((#0=(-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) #0#) |has| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (-288 (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019)))) +((($) -3309 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (|has| |#1| (-789)) (((|#2| (-713) (-1004)) . T)) (((|#1| |#2|) . T)) -(-3215 (|has| |#1| (-160)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-160)) (|has| |#1| (-517))) (|has| |#1| (-733)) (((|#1|) |has| |#1| (-160))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-3215 (|has| |#1| (-138)) (-12 (|has| |#1| (-341)) (|has| |#2| (-138)))) -(-3215 (|has| |#1| (-136)) (-12 (|has| |#1| (-341)) (|has| |#2| (-136)))) +(-3309 (|has| |#1| (-138)) (-12 (|has| |#1| (-341)) (|has| |#2| (-138)))) +(-3309 (|has| |#1| (-136)) (-12 (|has| |#1| (-341)) (|has| |#2| (-136)))) (((|#4|) . T)) (|has| |#1| (-136)) ((((-1073) |#1|) . T)) @@ -1324,10 +1324,10 @@ (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) (((|#3|) . T)) ((((-1164 |#1| |#2| |#3|)) |has| |#1| (-341))) -(-3215 (|has| |#1| (-789)) (|has| |#1| (-1019))) +(-3309 (|has| |#1| (-789)) (|has| |#1| (-1019))) (((|#1|) . T)) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019))) (((-891 |#1|)) . T)) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019))) (((-891 |#1|)) . T)) (|has| |#1| (-787)) (|has| |#1| (-787)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) @@ -1340,8 +1340,8 @@ ((($) . T)) ((((-366) (-1073)) . T)) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) -((((-797)) -3215 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-566 (-797))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976)) (|has| |#2| (-1019))) (((-1172 |#2|)) . T)) -(((#0=(-51)) . T) (((-2 (|:| -3160 (-1073)) (|:| -3978 #0#))) . T)) +((((-797)) -3309 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-566 (-797))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976)) (|has| |#2| (-1019))) (((-1172 |#2|)) . T)) +(((#0=(-51)) . T) (((-2 (|:| -3946 (-1073)) (|:| -2511 #0#))) . T)) (((|#1|) . T)) ((((-797)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019)))) @@ -1349,7 +1349,7 @@ (|has| |#2| (-136)) (|has| |#2| (-138)) (|has| |#1| (-450)) -(-3215 (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-834 (-1090))) (|has| |#1| (-976))) +(-3309 (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-834 (-1090))) (|has| |#1| (-976))) (|has| |#1| (-341)) ((((-797)) . T)) (|has| |#1| (-37 (-385 (-525)))) @@ -1358,8 +1358,8 @@ (|has| |#1| (-787)) (|has| |#1| (-787)) ((((-797)) . T)) -((((-385 (-525))) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3215 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1164 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) -(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3215 (|has| |#1| (-341)) (|has| |#1| (-517)))) +((((-385 (-525))) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3309 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1164 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) +(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3309 (|has| |#1| (-341)) (|has| |#1| (-517)))) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1| |#2|) . T)) ((((-1090)) |has| |#1| (-834 (-1090)))) @@ -1367,7 +1367,7 @@ ((((-797)) . T)) ((((-797)) . T)) (|has| |#1| (-1019)) -(((|#2| (-458 (-1696 |#1|) (-713)) (-799 |#1|)) . T)) +(((|#2| (-458 (-4140 |#1|) (-713)) (-799 |#1|)) . T)) ((((-385 (-525))) . #0=(|has| |#2| (-341))) (($) . #0#)) (((|#1| (-497 (-1090)) (-1090)) . T)) (((|#1|) . T)) @@ -1387,16 +1387,16 @@ (|has| |#1| (-138)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3160 (-1073)) (|:| -3978 |#1|))) . T)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) -((((-2 (|:| -3160 (-1090)) (|:| -3978 (-51)))) . T)) +(((|#1|) . T) (((-2 (|:| -3946 (-1073)) (|:| -2511 |#1|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3946 (-1090)) (|:| -2511 (-51)))) . T)) ((((-1088 |#1| |#2| |#3|)) |has| |#1| (-341))) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) ((((-1090) (-51)) . T)) ((($ $) . T)) (((|#1| (-525)) . T)) ((((-844 |#1|)) . T)) -(((|#1|) -3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-976))) (($) -3215 (|has| |#1| (-834 (-1090))) (|has| |#1| (-976)))) +(((|#1|) -3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-976))) (($) -3309 (|has| |#1| (-834 (-1090))) (|has| |#1| (-976)))) (((|#1|) . T) (((-525)) |has| |#1| (-967 (-525))) (((-385 (-525))) |has| |#1| (-967 (-385 (-525))))) (|has| |#1| (-789)) (|has| |#1| (-789)) @@ -1411,13 +1411,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1019)))) (((|#1|) |has| |#1| (-160))) (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1019)))) -(((|#3|) -3215 (|has| |#3| (-160)) (|has| |#3| (-341)))) +(((|#3|) -3309 (|has| |#3| (-160)) (|has| |#3| (-341)))) (|has| |#2| (-789)) (|has| |#1| (-789)) -(-3215 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-843))) +(-3309 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-843))) ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) ((((-525) |#2|) . T)) -(((|#2|) -3215 (|has| |#2| (-160)) (|has| |#2| (-341)))) +(((|#2|) -3309 (|has| |#2| (-160)) (|has| |#2| (-341)))) (|has| |#1| (-327)) (((|#3| |#3|) -12 (|has| |#3| (-288 |#3|)) (|has| |#3| (-1019)))) ((($) . T) (((-385 (-525))) . T)) @@ -1425,7 +1425,7 @@ (|has| |#1| (-762)) (|has| |#1| (-762)) (((|#1|) . T)) -(-3215 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3309 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-787)) (|has| |#1| (-787)) (|has| |#1| (-787)) @@ -1434,13 +1434,13 @@ ((((-525)) . T) (($) . T) (((-385 (-525))) . T)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-37 (-385 (-525)))) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) ((((-1090)) |has| |#1| (-834 (-1090))) (((-1004)) . T)) (((|#1|) . T)) (|has| |#1| (-787)) -(((#0=(-2 (|:| -3160 (-1073)) (|:| -3978 (-51))) #0#) |has| (-2 (|:| -3160 (-1073)) (|:| -3978 (-51))) (-288 (-2 (|:| -3160 (-1073)) (|:| -3978 (-51)))))) +(((#0=(-2 (|:| -3946 (-1073)) (|:| -2511 (-51))) #0#) |has| (-2 (|:| -3946 (-1073)) (|:| -2511 (-51))) (-288 (-2 (|:| -3946 (-1073)) (|:| -2511 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) (|has| |#1| (-1019)) (((|#1|) . T)) @@ -1459,7 +1459,7 @@ (((|#1|) . T)) ((((-135)) . T)) (((|#2|) |has| |#2| (-160))) -(-3215 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976)) (|has| |#2| (-1019))) +(-3309 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976)) (|has| |#2| (-1019))) (((|#1|) . T)) (|has| |#1| (-136)) (|has| |#1| (-138)) @@ -1481,32 +1481,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019))) ((#0=(-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) #0#) |has| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (-288 (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|))))) -(-3215 (|has| |#2| (-429)) (|has| |#2| (-843))) -(-3215 (|has| |#1| (-429)) (|has| |#1| (-843))) +(((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019))) ((#0=(-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) #0#) |has| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (-288 (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|))))) +(-3309 (|has| |#2| (-429)) (|has| |#2| (-843))) +(-3309 (|has| |#1| (-429)) (|has| |#1| (-843))) (((|#1|) . T) (($) . T)) (((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019)))) (((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(((|#3|) -3215 (|has| |#3| (-160)) (|has| |#3| (-341)))) +(((|#3|) -3309 (|has| |#3| (-160)) (|has| |#3| (-341)))) (|has| |#1| (-789)) (|has| |#1| (-517)) ((((-538 |#1|)) . T)) ((($) . T)) (((|#2|) . T)) -(-3215 (-12 (|has| |#1| (-341)) (|has| |#2| (-762))) (-12 (|has| |#1| (-341)) (|has| |#2| (-789)))) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (-12 (|has| |#1| (-341)) (|has| |#2| (-762))) (-12 (|has| |#1| (-341)) (|has| |#2| (-789)))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-517))) ((((-844 |#1|)) . T)) (((|#1| (-469 |#1| |#3|) (-469 |#1| |#2|)) . T)) (((|#1| |#4| |#5|) . T)) (((|#1| (-713)) . T)) ((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) |has| |#1| (-517))) -((((-385 (-525))) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3215 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1088 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) -(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3215 (|has| |#1| (-341)) (|has| |#1| (-517)))) +((((-385 (-525))) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3309 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1088 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) +(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3309 (|has| |#1| (-341)) (|has| |#1| (-517)))) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) -((((-2 (|:| -3160 (-1090)) (|:| -3978 (-51)))) . T)) +((((-2 (|:| -3946 (-1090)) (|:| -2511 (-51)))) . T)) ((((-385 |#2|)) . T) (((-385 (-525))) . T) (($) . T)) ((((-617 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1514,17 +1514,17 @@ ((((-797)) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) ((((-797)) . T)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3215 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3309 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843)))) ((((-797)) . T)) ((((-797)) . T)) ((((-797)) . T)) (((|#2|) . T)) -(-3215 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-976)) (|has| |#3| (-1019))) -(-3215 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(-3309 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-976)) (|has| |#3| (-1019))) +(-3309 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) ((((-385 (-525))) |has| |#1| (-967 (-385 (-525)))) (((-525)) |has| |#1| (-967 (-525))) ((|#1|) . T)) (|has| |#1| (-1112)) (|has| |#1| (-1112)) -(-3215 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976)) (|has| |#2| (-1019))) +(-3309 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976)) (|has| |#2| (-1019))) (|has| |#1| (-1112)) (|has| |#1| (-1112)) (((|#3| |#3|) . T)) @@ -1537,43 +1537,43 @@ (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) ((((-1073) (-51)) . T)) (|has| |#1| (-1019)) -(-3215 (|has| |#2| (-762)) (|has| |#2| (-789))) +(-3309 (|has| |#2| (-762)) (|has| |#2| (-789))) (((|#1|) . T)) -((($) -3215 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -3215 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) -3309 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -3309 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . 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T)) (((|#1|) . T)) ((((-525)) . T)) ((((-108)) . T)) -(-3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-37 (-385 (-525)))) (((|#1| (-525)) . T)) ((($) . T)) @@ -1595,7 +1595,7 @@ (((|#1| (-1136 |#1| |#2| |#3|)) . T)) (((|#1| (-713)) . T)) (((|#1|) . T)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) ((((-797)) . T)) (|has| |#1| (-1019)) ((((-1073) |#1|) . T)) @@ -1615,18 +1615,18 @@ (((|#1|) . T)) ((((-525)) . T)) ((((-797)) . T)) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-327))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-327))) (|has| |#1| (-138)) ((((-797)) . T)) (((|#3|) . T)) -(-3215 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-976))) +(-3309 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-976))) ((((-797)) . T)) ((((-1157 |#2| |#3| |#4|)) . T) (((-1158 |#1| |#2| |#3| |#4|)) . T)) ((((-797)) . T)) -((((-47)) -12 (|has| |#1| (-517)) (|has| |#1| (-967 (-525)))) (((-565 $)) . T) ((|#1|) . T) (((-525)) |has| |#1| (-967 (-525))) (((-385 (-525))) -3215 (-12 (|has| |#1| (-517)) (|has| |#1| (-967 (-525)))) (|has| |#1| (-967 (-385 (-525))))) (((-385 (-886 |#1|))) |has| |#1| (-517)) (((-886 |#1|)) |has| |#1| (-976)) (((-1090)) . T)) +((((-47)) -12 (|has| |#1| (-517)) (|has| |#1| (-967 (-525)))) (((-565 $)) . T) ((|#1|) . T) (((-525)) |has| |#1| (-967 (-525))) (((-385 (-525))) -3309 (-12 (|has| |#1| (-517)) (|has| |#1| (-967 (-525)))) (|has| |#1| (-967 (-385 (-525))))) (((-385 (-886 |#1|))) |has| |#1| (-517)) (((-886 |#1|)) |has| |#1| (-976)) (((-1090)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-713)) . T)) -((($) -3215 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) +((($) -3309 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) (((|#1|) |has| |#1| (-288 |#1|))) ((((-1158 |#1| |#2| |#3| |#4|)) . T)) ((((-525)) |has| |#1| (-820 (-525))) (((-357)) |has| |#1| (-820 (-357)))) @@ -1634,14 +1634,14 @@ (|has| |#1| (-517)) (((|#1|) . T)) ((((-797)) . T)) -(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) (((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) |has| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (-288 (-2 (|:| -3160 |#1|) (|:| -3978 |#2|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) (((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) |has| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (-288 (-2 (|:| -3946 |#1|) (|:| -2511 |#2|))))) (((|#1|) |has| |#1| (-160))) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019)))) (((|#1|) . T)) (((|#3|) |has| |#3| (-1019))) -(((|#2|) -3215 (|has| |#2| (-160)) (|has| |#2| (-341)))) +(((|#2|) -3309 (|has| |#2| (-160)) (|has| |#2| (-341)))) ((((-1157 |#2| |#3| |#4|)) . T)) ((((-108)) . T)) (|has| |#1| (-762)) @@ -1651,8 +1651,8 @@ (|has| |#1| (-787)) (|has| |#1| (-787)) (((|#1| (-525) (-1004)) . T)) -(-3215 (|has| |#1| (-834 (-1090))) (|has| |#1| (-976))) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +(-3309 (|has| |#1| (-834 (-1090))) (|has| |#1| (-976))) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) (((|#1| (-385 (-525)) (-1004)) . T)) (((|#1| (-713) (-1004)) . T)) (|has| |#1| (-789)) @@ -1668,28 +1668,28 @@ (((|#1|) . T)) (|has| |#1| (-1019)) ((((-525)) -12 (|has| |#1| (-341)) (|has| |#2| (-588 (-525)))) ((|#2|) |has| |#1| (-341))) -(-3215 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976)) (|has| |#2| (-1019))) +(-3309 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976)) (|has| |#2| (-1019))) (((|#2|) |has| |#2| (-160))) (((|#1|) |has| |#1| (-160))) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) -((((-2 (|:| -3160 (-1073)) (|:| -3978 |#1|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3946 (-1073)) (|:| -2511 |#1|))) . T)) ((((-797)) . T)) (|has| |#3| (-787)) ((((-797)) . T)) ((((-1157 |#2| |#3| |#4|) (-297 |#2| |#3| |#4|)) . T)) ((((-797)) . T)) -(((|#1| |#1|) -3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-976)))) +(((|#1| |#1|) -3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-976)))) (((|#1|) . T)) ((((-525)) . T)) ((((-525)) . T)) -(((|#1|) -3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-976)))) +(((|#1|) -3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-976)))) (((|#2|) |has| |#2| (-341))) ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-341))) (|has| |#1| (-789)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3160 (-1090)) (|:| -3978 (-51)))) |has| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (-288 (-2 (|:| -3160 (-1090)) (|:| -3978 (-51)))))) -(-3215 (|has| |#1| (-429)) (|has| |#1| (-843))) +((((-2 (|:| -3946 (-1090)) (|:| -2511 (-51)))) |has| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (-288 (-2 (|:| -3946 (-1090)) (|:| -2511 (-51)))))) +(-3309 (|has| |#1| (-429)) (|has| |#1| (-843))) (((|#2|) . T) (((-525)) |has| |#2| (-588 (-525)))) ((((-797)) . T)) ((((-797)) . T)) @@ -1724,18 +1724,18 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (((|#1|) . T)) -(-3215 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(-3309 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) (((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) . T) (($ $) . T)) ((((-797)) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) (|has| |#1| (-341)) (|has| |#1| (-341)) (|has| (-385 |#2|) (-213)) (|has| |#1| (-843)) (((|#2|) |has| |#2| (-976))) -(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) (((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) |has| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (-288 (-2 (|:| -3160 |#1|) (|:| -3978 |#2|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) (((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) |has| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (-288 (-2 (|:| -3946 |#1|) (|:| -2511 |#2|))))) (|has| |#1| (-341)) (((|#1|) |has| |#1| (-160))) (((|#1| |#1|) . T)) @@ -1760,7 +1760,7 @@ (((|#1| (-385 (-525)) (-1004)) . T)) (((|#1| (-713) (-1004)) . T)) (((#0=(-385 |#2|) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-525)) -3215 (|has| (-385 (-525)) (-967 (-525))) (|has| |#1| (-967 (-525)))) (((-385 (-525))) . T)) +(((|#1|) . T) (((-525)) -3309 (|has| (-385 (-525)) (-967 (-525))) (|has| |#1| (-967 (-525)))) (((-385 (-525))) . T)) (((|#1| (-556 |#1| |#3|) (-556 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) @@ -1779,24 +1779,24 @@ ((((-641)) . T)) (((|#2|) |has| |#2| (-160))) (|has| |#2| (-787)) -((((-108)) |has| |#1| (-1019)) (((-797)) -3215 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-834 (-1090))) (|has| |#1| (-976)) (|has| |#1| (-1031)) (|has| |#1| (-1019)))) +((((-108)) |has| |#1| (-1019)) (((-797)) -3309 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-834 (-1090))) (|has| |#1| (-976)) (|has| |#1| (-1031)) (|has| |#1| (-1019)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3160 (-1073)) (|:| -3978 (-51)))) . T)) +((((-2 (|:| -3946 (-1073)) (|:| -2511 (-51)))) . T)) ((((-797)) . T)) ((((-525) |#1|) . T)) ((((-641)) . T) (((-385 (-525))) . T) (((-525)) . T)) (((|#1| |#1|) |has| |#1| (-160))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) (((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) |has| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (-288 (-2 (|:| -3160 |#1|) (|:| -3978 |#2|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) (((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) |has| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (-288 (-2 (|:| -3946 |#1|) (|:| -2511 |#2|))))) ((((-357)) . T)) ((((-641)) . T)) ((((-385 (-525))) . #0=(|has| |#2| (-341))) (($) . #0#)) (((|#1|) |has| |#1| (-160))) ((((-385 (-886 |#1|))) . T)) (((|#2| |#2|) . T)) -(-3215 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843))) -(-3215 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) +(-3309 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843))) +(-3309 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) (((|#2|) . T)) (|has| |#2| (-789)) (((|#3|) |has| |#3| (-976))) @@ -1806,14 +1806,14 @@ (|has| |#1| (-789)) ((((-1090)) |has| |#2| (-834 (-1090)))) ((((-797)) . T)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) ((((-385 (-525))) . T) (($) . T)) (|has| |#1| (-450)) (|has| |#1| (-346)) (|has| |#1| (-346)) (|has| |#1| (-346)) (|has| |#1| (-341)) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-976)) (|has| |#1| (-1031))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-976)) (|has| |#1| (-1031))) (|has| |#1| (-37 (-385 (-525)))) ((((-112 |#1|)) . T)) ((((-112 |#1|)) . T)) @@ -1834,11 +1834,11 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-789)) -((((-2 (|:| -3160 (-1073)) (|:| -3978 |#1|))) . T)) +((((-2 (|:| -3946 (-1073)) (|:| -2511 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-138)) (|has| |#1| (-136)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) |has| (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)) (-288 (-2 (|:| -3160 |#1|) (|:| -3978 |#2|)))) ((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019)))) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) |has| (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)) (-288 (-2 (|:| -3946 |#1|) (|:| -2511 |#2|)))) ((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019)))) (((|#2|) . T)) (((|#3|) . T)) ((((-112 |#1|)) . T)) @@ -1856,11 +1856,11 @@ ((((-501)) |has| |#1| (-567 (-501))) (((-826 (-525))) |has| |#1| (-567 (-826 (-525)))) (((-826 (-357))) |has| |#1| (-567 (-826 (-357)))) (((-357)) . #0=(|has| |#1| (-952))) (((-205)) . #0#)) (((|#1|) |has| |#1| (-341))) ((((-797)) . T)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) ((($ $) . T) (((-565 $) $) . T)) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-517))) ((($) . T) (((-1158 |#1| |#2| |#3| |#4|)) . T) (((-385 (-525))) . T)) -((($) -3215 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-976))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-517))) +((($) -3309 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-976))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-517))) (|has| |#1| (-341)) (|has| |#1| (-341)) (|has| |#1| (-341)) @@ -1871,11 +1871,11 @@ ((((-357)) . T)) (((|#3|) -12 (|has| |#3| (-288 |#3|)) (|has| |#3| (-1019)))) ((((-797)) . T)) -(-3215 (|has| |#2| (-429)) (|has| |#2| (-843))) +(-3309 (|has| |#2| (-429)) (|has| |#2| (-843))) (((|#1|) . T)) (|has| |#1| (-789)) (|has| |#1| (-789)) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) ((((-501)) |has| |#1| (-567 (-501)))) (((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019)))) (|has| |#1| (-1019)) @@ -1884,13 +1884,13 @@ (|has| |#1| (-136)) (|has| |#1| (-138)) ((((-525)) . T)) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-517))) (((#0=(-1157 |#2| |#3| |#4|)) . T) (((-385 (-525))) |has| #0# (-37 (-385 (-525)))) (($) . T)) ((((-525)) . T)) (|has| |#1| (-341)) -(-3215 (-12 (|has| (-1164 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) -(-3215 (-12 (|has| (-1164 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) +(-3309 (-12 (|has| (-1164 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) +(-3309 (-12 (|has| (-1164 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) (|has| |#1| (-341)) (|has| |#1| (-136)) (|has| |#1| (-138)) @@ -1907,18 +1907,18 @@ (((|#1| |#2|) . T)) (((|#1|) . T) (((-525)) |has| |#1| (-588 (-525)))) (((|#3|) |has| |#3| (-160))) -(-3215 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976)) (|has| |#2| (-1019))) +(-3309 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976)) (|has| |#2| (-1019))) ((((-525)) . T)) (((|#1| $) |has| |#1| (-265 |#1| |#1|))) ((((-385 (-525))) . T) (($) . T) (((-385 |#1|)) . T) ((|#1|) . T)) ((((-797)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -3215 (|has| |#1| (-269)) (|has| |#1| (-341))) ((#0=(-385 (-525)) #0#) |has| |#1| (-341))) -((((-2 (|:| -3160 (-1090)) (|:| -3978 (-51)))) . T)) +(((|#1| |#1|) . T) (($ $) -3309 (|has| |#1| (-269)) (|has| |#1| (-341))) ((#0=(-385 (-525)) #0#) |has| |#1| (-341))) +((((-2 (|:| -3946 (-1090)) (|:| -2511 (-51)))) . T)) ((($) . T)) ((((-525) |#1|) . T)) ((((-1090)) |has| (-385 |#2|) (-834 (-1090)))) -(((|#1|) . T) (($) -3215 (|has| |#1| (-269)) (|has| |#1| (-341))) (((-385 (-525))) |has| |#1| (-341))) +(((|#1|) . T) (($) -3309 (|has| |#1| (-269)) (|has| |#1| (-341))) (((-385 (-525))) |has| |#1| (-341))) ((((-501)) |has| |#2| (-567 (-501)))) ((((-632 |#2|)) . T) (((-797)) . T)) (((|#1|) . T)) @@ -1926,8 +1926,8 @@ (((|#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1019)))) ((((-804 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) -(-3215 (|has| |#4| (-735)) (|has| |#4| (-787))) -(-3215 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-3309 (|has| |#4| (-735)) (|has| |#4| (-787))) +(-3309 (|has| |#3| (-735)) (|has| |#3| (-787))) ((((-797)) . T)) ((((-797)) . T)) (((|#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1019)))) @@ -1943,17 +1943,17 @@ ((((-385 (-525))) . T) (($) . T)) ((((-385 (-525))) . T) (($) . T)) ((((-385 (-525))) . T) (($) . T)) -(-3215 (|has| |#1| (-429)) (|has| |#1| (-1130))) +(-3309 (|has| |#1| (-429)) (|has| |#1| (-1130))) ((($) . T)) ((((-385 (-525))) |has| #0=(-385 |#2|) (-967 (-385 (-525)))) (((-525)) |has| #0# (-967 (-525))) ((#0#) . T)) (((|#2|) . T) (((-525)) |has| |#2| (-588 (-525)))) (((|#1| (-713)) . T)) (|has| |#1| (-789)) (((|#1|) . T) (((-525)) |has| |#1| (-588 (-525)))) -((($) -3215 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -3215 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) -3309 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -3309 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) ((((-525)) . T)) (|has| |#1| (-37 (-385 (-525)))) -((((-2 (|:| -3160 (-1073)) (|:| -3978 (-51)))) |has| (-2 (|:| -3160 (-1073)) (|:| -3978 (-51))) (-288 (-2 (|:| -3160 (-1073)) (|:| -3978 (-51)))))) +((((-2 (|:| -3946 (-1073)) (|:| -2511 (-51)))) |has| (-2 (|:| -3946 (-1073)) (|:| -2511 (-51))) (-288 (-2 (|:| -3946 (-1073)) (|:| -2511 (-51)))))) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) (|has| |#1| (-787)) (|has| |#1| (-37 (-385 (-525)))) @@ -1978,24 +1978,24 @@ (((|#1| |#2|) . T)) ((((-135)) . T)) ((((-722 |#1| (-799 |#2|))) . T)) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) (|has| |#1| (-1112)) (((|#1|) . T)) -(-3215 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-976)) (|has| |#3| (-1019))) +(-3309 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-976)) (|has| |#3| (-1019))) ((((-1090) |#1|) |has| |#1| (-486 (-1090) |#1|))) (((|#2|) . T)) -((($ $) -3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) -((($) -3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($ $) -3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($) -3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-844 |#1|)) . T)) ((($) . T)) ((((-385 (-886 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) ((((-501)) |has| |#4| (-567 (-501)))) ((((-797)) . T) (((-592 |#4|)) . T)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-787)) -(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019))) (((-2 (|:| -3160 (-1073)) (|:| -3978 |#1|))) |has| (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|)) (-288 (-2 (|:| -3160 (-1073)) (|:| -3978 |#1|))))) +(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019))) (((-2 (|:| -3946 (-1073)) (|:| -2511 |#1|))) |has| (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|)) (-288 (-2 (|:| -3946 (-1073)) (|:| -2511 |#1|))))) (|has| |#1| (-1019)) (|has| |#1| (-341)) (|has| |#1| (-789)) @@ -2003,16 +2003,16 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-385 (-525))) . T)) -((($) -3215 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) +((($) -3309 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) (|has| |#1| (-136)) (|has| |#1| (-138)) -(-3215 (-12 (|has| (-1088 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) -(-3215 (-12 (|has| (-1088 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) +(-3309 (-12 (|has| (-1088 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) +(-3309 (-12 (|has| (-1088 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-138)) (|has| |#1| (-136)) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) ((((-1164 |#1| |#2| |#3|)) |has| |#1| (-341))) (|has| |#1| (-787)) (((|#1| |#2|) . T)) @@ -2035,9 +2035,9 @@ ((((-797)) . T)) ((((-797)) . T)) ((((-501)) |has| |#1| (-567 (-501)))) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) ((((-1090) |#1|) |has| |#1| (-486 (-1090) |#1|)) ((|#1| |#1|) |has| |#1| (-288 |#1|))) -(((|#1|) -3215 (|has| |#1| (-160)) (|has| |#1| (-341)))) +(((|#1|) -3309 (|has| |#1| (-160)) (|has| |#1| (-341)))) ((((-294 |#1|)) . T)) (((|#2|) |has| |#2| (-341))) (((|#2|) . T)) @@ -2058,14 +2058,14 @@ (|has| |#1| (-136)) (|has| |#1| (-138)) ((($ $) . T)) -(-3215 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-834 (-1090))) (|has| |#1| (-976)) (|has| |#1| (-1031)) (|has| |#1| (-1019))) +(-3309 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-834 (-1090))) (|has| |#1| (-976)) (|has| |#1| (-1031)) (|has| |#1| (-1019))) (|has| |#1| (-517)) (((|#2|) . T)) ((((-525)) . T)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-976))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-976))) ((((-538 |#1|)) . T)) ((($) . T)) (((|#1| (-57 |#1|) (-57 |#1|)) . T)) @@ -2090,12 +2090,12 @@ (((|#1| |#2|) . T)) ((((-1090) |#1|) . T)) (((|#4|) . T)) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-327))) ((((-1090) (-51)) . T)) ((((-1157 |#2| |#3| |#4|) (-297 |#2| |#3| |#4|)) . T)) ((((-385 (-525))) |has| |#1| (-967 (-385 (-525)))) (((-525)) |has| |#1| (-967 (-525))) ((|#1|) . T)) ((((-797)) . T)) -(-3215 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976)) (|has| |#2| (-1019))) +(-3309 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976)) (|has| |#2| (-1019))) (((#0=(-1158 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-160)) ((#0=(-385 (-525)) #0#) |has| |#1| (-517)) (($ $) |has| |#1| (-517))) (((|#1|) . T) (($) . T) (((-385 (-525))) . T)) @@ -2114,14 +2114,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019)))) (((|#2| |#3|) . T)) -(-3215 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843))) +(-3309 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843))) (((|#1| (-497 |#2|)) . T)) (((|#1| (-713)) . T)) (((|#1| (-497 (-1009 (-1090)))) . T)) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) (|has| |#2| (-843)) -(-3215 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3309 (|has| |#2| (-735)) (|has| |#2| (-787))) ((((-797)) . T)) ((($ $) . T) ((#0=(-1157 |#2| |#3| |#4|) #0#) . T) ((#1=(-385 (-525)) #1#) |has| #0# (-37 (-385 (-525))))) ((((-844 |#1|)) . T)) @@ -2130,13 +2130,13 @@ ((($) . T)) ((($) . T)) (|has| |#1| (-341)) -(-3215 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327)) (|has| |#1| (-517))) (|has| |#1| (-341)) ((($) . T) ((#0=(-1157 |#2| |#3| |#4|)) . T) (((-385 (-525))) |has| #0# (-37 (-385 (-525))))) (((|#1| |#2|) . T)) ((((-1088 |#1| |#2| |#3|)) |has| |#1| (-341))) -(-3215 (-12 (|has| |#1| (-286)) (|has| |#1| (-843))) (|has| |#1| (-341)) (|has| |#1| (-327))) -(-3215 (|has| |#1| (-834 (-1090))) (|has| |#1| (-976))) +(-3309 (-12 (|has| |#1| (-286)) (|has| |#1| (-843))) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3309 (|has| |#1| (-834 (-1090))) (|has| |#1| (-976))) ((((-525)) |has| |#1| (-588 (-525))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-797)) . T)) @@ -2168,27 +2168,27 @@ (((|#1|) |has| |#1| (-160))) ((((-797)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1019)))) -(((|#2|) -3215 (|has| |#2| (-6 (-4256 "*"))) (|has| |#2| (-160)))) -(-3215 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843))) -(-3215 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) +(((|#2|) -3309 (|has| |#2| (-6 (-4256 "*"))) (|has| |#2| (-160)))) +(-3309 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843))) +(-3309 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) (|has| |#2| (-789)) (|has| |#2| (-843)) (|has| |#1| (-843)) (((|#2|) |has| |#2| (-160))) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) ((((-1164 |#1| |#2| |#3|)) |has| |#1| (-341))) ((((-797)) . T)) ((((-797)) . T)) ((((-501)) . T) (((-525)) . T) (((-826 (-525))) . T) (((-357)) . T) (((-205)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) -((((-2 (|:| -3160 (-1073)) (|:| -3978 (-51)))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3946 (-1073)) (|:| -2511 (-51)))) . T)) (((|#1|) . T)) ((((-797)) . T)) (((|#1| |#2|) . T)) (((|#1| (-385 (-525))) . T)) (((|#1|) . T)) -(-3215 (|has| |#1| (-269)) (|has| |#1| (-341))) +(-3309 (|has| |#1| (-269)) (|has| |#1| (-341))) ((((-135)) . T)) ((((-385 |#2|)) . T) (((-385 (-525))) . T) (($) . T)) (|has| |#1| (-787)) @@ -2203,7 +2203,7 @@ ((((-385 (-525))) . T) (($) . T)) ((((-797)) . T)) ((((-797)) . T)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-797)) . T)) ((((-797)) . T)) @@ -2214,7 +2214,7 @@ (((|#1|) . T)) ((((-592 (-135))) . T) (((-1073)) . T)) ((((-797)) . T)) -((((-2 (|:| -3160 (-1073)) (|:| -3978 |#1|))) . T)) +((((-2 (|:| -3946 (-1073)) (|:| -2511 |#1|))) . T)) ((((-1090) |#1|) |has| |#1| (-486 (-1090) |#1|)) ((|#1| |#1|) |has| |#1| (-288 |#1|))) (|has| |#1| (-789)) ((((-797)) . T)) @@ -2226,16 +2226,16 @@ ((((-797)) . T) (((-592 |#4|)) . T)) (((|#2|) . T)) ((((-844 |#1|)) . T) (((-385 (-525))) . T) (($) . T)) -(-3215 (|has| |#4| (-160)) (|has| |#4| (-787)) (|has| |#4| (-976))) -(-3215 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-976))) +(-3309 (|has| |#4| (-160)) (|has| |#4| (-787)) (|has| |#4| (-976))) +(-3309 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-976))) ((((-1090) (-51)) . T)) -(-3215 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) +(-3309 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3215 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976))) -(-3215 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(-3309 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(-3309 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-787)) (|has| |#2| (-976))) (|has| |#1| (-843)) (|has| |#1| (-843)) (((|#2|) . T)) @@ -2250,12 +2250,12 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) (|has| |#1| (-762)) (((#0=(-844 |#1|) #0#) . T) (($ $) . T) ((#1=(-385 (-525)) #1#) . T)) ((((-385 |#2|)) . T)) (|has| |#1| (-787)) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) (((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) . T) ((#1=(-525) #1#) . T) (($ $) . T)) ((((-844 |#1|)) . T) (($) . T) (((-385 (-525))) . T)) (((|#2|) |has| |#2| (-976)) (((-525)) -12 (|has| |#2| (-588 (-525))) (|has| |#2| (-976)))) @@ -2265,25 +2265,25 @@ (|has| |#1| (-136)) (((|#2|) . T)) ((((-797)) . T)) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-346))) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-346))) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-346))) -((((-2 (|:| -3160 (-1090)) (|:| -3978 (-51)))) . T)) -(((#0=(-51)) . T) (((-2 (|:| -3160 (-1090)) (|:| -3978 #0#))) . T)) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-346))) +((((-2 (|:| -3946 (-1090)) (|:| -2511 (-51)))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -3946 (-1090)) (|:| -2511 #0#))) . T)) (|has| |#1| (-327)) ((((-525)) . T)) ((((-797)) . T)) (((#0=(-1158 |#1| |#2| |#3| |#4|) $) |has| #0# (-265 #0# #0#))) (|has| |#1| (-341)) (((#0=(-1004) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-327))) (((#0=(-385 (-525)) #0#) . T) ((#1=(-641) #1#) . T) (($ $) . T)) ((((-294 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) |has| |#1| (-341))) (|has| |#1| (-1019)) (((|#1|) . T)) -(((|#1|) -3215 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) -(((|#1|) -3215 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) +(((|#1|) -3309 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) +(((|#1|) -3309 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) (((|#2|) . T)) ((((-385 (-525))) . T) (((-641)) . T) (($) . T)) (((|#3| |#3|) . T)) @@ -2302,7 +2302,7 @@ (((|#2|) . T)) (((|#1|) . T)) ((((-525)) . T)) -(-3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) +(-3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) (((|#2|) . T) (((-525)) |has| |#2| (-588 (-525)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2339,7 +2339,7 @@ (|has| |#2| (-952)) ((($) . T)) (|has| |#1| (-843)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2347,24 +2347,24 @@ ((($) . T)) (|has| |#1| (-341)) ((((-844 |#1|)) . T)) -((($) -3215 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3309 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) -(-3215 (|has| |#1| (-346)) (|has| |#1| (-789))) +(-3309 (|has| |#1| (-346)) (|has| |#1| (-789))) (((|#1|) . T)) ((((-797)) . T)) ((((-1090)) -12 (|has| |#1| (-15 * (|#1| (-385 (-525)) |#1|))) (|has| |#1| (-834 (-1090))))) ((((-385 |#2|) |#3|) . T)) ((($) . T) (((-385 (-525))) . T)) ((((-713) |#1|) . T)) -(((|#2| (-220 (-1696 |#1|) (-713))) . T)) +(((|#2| (-220 (-4140 |#1|) (-713))) . T)) (((|#1| (-497 |#3|)) . T)) ((((-385 (-525))) . T)) -(-3215 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) +(-3309 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((((-797)) . T)) -(((#0=(-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) #0#) |has| (-2 (|:| -3160 (-1090)) (|:| -3978 (-51))) (-288 (-2 (|:| -3160 (-1090)) (|:| -3978 (-51)))))) +(((#0=(-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) #0#) |has| (-2 (|:| -3946 (-1090)) (|:| -2511 (-51))) (-288 (-2 (|:| -3946 (-1090)) (|:| -2511 (-51)))))) (|has| |#1| (-843)) (|has| |#2| (-341)) -(-3215 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(-3309 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976))) ((((-157 (-357))) . T) (((-205)) . T) (((-357)) . T)) ((((-797)) . T)) (((|#1|) . T)) @@ -2381,11 +2381,11 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3215 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3309 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-37 (-385 (-525)))) (-12 (|has| |#1| (-510)) (|has| |#1| (-770))) ((((-797)) . T)) -((((-1090)) -3215 (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-834 (-1090)))) (-12 (|has| |#1| (-341)) (|has| |#2| (-834 (-1090)))))) +((((-1090)) -3309 (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-834 (-1090)))) (-12 (|has| |#1| (-341)) (|has| |#2| (-834 (-1090)))))) (|has| |#1| (-341)) ((((-1090)) -12 (|has| |#1| (-15 * (|#1| (-385 (-525)) |#1|))) (|has| |#1| (-834 (-1090))))) (|has| |#1| (-341)) @@ -2395,7 +2395,7 @@ (((|#1|) . T)) (((|#2|) |has| |#1| (-341))) (((|#2|) |has| |#1| (-341))) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) @@ -2418,31 +2418,31 @@ (((|#2|) |has| |#1| (-341))) ((((-357)) -12 (|has| |#1| (-341)) (|has| |#2| (-820 (-357)))) (((-525)) -12 (|has| |#1| (-341)) (|has| |#2| (-820 (-525))))) (|has| |#1| (-341)) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-341)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-341)) (|has| |#1| (-517)) (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1019)))) (((|#3|) . T)) (((|#1|) . T)) -(-3215 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(-3309 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976))) (((|#2|) . T)) (((|#2|) . T)) -(-3215 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) -((((-2 (|:| -3160 (-1073)) (|:| -3978 |#1|))) . T)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +(-3309 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3946 (-1073)) (|:| -2511 |#1|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) (|has| |#1| (-37 (-385 (-525)))) (((|#1| |#2|) . T)) (|has| |#1| (-37 (-385 (-525)))) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) ((((-1073) |#1|) . T)) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) ((((-538 |#1|)) . T)) ((($) . T)) @@ -2450,7 +2450,7 @@ (|has| |#1| (-517)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-327))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-327))) (|has| |#1| (-138)) ((((-797)) . T)) ((($) . T)) @@ -2475,7 +2475,7 @@ (|has| |#1| (-733)) (|has| |#1| (-733)) ((((-501)) |has| |#1| (-567 (-501)))) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-789)) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-789)) (|has| |#1| (-1019)))) ((((-110)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2496,7 +2496,7 @@ ((((-525)) . T)) ((((-797)) . T)) ((((-525)) . T)) -(-3215 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3309 (|has| |#2| (-735)) (|has| |#2| (-787))) ((((-157 (-357))) . T) (((-205)) . T) (((-357)) . T)) ((((-797)) . T)) ((((-797)) . T)) @@ -2508,9 +2508,9 @@ (((|#1|) . T) (($) . T) (((-385 (-525))) . T)) (|has| |#1| (-341)) (|has| |#1| (-341)) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) -(-3215 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-834 (-1090))) (|has| |#1| (-976)) (|has| |#1| (-1031)) (|has| |#1| (-1019))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +(-3309 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-834 (-1090))) (|has| |#1| (-976)) (|has| |#1| (-1031)) (|has| |#1| (-1019))) (|has| |#1| (-1066)) ((((-525) |#1|) . T)) (((|#1|) . T)) @@ -2528,8 +2528,8 @@ (((|#1|) . T)) (|has| |#1| (-517)) ((((-385 |#2|)) . T) (((-385 (-525))) . T) (($) . T)) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-517))) ((((-357)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2538,7 +2538,7 @@ (|has| |#1| (-517)) (|has| |#1| (-1019)) ((((-722 |#1| (-799 |#2|))) |has| (-722 |#1| (-799 |#2|)) (-288 (-722 |#1| (-799 |#2|))))) -(-3215 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843))) +(-3309 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843))) (((|#1|) . T)) (((|#2| |#3|) . T)) (|has| |#2| (-843)) @@ -2548,12 +2548,12 @@ (|has| |#1| (-213)) (((|#1| (-497 (-1009 (-1090)))) . T)) (|has| |#2| (-341)) -((((-2 (|:| -3160 (-1073)) (|:| -3978 (-51)))) . T)) +((((-2 (|:| -3946 (-1073)) (|:| -2511 (-51)))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) ((((-797)) . T)) ((((-797)) . T)) -(-3215 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-3309 (|has| |#3| (-735)) (|has| |#3| (-787))) ((((-797)) . T)) ((((-797)) . T)) (((|#1|) . T)) @@ -2562,8 +2562,8 @@ ((((-525)) . T)) (((|#3|) . T)) ((((-797)) . T)) -(-3215 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) -(-3215 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-976))) +(-3309 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3309 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-976))) (((#0=(-538 |#1|) #0#) . T) (($ $) . T) ((#1=(-385 (-525)) #1#) . T)) ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) (((|#1|) |has| |#1| (-160))) @@ -2576,7 +2576,7 @@ (((|#1|) . T)) ((((-797)) |has| |#1| (-566 (-797)))) ((((-273 |#3|)) . T)) -(((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525)))) ((|#2| |#2|) . T) (($ $) -3215 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843)))) +(((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525)))) ((|#2| |#2|) . T) (($ $) -3309 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) . T)) @@ -2584,20 +2584,20 @@ (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) -((($ $) -3215 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) -((($ $) -3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1| |#1|) . 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T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (|has| |#2| (-843)) (|has| |#1| (-843)) -((($) -3215 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3309 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1|) . T)) -((((-2 (|:| -3160 (-1073)) (|:| -3978 |#1|))) . T)) +((((-2 (|:| -3946 (-1073)) (|:| -2511 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) @@ -2611,10 +2611,10 @@ (((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019)))) (((#0=(-385 (-525)) #0#) . T)) ((((-385 (-525))) . T)) -(-3215 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(-3309 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976))) (((|#1|) . T)) (((|#1|) . T)) -(-3215 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(-3309 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-787)) (|has| |#2| (-976))) ((((-501)) . T)) ((((-797)) . T)) ((((-1090)) |has| |#2| (-834 (-1090))) (((-1004)) . T)) @@ -2628,12 +2628,12 @@ ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) ((((-1090)) |has| |#1| (-834 (-1090)))) ((((-844 |#1|)) . T) (((-385 (-525))) . T) (($) . T)) -((($) . T) (((-385 (-525))) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) -(((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525)))) ((|#1| |#1|) . T) (($ $) -3215 (|has| |#1| (-160)) (|has| |#1| (-517)))) +((($) . T) (((-385 (-525))) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) +(((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525)))) ((|#1| |#1|) . T) (($ $) -3309 (|has| |#1| (-160)) (|has| |#1| (-517)))) ((($) . T) (((-385 (-525))) . T)) (((|#1|) . T) (((-385 (-525))) . T) (((-525)) . T) (($) . T)) (((|#2|) |has| |#2| (-976)) (((-525)) -12 (|has| |#2| (-588 (-525))) (|has| |#2| (-976)))) -((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T) (($) -3215 (|has| |#1| (-160)) (|has| |#1| (-517)))) +((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T) (($) -3309 (|has| |#1| (-160)) (|has| |#1| (-517)))) (|has| |#1| (-517)) (((|#1|) |has| |#1| (-341))) ((((-525)) . T)) @@ -2652,8 +2652,8 @@ ((((-797)) . T)) (|has| |#2| (-762)) (|has| |#2| (-762)) -((((-385 (-525))) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#2|) |has| |#1| (-341)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-385 (-525))) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) . T)) +((((-385 (-525))) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#2|) |has| |#1| (-341)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-385 (-525))) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) (((|#1|) . T) (((-525)) |has| |#1| (-967 (-525))) (((-385 (-525))) |has| |#1| (-967 (-385 (-525))))) ((((-525)) |has| |#1| (-820 (-525))) (((-357)) |has| |#1| (-820 (-357)))) @@ -2679,12 +2679,12 @@ (((|#2| (-713)) . T)) ((((-1090)) . T)) ((((-804 |#1|)) . T)) -(-3215 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-976))) -(-3215 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-787)) (|has| |#3| (-976))) +(-3309 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-976))) +(-3309 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-787)) (|has| |#3| (-976))) ((((-797)) . T)) (((|#1|) . T)) -(-3215 (|has| |#2| (-735)) (|has| |#2| (-787))) -(-3215 (-12 (|has| |#1| (-735)) (|has| |#2| (-735))) (-12 (|has| |#1| (-789)) (|has| |#2| (-789)))) +(-3309 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3309 (-12 (|has| |#1| (-735)) (|has| |#2| (-735))) (-12 (|has| |#1| (-789)) (|has| |#2| (-789)))) ((((-804 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-346)) @@ -2710,7 +2710,7 @@ (((|#1|) . T)) ((((-797)) . T)) (|has| |#2| (-843)) -((((-2 (|:| -3160 (-1090)) (|:| -3978 (-51)))) . T)) +((((-2 (|:| -3946 (-1090)) (|:| -2511 (-51)))) . T)) ((((-501)) |has| |#2| (-567 (-501))) (((-826 (-357))) |has| |#2| (-567 (-826 (-357)))) (((-826 (-525))) |has| |#2| (-567 (-826 (-525))))) ((((-797)) . T)) ((((-797)) . T)) @@ -2743,11 +2743,11 @@ ((((-385 |#2|) |#3|) . T)) (((|#1|) . T)) (|has| |#1| (-1019)) -(((|#2| (-458 (-1696 |#1|) (-713))) . T)) +(((|#2| (-458 (-4140 |#1|) (-713))) . T)) ((((-525) |#1|) . T)) (((|#2| |#2|) . T)) (((|#1| (-497 (-1090))) . T)) -(-3215 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(-3309 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976))) ((((-525)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -2757,9 +2757,9 @@ ((($) . T) (((-385 (-525))) . T)) ((($) . T)) ((($) . T)) -(-3215 (|has| |#1| (-789)) (|has| |#1| (-1019))) +(-3309 (|has| |#1| (-789)) (|has| |#1| (-1019))) (((|#1|) . 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T)) +(((#0=(-385 (-525)) #0#) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($ $) -3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1| |#1|) . T)) ((((-525) |#1|) . T)) ((((-294 |#1|)) . T)) (((#0=(-641) (-1086 #0#)) . T)) -((((-385 (-525))) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1|) . T)) +((((-385 (-525))) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . T)) (|has| |#1| (-787)) ((($ $) . T) ((#0=(-799 |#1|) $) . T) ((#0# |#2|) . T)) @@ -2909,12 +2909,12 @@ (((#0=(-1158 |#1| |#2| |#3| |#4|)) |has| #0# (-288 #0#))) ((($) . T)) (((|#1|) . T)) -((($ $) -3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((#0=(-385 (-525)) #0#) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#2| |#2|) |has| |#1| (-341)) ((|#1| |#1|) . T)) -(((|#1| |#1|) . T) (($ $) -3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((#0=(-385 (-525)) #0#) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341)))) +((($ $) -3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((#0=(-385 (-525)) #0#) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#2| |#2|) |has| |#1| (-341)) ((|#1| |#1|) . T)) +(((|#1| |#1|) . T) (($ $) -3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((#0=(-385 (-525)) #0#) -3309 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341)))) (|has| |#2| (-213)) (|has| $ (-138)) ((((-797)) . T)) -((($) . T) (((-385 (-525))) -3215 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) . T) (((-385 (-525))) -3309 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) ((((-797)) . T)) (|has| |#1| (-787)) ((((-1090)) -12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-834 (-1090))))) @@ -2926,23 +2926,23 @@ (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1019)))) (((|#4|) . T)) (|has| |#1| (-517)) -((($) -3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3215 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#2|) |has| |#1| (-341)) ((|#1|) . T)) -((((-1090)) -3215 (-12 (|has| (-1164 |#1| |#2| |#3|) (-834 (-1090))) (|has| |#1| (-341))) (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-834 (-1090)))))) -(((|#1|) . 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T)) -(-3215 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843))) +(-3309 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843))) (((|#1|) . T)) (((|#1| (-497 (-760 (-1090)))) . T)) -(-3215 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) -(-3215 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) +(-3309 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) +(-3309 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) (((|#1|) . T)) -(-3215 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) +(-3309 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) (((|#1|) . T)) -(-3215 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976))) -(-3215 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-126)) (|has| |#2| (-126))) (-12 (|has| |#1| (-735)) (|has| |#2| (-735)))) +(-3309 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(-3309 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-126)) (|has| |#2| (-126))) (-12 (|has| |#1| (-735)) (|has| |#2| (-735)))) ((((-1164 |#1| |#2| |#3|)) |has| |#1| (-341))) ((($) . T) (((-804 |#1|)) . T) (((-385 (-525))) . T)) ((((-1164 |#1| |#2| |#3|)) |has| |#1| (-341))) @@ -2951,15 +2951,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-385 |#2|)) . T)) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-327))) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-789)) (|has| |#1| (-1019)))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-327))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-789)) (|has| |#1| (-1019)))) ((((-501)) |has| |#1| (-567 (-501)))) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-789)) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-789)) (|has| |#1| (-1019)))) ((((-501)) |has| |#1| (-567 (-501)))) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-789)) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-789)) (|has| |#1| (-1019)))) ((((-501)) |has| |#1| (-567 (-501)))) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) (((|#1|) . T)) (((|#2| |#2|) . T) ((#0=(-385 (-525)) #0#) . T) (($ $) . T)) ((((-525)) . T)) @@ -2988,32 +2988,32 @@ ((((-1164 |#1| |#2| |#3|)) |has| |#1| (-341))) ((((-1090)) . T) (((-797)) . T)) (|has| |#1| (-341)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3215 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3309 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-843)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) . T)) -((($) -3215 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3309 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-1023)) . T)) ((((-797)) . T)) -((($) -3215 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3309 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((($) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T)) ((($) . T)) -((($) -3215 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3309 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-843))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (|has| |#2| (-843)) (|has| |#1| (-843)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-160))) ((((-641)) . T)) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) (((|#1|) |has| |#1| (-160))) (((|#1|) |has| |#1| (-160))) ((((-385 (-525))) . T) (($) . T)) (((|#1| (-525)) . T)) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-341)) (|has| |#1| (-341)) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-327))) -(-3215 (|has| |#1| (-160)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3309 (|has| |#1| (-160)) (|has| |#1| (-517))) (((|#1| (-525)) . T)) (((|#1| (-385 (-525))) . T)) (((|#1| (-713)) . T)) @@ -3028,16 +3028,16 @@ ((((-826 (-357))) . T) (((-826 (-525))) . T) (((-1090)) . T) (((-501)) . T)) (((|#1|) . T)) ((((-797)) . T)) -(-3215 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976))) -(-3215 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-126)) (|has| |#2| (-126))) (-12 (|has| |#1| (-735)) (|has| |#2| (-735)))) +(-3309 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(-3309 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-126)) (|has| |#2| (-126))) (-12 (|has| |#1| (-735)) (|has| |#2| (-735)))) ((((-525)) . T)) ((((-525)) . T)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-3215 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) +(-3309 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-976))) ((((-1090)) -12 (|has| |#2| (-834 (-1090))) (|has| |#2| (-976)))) -(-3215 (-12 (|has| |#1| (-450)) (|has| |#2| (-450))) (-12 (|has| |#1| (-669)) (|has| |#2| (-669)))) +(-3309 (-12 (|has| |#1| (-450)) (|has| |#2| (-450))) (-12 (|has| |#1| (-669)) (|has| |#2| (-669)))) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-341)) @@ -3061,7 +3061,7 @@ ((((-1073) (-1090) (-525) (-205) (-797)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) -(-3215 (|has| |#1| (-327)) (|has| |#1| (-346))) +(-3309 (|has| |#1| (-327)) (|has| |#1| (-346))) (((|#1| |#2|) . T)) ((($) . T) ((|#1|) . T)) ((((-797)) . T)) @@ -3069,7 +3069,7 @@ ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2|) |has| |#2| (-1019)) (((-525)) -12 (|has| |#2| (-967 (-525))) (|has| |#2| (-1019))) (((-385 (-525))) -12 (|has| |#2| (-967 (-385 (-525)))) (|has| |#2| (-1019)))) ((((-501)) |has| |#1| (-567 (-501)))) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-789)) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-789)) (|has| |#1| (-1019)))) ((($) . T) (((-385 (-525))) . T)) (|has| |#1| (-843)) (|has| |#1| (-843)) @@ -3078,14 +3078,14 @@ ((((-797)) . T)) (((|#2| |#2|) . T)) (((|#1| |#1|) |has| |#1| (-160))) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3215 (|has| |#1| (-21)) (|has| |#1| (-787))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3309 (|has| |#1| (-21)) (|has| |#1| (-787))) (((|#2|) . T)) -(-3215 (|has| |#1| (-21)) (|has| |#1| (-787))) +(-3309 (|has| |#1| (-21)) (|has| |#1| (-787))) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) (((|#1|) . T)) -((((-797)) -3215 (-12 (|has| |#1| (-566 (-797))) (|has| |#2| (-566 (-797)))) (-12 (|has| |#1| (-1019)) (|has| |#2| (-1019))))) +((((-797)) -3309 (-12 (|has| |#1| (-566 (-797))) (|has| |#2| (-566 (-797)))) (-12 (|has| |#1| (-1019)) (|has| |#2| (-1019))))) ((((-385 |#2|) |#3|) . T)) ((((-385 (-525))) . T) (($) . T)) (|has| |#1| (-37 (-385 (-525)))) @@ -3097,17 +3097,17 @@ (((|#1|) . T) (((-385 (-525))) . T) (((-525)) . T) (($) . T)) (((#0=(-525) #0#) . T)) ((($) . T) (((-385 (-525))) . T)) -(-3215 (|has| |#4| (-160)) (|has| |#4| (-787)) (|has| |#4| (-976))) -(-3215 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-976))) +(-3309 (|has| |#4| (-160)) (|has| |#4| (-787)) (|has| |#4| (-976))) +(-3309 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-976))) (|has| |#4| (-735)) -(-3215 (|has| |#4| (-735)) (|has| |#4| (-787))) +(-3309 (|has| |#4| (-735)) (|has| |#4| (-787))) (|has| |#4| (-787)) (|has| |#3| (-735)) -(-3215 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-3309 (|has| |#3| (-735)) (|has| |#3| (-787))) (|has| |#3| (-787)) ((((-525)) . T)) (((|#2|) . T)) -((((-1090)) -3215 (-12 (|has| (-1088 |#1| |#2| |#3|) (-834 (-1090))) (|has| |#1| (-341))) (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-834 (-1090)))))) +((((-1090)) -3309 (-12 (|has| (-1088 |#1| |#2| |#3|) (-834 (-1090))) (|has| |#1| (-341))) (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-834 (-1090)))))) ((((-1090)) -12 (|has| |#1| (-15 * (|#1| (-385 (-525)) |#1|))) (|has| |#1| (-834 (-1090))))) ((((-1090)) -12 (|has| |#1| (-15 * (|#1| (-713) |#1|))) (|has| |#1| (-834 (-1090))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3122,11 +3122,11 @@ ((((-1088 |#1| |#2| |#3|)) |has| |#1| (-341))) ((((-1088 |#1| |#2| |#3|)) |has| |#1| (-341))) ((((-1055 |#1| |#2|)) . T)) -(((|#2|) . T) (((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) -((((-2 (|:| -3160 (-1090)) (|:| -3978 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3946 (-1090)) (|:| -2511 (-51)))) . T)) ((($) . T)) (|has| |#1| (-952)) -(((|#2|) . T) (((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) ((((-797)) . T)) ((((-501)) |has| |#2| (-567 (-501))) (((-826 (-525))) |has| |#2| (-567 (-826 (-525)))) (((-826 (-357))) |has| |#2| (-567 (-826 (-357)))) (((-357)) . #0=(|has| |#2| (-952))) (((-205)) . #0#)) ((((-1090) (-51)) . T)) @@ -3138,15 +3138,15 @@ ((((-1088 |#1| |#2| |#3|)) . T)) ((((-1088 |#1| |#2| |#3|)) . T) (((-1081 |#1| |#2| |#3|)) . T)) ((((-797)) . T)) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) ((((-525) |#1|) . T)) ((((-1088 |#1| |#2| |#3|)) |has| |#1| (-341))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-341)) -(((|#3|) . T) ((|#2|) . T) (($) -3215 (|has| |#4| (-160)) (|has| |#4| (-787)) (|has| |#4| (-976))) ((|#4|) -3215 (|has| |#4| (-160)) (|has| |#4| (-341)) (|has| |#4| (-976)))) -(((|#2|) . T) (($) -3215 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-976))) ((|#3|) -3215 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-976)))) +(((|#3|) . T) ((|#2|) . T) (($) -3309 (|has| |#4| (-160)) (|has| |#4| (-787)) (|has| |#4| (-976))) ((|#4|) -3309 (|has| |#4| (-160)) (|has| |#4| (-341)) (|has| |#4| (-976)))) +(((|#2|) . T) (($) -3309 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-976))) ((|#3|) -3309 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-976)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-341)) @@ -3158,7 +3158,7 @@ ((((-797)) . T)) ((((-797)) . T)) (((|#1|) . T)) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) ((((-125)) . T) (((-797)) . T)) ((((-525) |#1|) . T)) (((|#1|) . T)) @@ -3166,30 +3166,30 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-341)) (|has| |#2| (-265 |#2| |#2|))) (($ $) . T)) ((($ $) . 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T)) -((((-797)) -3215 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) +((((-797)) -3309 (|has| |#1| (-566 (-797))) (|has| |#1| (-1019)))) (((|#1|) . T)) (((|#1| |#2|) . T)) ((((-1073) |#1|) . T)) ((((-385 |#2|)) . T)) -((((-2 (|:| -3160 |#1|) (|:| -3978 |#2|))) . T)) +((((-2 (|:| -3946 |#1|) (|:| -2511 |#2|))) . T)) (|has| |#1| (-517)) (|has| |#1| (-517)) ((($) . T) ((|#2|) . T)) @@ -3197,12 +3197,12 @@ (((|#1| |#2|) . T)) (((|#2| $) |has| |#2| (-265 |#2| |#2|))) (((|#1| (-592 |#1|)) |has| |#1| (-787))) -(-3215 (|has| |#1| (-213)) (|has| |#1| (-327))) -(-3215 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3309 (|has| |#1| (-213)) (|has| |#1| (-327))) +(-3309 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-1019)) (((|#1|) . T)) ((((-385 (-525))) . T) (($) . T)) -((((-930 |#1|)) . T) ((|#1|) . 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137702) ((-230 . -735) 137681) ((-229 . -733) 137660) ((-229 . -736) 137611) ((-229 . -735) 137590) ((-49 . -983) T) ((-230 . -669) 137521) ((-229 . -669) 137452) ((-1121 . -1019) T) ((-616 . -23) T) ((-538 . -983) T) ((-489 . -983) T) ((-357 . -982) 137417) ((-300 . -107) 137392) ((-71 . -361) T) ((-71 . -373) T) ((-954 . -37) 137329) ((-636 . -378) 137311) ((-94 . -97) T) ((-654 . -1019) T) ((-934 . -136) 137283) ((-934 . -138) 137255) ((-357 . -107) 137211) ((-297 . -1130) 137190) ((-451 . -933) 137156) ((-332 . -37) 137121) ((-39 . -348) 137093) ((-807 . -566) 136965) ((-123 . -121) 136949) ((-117 . -121) 136933) ((-776 . -982) 136903) ((-775 . -21) 136855) ((-769 . -982) 136839) ((-775 . -25) 136791) ((-297 . -517) 136742) ((-525 . -770) T) ((-220 . -1126) T) ((-776 . -107) 136707) ((-769 . -107) 136686) ((-1156 . -566) 136668) ((-1135 . -566) 136650) ((-1135 . -567) 136323) ((-1086 . -843) 136302) ((-1042 . -843) 136281) ((-47 . -37) 136246) ((-1192 . -1031) T) ((-556 . -566) 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. -566) 128532) ((-329 . -138) 128514) ((-329 . -136) T) ((-337 . -1031) T) ((-331 . -1031) T) ((-323 . -1031) T) ((-935 . -286) T) ((-848 . -286) T) ((-806 . -223) T) ((-103 . -1031) T) ((-806 . -213) 128493) ((-1156 . -107) 128314) ((-1135 . -107) 128103) ((-225 . -1160) 128087) ((-525 . -787) T) ((-337 . -23) T) ((-332 . -327) T) ((-294 . -288) 128074) ((-291 . -288) 128015) ((-331 . -23) T) ((-297 . -126) T) ((-323 . -23) T) ((-935 . -952) T) ((-103 . -23) T) ((-225 . -558) 127992) ((-1158 . -37) 127884) ((-1145 . -843) 127863) ((-108 . -1019) T) ((-965 . -97) T) ((-1145 . -594) 127788) ((-805 . -736) NIL) ((-794 . -594) 127762) ((-805 . -733) NIL) ((-758 . -820) NIL) ((-805 . -669) T) ((-1008 . -486) 127635) ((-724 . -486) 127582) ((-722 . -486) 127534) ((-532 . -594) 127521) ((-758 . -967) 127351) ((-431 . -486) 127294) ((-366 . -367) T) ((-58 . -1126) T) ((-571 . -789) 127273) ((-473 . -607) T) ((-1061 . -908) 127242) ((-934 . -429) T) ((-641 . -787) T) ((-482 . -734) T) ((-451 . -982) 127077) ((-321 . -1019) T) ((-291 . -1066) NIL) ((-268 . -126) T) ((-372 . -1019) T) ((-636 . -348) 127044) ((-804 . -983) T) ((-203 . -570) 127021) ((-305 . -265) 126998) ((-451 . -107) 126819) ((-1156 . -976) T) ((-1135 . -976) T) ((-758 . -355) 126803) ((-157 . -669) T) ((-600 . -97) T) ((-1156 . -223) 126782) ((-1156 . -213) 126734) ((-1135 . -213) 126639) ((-1135 . -223) 126618) ((-934 . -380) NIL) ((-616 . -588) 126566) ((-294 . -37) 126476) ((-291 . -37) 126405) ((-67 . -566) 126387) ((-297 . -466) 126353) ((-1100 . -267) 126332) ((-1032 . -1031) 126263) ((-81 . -1126) T) ((-59 . -566) 126245) ((-455 . -267) 126224) ((-1185 . -967) 126201) ((-1079 . -1019) T) ((-1032 . -23) 126072) ((-758 . -834) 126008) ((-1145 . -669) T) ((-1021 . -1126) T) ((-1008 . -269) 125939) ((-827 . -97) T) ((-724 . -269) 125850) ((-305 . -19) 125834) ((-57 . -267) 125811) ((-722 . -269) 125742) ((-794 . -669) T) ((-113 . -787) NIL) ((-488 . -267) 125719) ((-305 . -558) 125696) ((-469 . -267) 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. -588) 118332) ((-438 . -566) 118314) ((-431 . -566) 118296) ((-431 . -567) 118157) ((-965 . -209) 118103) ((-122 . -33) T) ((-759 . -126) T) ((-806 . -843) 118082) ((-595 . -566) 118064) ((-333 . -1189) 118048) ((-330 . -1189) 118032) ((-322 . -1189) 118016) ((-123 . -486) 117949) ((-117 . -486) 117882) ((-483 . -734) T) ((-483 . -737) T) ((-482 . -736) T) ((-98 . -288) 117820) ((-202 . -97) 117798) ((-636 . -1019) T) ((-641 . -160) T) ((-806 . -594) 117750) ((-63 . -362) T) ((-254 . -566) 117732) ((-63 . -373) T) ((-886 . -355) 117716) ((-804 . -269) T) ((-49 . -566) 117698) ((-930 . -37) 117646) ((-538 . -566) 117628) ((-457 . -355) 117612) ((-538 . -567) 117594) ((-489 . -566) 117576) ((-844 . -1189) 117563) ((-805 . -1126) T) ((-643 . -429) T) ((-468 . -486) 117529) ((-462 . -341) T) ((-333 . -346) 117508) ((-330 . -346) 117487) ((-322 . -346) 117466) ((-198 . -341) T) ((-657 . -669) T) ((-112 . -429) T) ((-1193 . -1184) 117450) ((-805 . -818) 117427) ((-805 . -820) NIL) ((-897 . -789) 117326) ((-757 . -789) 117277) ((-600 . -602) 117261) ((-1113 . -33) T) ((-159 . -566) 117243) ((-1032 . -21) 117154) ((-1032 . -25) 117006) ((-805 . -967) 116983) ((-886 . -834) 116964) ((-1145 . -46) 116941) ((-844 . -346) T) ((-57 . -597) 116925) ((-488 . -597) 116909) ((-457 . -834) 116886) ((-69 . -418) T) ((-69 . -373) T) ((-469 . -597) 116870) ((-57 . -351) 116854) ((-573 . -160) T) ((-488 . -351) 116838) ((-469 . -351) 116822) ((-769 . -651) 116806) ((-1086 . -286) 116785) ((-1092 . -126) T) ((-113 . -160) T) ((-1061 . -288) 116723) ((-157 . -1126) T) ((-584 . -687) 116707) ((-560 . -687) 116691) ((-1182 . -126) T) ((-1157 . -854) 116670) ((-1136 . -854) 116649) ((-1136 . -762) NIL) ((-636 . -660) 116599) ((-1135 . -843) 116552) ((-954 . -1019) T) ((-805 . -355) 116529) ((-805 . -316) 116506) ((-839 . -1031) T) ((-157 . -818) 116490) ((-157 . -820) 116415) ((-462 . -1031) T) ((-332 . -1019) T) ((-198 . -1031) T) ((-74 . -418) T) ((-74 . -373) T) ((-157 . -967) 116313) 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114900) ((-451 . -594) 114797) ((-332 . -660) 114742) ((-157 . -834) 114701) ((-641 . -269) T) ((-636 . -160) T) ((-654 . -107) 114657) ((-1198 . -983) T) ((-1145 . -355) 114641) ((-396 . -1130) 114619) ((-291 . -787) NIL) ((-396 . -517) T) ((-205 . -286) T) ((-1135 . -733) 114572) ((-1135 . -736) 114525) ((-1156 . -669) T) ((-1135 . -669) T) ((-47 . -660) 114490) ((-205 . -952) T) ((-329 . -1179) 114467) ((-1158 . -389) 114433) ((-661 . -669) T) ((-1145 . -834) 114376) ((-108 . -566) 114358) ((-108 . -567) 114340) ((-661 . -450) T) ((-458 . -21) 114251) ((-123 . -464) 114235) ((-117 . -464) 114219) ((-458 . -25) 114071) ((-573 . -269) T) ((-542 . -982) 114046) ((-415 . -1019) T) ((-987 . -286) T) ((-113 . -269) T) ((-1023 . -97) T) ((-934 . -97) T) ((-542 . -107) 114014) ((-1057 . -288) 113952) ((-1121 . -976) T) ((-987 . -952) T) ((-64 . -1126) T) ((-980 . -25) T) ((-980 . -21) T) ((-654 . -976) T) ((-363 . -21) T) ((-363 . -25) T) ((-636 . -486) NIL) ((-954 . -160) T) ((-654 . -223) T) ((-987 . -510) T) ((-475 . -97) T) ((-332 . -160) T) ((-321 . -566) 113934) ((-372 . -566) 113916) ((-451 . -669) T) ((-1037 . -787) T) ((-826 . -967) 113884) ((-103 . -789) T) ((-604 . -982) 113868) ((-462 . -126) T) ((-1158 . -983) T) ((-198 . -126) T) ((-1071 . -97) 113846) ((-94 . -1019) T) ((-225 . -612) 113830) ((-225 . -597) 113814) ((-604 . -107) 113793) ((-294 . -389) 113777) ((-225 . -351) 113761) ((-1074 . -215) 113708) ((-930 . -211) 113692) ((-72 . -1126) T) ((-47 . -160) T) ((-643 . -365) T) ((-643 . -134) T) ((-1193 . -97) T) ((-1008 . -982) 113535) ((-243 . -843) 113514) ((-227 . -843) 113493) ((-724 . -982) 113316) ((-722 . -982) 113159) ((-561 . -1126) T) ((-1079 . -566) 113141) ((-1008 . -107) 112970) ((-973 . -97) T) ((-452 . -1126) T) ((-438 . -982) 112941) ((-431 . -982) 112784) ((-610 . -594) 112768) ((-805 . -286) T) ((-724 . -107) 112577) ((-722 . -107) 112406) ((-333 . -594) 112358) ((-330 . -594) 112310) ((-322 . -594) 112262) ((-243 . -594) 112187) ((-227 . -594) 112112) ((-1073 . -789) T) ((-1009 . -967) 112096) ((-438 . -107) 112057) ((-431 . -107) 111886) ((-998 . -967) 111863) ((-931 . -33) T) ((-899 . -566) 111824) ((-891 . -1126) T) ((-122 . -941) 111808) ((-896 . -1031) T) ((-805 . -952) NIL) ((-678 . -1031) T) ((-658 . -1031) T) ((-1172 . -464) 111792) ((-1057 . -37) 111752) ((-896 . -23) T) ((-782 . -97) T) ((-759 . -21) T) ((-759 . -25) T) ((-678 . -23) T) ((-658 . -23) T) ((-106 . -607) T) ((-844 . -594) 111717) ((-538 . -982) 111682) ((-489 . -982) 111627) ((-207 . -55) 111585) ((-430 . -23) T) ((-385 . -97) T) ((-242 . -97) T) ((-636 . -269) T) ((-800 . -37) 111555) ((-538 . -107) 111511) ((-489 . -107) 111440) ((-396 . -1031) T) ((-294 . -983) 111331) ((-291 . -983) T) ((-604 . -976) T) ((-1198 . -1019) T) ((-157 . -286) 111262) ((-396 . -23) T) ((-39 . -566) 111244) ((-39 . -567) 111228) ((-103 . -924) 111210) ((-112 . -803) 111194) ((-47 . -486) 111160) ((-1113 . -941) 111144) ((-1095 . -566) 111126) ((-1100 . -33) T) 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97082) ((-205 . -1130) T) ((-385 . -983) T) ((-1073 . -142) 97064) ((-930 . -269) 97015) ((-205 . -517) T) ((-297 . -1153) 96999) ((-297 . -1150) 96969) ((-1100 . -1103) 96948) ((-997 . -566) 96930) ((-593 . -142) 96914) ((-581 . -142) 96860) ((-1100 . -102) 96810) ((-455 . -1103) 96789) ((-462 . -138) T) ((-462 . -136) NIL) ((-1037 . -567) 96704) ((-416 . -566) 96686) ((-198 . -138) T) ((-198 . -136) NIL) ((-1037 . -566) 96668) ((-125 . -97) T) ((-51 . -97) T) ((-1136 . -588) 96620) ((-455 . -102) 96570) ((-925 . -23) T) ((-1194 . -37) 96540) ((-1086 . -1031) T) ((-1042 . -1031) T) ((-987 . -1130) T) ((-793 . -1031) T) ((-886 . -1130) 96519) ((-457 . -1130) 96498) ((-674 . -789) 96477) ((-987 . -517) T) ((-886 . -517) 96408) ((-1086 . -23) T) ((-1042 . -23) T) ((-793 . -23) T) ((-457 . -517) 96339) ((-1057 . -660) 96271) ((-1061 . -486) 96204) ((-965 . -567) NIL) ((-965 . -566) 96186) ((-800 . -660) 96156) ((-1121 . -46) 96125) ((-229 . -126) T) ((-230 . -126) T) ((-1023 . -1019) T) 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. -908) 95539) ((-440 . -908) 95508) ((-106 . -142) 95490) ((-71 . -566) 95472) ((-827 . -566) 95454) ((-1002 . -667) 95433) ((-1198 . -976) T) ((-758 . -588) 95381) ((-273 . -983) 95324) ((-157 . -1130) 95229) ((-205 . -1031) T) ((-302 . -23) T) ((-1081 . -924) 95181) ((-782 . -1019) T) ((-1043 . -683) 95160) ((-1158 . -982) 95065) ((-1156 . -854) 95044) ((-804 . -669) T) ((-157 . -517) 94955) ((-1135 . -854) 94934) ((-537 . -594) 94921) ((-385 . -1019) T) ((-525 . -594) 94908) ((-242 . -1019) T) ((-468 . -594) 94873) ((-205 . -23) T) ((-1135 . -762) 94826) ((-1192 . -97) T) ((-332 . -1189) 94803) ((-1190 . -97) T) ((-1158 . -107) 94695) ((-135 . -566) 94677) ((-925 . -126) T) ((-43 . -97) T) ((-220 . -789) 94628) ((-1145 . -1130) 94607) ((-98 . -464) 94591) ((-1193 . -660) 94561) ((-1008 . -46) 94522) ((-987 . -1031) T) ((-886 . -1031) T) ((-123 . -33) T) ((-117 . -33) T) ((-724 . -46) 94499) ((-722 . -46) 94471) ((-1145 . -517) 94382) ((-332 . -346) T) ((-457 . -1031) T) ((-1086 . 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-669) T) ((-1061 . -464) 93130) ((-1008 . -820) NIL) ((-805 . -1031) T) ((-113 . -843) NIL) ((-1192 . -1191) 93106) ((-1190 . -1191) 93085) ((-724 . -820) NIL) ((-722 . -820) 92944) ((-1185 . -25) T) ((-1185 . -21) T) ((-1124 . -97) 92922) ((-1025 . -373) T) ((-573 . -594) 92909) ((-431 . -820) NIL) ((-620 . -97) 92887) ((-1008 . -967) 92716) ((-805 . -23) T) ((-724 . -967) 92577) ((-722 . -967) 92436) ((-113 . -594) 92381) ((-431 . -967) 92259) ((-595 . -967) 92243) ((-576 . -97) T) ((-202 . -464) 92227) ((-1172 . -33) T) ((-584 . -660) 92211) ((-560 . -660) 92195) ((-616 . -37) 92155) ((-297 . -97) T) ((-83 . -566) 92137) ((-49 . -967) 92121) ((-1037 . -982) 92108) ((-1008 . -355) 92092) ((-58 . -55) 92054) ((-641 . -736) T) ((-641 . -733) T) ((-538 . -967) 92041) ((-489 . -967) 92018) ((-641 . -669) T) ((-294 . -976) 91909) ((-302 . -126) T) ((-291 . -976) T) ((-157 . -1031) T) ((-724 . -355) 91893) ((-722 . -355) 91877) ((-44 . -142) 91827) ((-935 . -924) 91809) ((-431 . -355) 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-588) 89862) ((-363 . -481) 89841) ((-775 . -787) 89820) ((-357 . -1130) T) ((-636 . -669) T) ((-317 . -983) T) ((-1136 . -924) 89772) ((-161 . -983) T) ((-98 . -566) 89704) ((-1088 . -136) 89683) ((-1088 . -138) 89662) ((-357 . -517) T) ((-1087 . -138) 89641) ((-1087 . -136) 89620) ((-1081 . -136) 89527) ((-385 . -269) T) ((-1081 . -138) 89434) ((-1043 . -138) 89413) ((-1043 . -136) 89392) ((-297 . -37) 89233) ((-157 . -126) T) ((-291 . -737) NIL) ((-291 . -734) NIL) ((-600 . -976) T) ((-47 . -594) 89198) ((-925 . -21) T) ((-123 . -941) 89182) ((-117 . -941) 89166) ((-925 . -25) T) ((-835 . -115) 89150) ((-1073 . -97) T) ((-758 . -789) 89129) ((-1145 . -126) T) ((-1086 . -25) T) ((-1086 . -21) T) ((-794 . -126) T) ((-1042 . -25) T) ((-1042 . -21) T) ((-793 . -25) T) ((-793 . -21) T) ((-724 . -286) 89108) ((-593 . -97) 89086) ((-581 . -97) T) ((-1074 . -288) 88881) ((-532 . -126) T) ((-571 . -787) 88860) ((-1071 . -464) 88844) ((-1065 . -142) 88794) ((-1061 . -566) 88756) ((-1061 . -567) 88717) ((-954 . -733) T) ((-954 . -736) T) ((-954 . -669) T) ((-459 . -288) 88655) ((-430 . -395) 88625) ((-329 . -160) T) ((-268 . -37) 88612) ((-253 . -97) T) ((-252 . -97) T) ((-251 . -97) T) ((-250 . -97) T) ((-249 . -97) T) ((-248 . -97) T) ((-247 . -97) T) ((-321 . -967) 88589) ((-194 . -97) T) ((-193 . -97) T) ((-191 . -97) T) ((-190 . -97) T) ((-189 . -97) T) ((-188 . -97) T) ((-185 . -97) T) ((-184 . -97) T) ((-655 . -982) 88412) ((-183 . -97) T) ((-182 . -97) T) ((-181 . -97) T) ((-180 . -97) T) ((-179 . -97) T) ((-178 . -97) T) ((-177 . -97) T) ((-176 . -97) T) ((-175 . -97) T) ((-332 . -669) T) ((-655 . -107) 88221) ((-616 . -211) 88205) ((-538 . -286) T) ((-489 . -286) T) ((-273 . -486) 88154) ((-103 . -288) NIL) ((-70 . -373) T) ((-1032 . -97) 87965) ((-775 . -389) 87949) ((-1037 . -737) T) ((-1037 . -734) T) ((-643 . -1019) T) ((-357 . -341) T) ((-157 . -466) 87927) ((-202 . -566) 87859) ((-128 . -1019) T) ((-112 . -1019) T) ((-47 . -669) T) ((-973 . -464) 87824) 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86679) ((-457 . -588) 86627) ((-39 . -967) 86517) ((-643 . -660) 86504) ((-655 . -213) T) ((-317 . -1019) T) ((-161 . -1019) T) ((-309 . -789) T) ((-396 . -429) 86454) ((-357 . -23) T) ((-337 . -37) 86419) ((-331 . -37) 86384) ((-323 . -37) 86349) ((-78 . -418) T) ((-78 . -373) T) ((-205 . -25) T) ((-205 . -21) T) ((-776 . -1031) T) ((-103 . -37) 86299) ((-769 . -1031) T) ((-716 . -1019) T) ((-112 . -660) 86286) ((-617 . -967) 86270) ((-565 . -97) T) ((-776 . -23) T) ((-769 . -23) T) ((-1071 . -265) 86247) ((-1032 . -288) 86185) ((-1021 . -215) 86169) ((-62 . -374) T) ((-62 . -373) T) ((-106 . -97) T) ((-39 . -355) 86146) ((-599 . -791) 86130) ((-987 . -21) T) ((-987 . -25) T) ((-757 . -211) 86100) ((-886 . -25) T) ((-886 . -21) T) ((-571 . -983) T) ((-457 . -25) T) ((-457 . -21) T) ((-957 . -288) 86038) ((-823 . -566) 86020) ((-819 . -566) 86002) ((-230 . -789) 85953) ((-229 . -789) 85904) ((-494 . -486) 85837) ((-805 . -588) 85814) ((-453 . -288) 85752) ((-440 . -288) 85690) ((-329 . -269) T) ((-1071 . -1160) 85674) ((-1057 . -566) 85636) ((-1057 . -567) 85597) ((-1055 . -97) T) ((-930 . -982) 85493) ((-39 . -834) 85445) ((-1071 . -558) 85422) ((-1198 . -594) 85409) ((-988 . -142) 85355) ((-806 . -1130) T) ((-930 . -107) 85237) ((-317 . -660) 85221) ((-800 . -566) 85203) ((-161 . -660) 85135) ((-385 . -265) 85093) ((-806 . -517) T) ((-103 . -378) 85075) ((-82 . -362) T) ((-82 . -373) T) ((-643 . -160) T) ((-94 . -669) T) ((-458 . -97) 84886) ((-94 . -450) T) ((-112 . -160) T) ((-1032 . -37) 84856) ((-157 . -588) 84804) ((-980 . -97) T) ((-805 . -25) T) ((-757 . -218) 84783) ((-805 . -21) T) ((-760 . -97) T) ((-392 . -97) T) ((-363 . -97) T) ((-106 . -288) NIL) ((-207 . -97) 84761) ((-123 . -1126) T) ((-117 . -1126) T) ((-964 . -126) T) ((-616 . -345) 84745) ((-930 . -976) T) ((-1145 . -588) 84693) ((-1023 . -566) 84675) ((-934 . -566) 84657) ((-487 . -23) T) ((-482 . -23) T) ((-321 . -286) T) ((-480 . -23) T) ((-300 . -126) T) ((-3 . -1019) T) ((-934 . -567) 84641) 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. -33) T) ((-113 . -818) 82463) ((-113 . -820) NIL) ((-573 . -967) 82348) ((-592 . -789) 82327) ((-1182 . -97) T) ((-274 . -97) T) ((-655 . -346) 82306) ((-113 . -967) 82283) ((-368 . -660) 82267) ((-571 . -660) 82251) ((-44 . -288) 82055) ((-758 . -136) 82034) ((-758 . -138) 82013) ((-1193 . -360) 81992) ((-761 . -789) T) ((-1174 . -1019) T) ((-1074 . -209) 81939) ((-364 . -789) 81918) ((-1164 . -1115) 81884) ((-1164 . -1112) 81850) ((-1157 . -1112) 81816) ((-487 . -126) T) ((-1157 . -1115) 81782) ((-1136 . -1112) 81748) ((-1136 . -1115) 81714) ((-1164 . -34) 81680) ((-1164 . -91) 81646) ((-584 . -566) 81615) ((-560 . -566) 81584) ((-205 . -789) T) ((-1157 . -91) 81550) ((-1157 . -34) 81516) ((-1156 . -1031) T) ((-1037 . -594) 81503) ((-1136 . -91) 81469) ((-1135 . -1031) T) ((-548 . -142) 81451) ((-1002 . -327) 81430) ((-113 . -355) 81407) ((-113 . -316) 81384) ((-161 . -269) T) ((-1136 . -34) 81350) ((-804 . -286) T) ((-291 . -736) NIL) ((-291 . -733) NIL) ((-294 . -669) 81200) 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. -663) T) ((-560 . -663) T) ((-757 . -486) 71959) ((-965 . -1126) T) ((-877 . -142) 71943) ((-491 . -97) 71893) ((-1008 . -1130) 71872) ((-454 . -566) 71824) ((-454 . -567) 71746) ((-60 . -1126) T) ((-724 . -1130) 71725) ((-722 . -1130) 71704) ((-1086 . -429) 71635) ((-1073 . -1019) T) ((-1057 . -594) 71609) ((-1008 . -517) 71540) ((-458 . -389) 71509) ((-573 . -854) 71488) ((-431 . -1130) 71467) ((-1042 . -429) 71418) ((-376 . -566) 71400) ((-620 . -486) 71333) ((-724 . -517) 71244) ((-722 . -517) 71175) ((-674 . -288) 71162) ((-610 . -25) T) ((-610 . -21) T) ((-431 . -517) 71093) ((-113 . -854) T) ((-113 . -762) NIL) ((-333 . -25) T) ((-333 . -21) T) ((-330 . -25) T) ((-330 . -21) T) ((-322 . -25) T) ((-322 . -21) T) ((-243 . -25) T) ((-243 . -21) T) ((-81 . -362) T) ((-81 . -373) T) ((-227 . -25) T) ((-227 . -21) T) ((-1174 . -566) 71075) ((-1121 . -1031) T) ((-1121 . -23) T) ((-1081 . -288) 70960) ((-1043 . -288) 70947) ((-800 . -594) 70907) ((-1002 . -660) 70775) ((-877 . -912) 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70042) ((-157 . -34) 70020) ((-157 . -91) 69998) ((-600 . -967) 69896) ((-458 . -983) 69827) ((-1032 . -1019) 69638) ((-1057 . -33) T) ((-616 . -464) 69622) ((-71 . -1126) T) ((-100 . -566) 69604) ((-1194 . -566) 69586) ((-359 . -566) 69568) ((-532 . -1115) T) ((-532 . -1112) T) ((-674 . -37) 69417) ((-497 . -566) 69399) ((-491 . -288) 69337) ((-473 . -566) 69319) ((-473 . -567) 69301) ((-1081 . -1066) NIL) ((-957 . -995) 69270) ((-957 . -1019) T) ((-935 . -97) T) ((-903 . -97) T) ((-848 . -97) T) ((-827 . -967) 69247) ((-1057 . -669) T) ((-934 . -594) 69192) ((-453 . -1019) T) ((-440 . -1019) T) ((-542 . -23) T) ((-532 . -34) T) ((-532 . -91) T) ((-405 . -97) T) ((-988 . -209) 69138) ((-124 . -97) T) ((-1088 . -37) 69035) ((-800 . -669) T) ((-636 . -854) T) ((-483 . -25) T) ((-479 . -21) T) ((-479 . -25) T) ((-1087 . -37) 68876) ((-317 . -976) T) ((-1081 . -37) 68672) ((-1002 . -160) T) ((-161 . -976) T) ((-1043 . -37) 68569) ((-655 . -46) 68546) ((-337 . -160) T) ((-331 . -160) T) 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. -660) 40639) ((-988 . -567) NIL) ((-988 . -566) 40621) ((-1157 . -660) 40462) ((-1136 . -660) 40258) ((-934 . -854) T) ((-645 . -566) 40227) ((-143 . -669) T) ((-1032 . -346) 40206) ((-935 . -486) NIL) ((-230 . -389) 40175) ((-229 . -389) 40144) ((-954 . -25) T) ((-954 . -21) T) ((-551 . -660) 40117) ((-550 . -660) 40014) ((-741 . -265) 39972) ((-122 . -97) 39950) ((-775 . -967) 39848) ((-157 . -770) 39827) ((-297 . -594) 39724) ((-757 . -33) T) ((-657 . -97) T) ((-1037 . -1031) T) ((-124 . -486) NIL) ((-956 . -1126) T) ((-357 . -37) 39689) ((-332 . -25) T) ((-332 . -21) T) ((-150 . -97) T) ((-146 . -97) T) ((-333 . -1179) 39673) ((-330 . -1179) 39657) ((-322 . -1179) 39641) ((-157 . -327) 39620) ((-525 . -789) T) ((-468 . -789) T) ((-1037 . -23) T) ((-85 . -566) 39602) ((-643 . -286) T) ((-776 . -37) 39572) ((-769 . -37) 39542) ((-1158 . -126) T) ((-1065 . -267) 39521) ((-897 . -735) 39474) ((-897 . -736) 39427) ((-757 . -733) 39406) ((-112 . -286) T) ((-89 . -288) 39344) ((-620 . 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. -1031) T) ((-556 . -1170) 10313) ((-643 . -23) T) ((-556 . -1019) 10263) ((-89 . -486) 10196) ((-161 . -341) T) ((-294 . -91) 10175) ((-294 . -34) 10154) ((-561 . -464) 10088) ((-128 . -23) T) ((-112 . -23) T) ((-661 . -1019) T) ((-452 . -464) 10025) ((-385 . -588) 9973) ((-599 . -967) 9871) ((-891 . -464) 9855) ((-333 . -983) T) ((-330 . -983) T) ((-322 . -983) T) ((-243 . -983) T) ((-227 . -983) T) ((-805 . -567) NIL) ((-805 . -566) 9837) ((-1193 . -21) T) ((-532 . -933) T) ((-674 . -669) T) ((-1193 . -25) T) ((-230 . -976) 9768) ((-229 . -976) 9699) ((-70 . -1126) T) ((-230 . -213) 9652) ((-229 . -213) 9605) ((-39 . -97) T) ((-844 . -983) T) ((-1095 . -97) T) ((-1088 . -669) T) ((-1087 . -669) T) ((-1081 . -669) T) ((-1081 . -733) NIL) ((-1081 . -736) NIL) ((-855 . -97) T) ((-1043 . -669) T) ((-713 . -97) T) ((-617 . -97) T) ((-451 . -1019) T) ((-317 . -1031) T) ((-161 . -1031) T) ((-297 . -854) 9584) ((-1156 . -660) 9425) ((-806 . -160) T) ((-1135 . -660) 9239) ((-782 . -21) 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. -594) 128550) ((-479 . -566) 128532) ((-329 . -138) 128514) ((-329 . -136) T) ((-337 . -1031) T) ((-331 . -1031) T) ((-323 . -1031) T) ((-935 . -286) T) ((-848 . -286) T) ((-806 . -223) T) ((-103 . -1031) T) ((-806 . -213) 128493) ((-1156 . -107) 128314) ((-1135 . -107) 128103) ((-225 . -1160) 128087) ((-525 . -787) T) ((-337 . -23) T) ((-332 . -327) T) ((-294 . -288) 128074) ((-291 . -288) 128015) ((-331 . -23) T) ((-297 . -126) T) ((-323 . -23) T) ((-935 . -952) T) ((-103 . -23) T) ((-225 . -558) 127992) ((-1158 . -37) 127884) ((-1145 . -843) 127863) ((-108 . -1019) T) ((-965 . -97) T) ((-1145 . -594) 127788) ((-805 . -736) NIL) ((-794 . -594) 127762) ((-805 . -733) NIL) ((-758 . -820) NIL) ((-805 . -669) T) ((-1008 . -486) 127635) ((-724 . -486) 127582) ((-722 . -486) 127534) ((-532 . -594) 127521) ((-758 . -967) 127351) ((-431 . -486) 127294) ((-366 . -367) T) ((-58 . -1126) T) ((-571 . -789) 127273) ((-473 . -607) T) ((-1061 . -908) 127242) ((-934 . -429) T) ((-641 . -787) T) 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125696) ((-469 . -267) 125673) ((-431 . -269) 125604) ((-965 . -288) 125455) ((-532 . -669) T) ((-608 . -566) 125437) ((-225 . -567) 125398) ((-225 . -566) 125310) ((-1062 . -33) T) ((-877 . -1126) T) ((-321 . -660) 125255) ((-616 . -25) T) ((-616 . -21) T) ((-451 . -976) T) ((-584 . -395) 125220) ((-560 . -395) 125185) ((-1037 . -1066) T) ((-538 . -269) T) ((-489 . -269) T) ((-1157 . -286) 125164) ((-451 . -213) 125116) ((-451 . -223) 125095) ((-1136 . -286) 125074) ((-1002 . -126) T) ((-806 . -737) 125053) ((-135 . -97) T) ((-39 . -1019) T) ((-806 . -734) 125032) ((-592 . -941) 125016) ((-537 . -983) T) ((-525 . -983) T) ((-468 . -983) T) ((-385 . -429) T) ((-337 . -126) T) ((-294 . -378) 125000) ((-291 . -378) 124961) ((-331 . -126) T) ((-323 . -126) T) ((-1136 . -952) NIL) ((-1095 . -1019) T) ((-1014 . -566) 124928) ((-103 . -126) T) ((-1037 . -37) 124915) ((-855 . -1019) T) ((-713 . -1019) T) ((-617 . -1019) T) ((-643 . -138) T) ((-112 . -138) T) ((-1192 . -21) T) ((-1192 . -25) T) ((-1190 . -21) T) ((-1190 . -25) T) ((-610 . -982) 124899) ((-497 . -789) T) ((-473 . -789) T) ((-333 . -982) 124851) ((-330 . -982) 124803) ((-322 . -982) 124755) ((-230 . -1126) T) ((-229 . -1126) T) ((-243 . -982) 124598) ((-227 . -982) 124441) ((-610 . -107) 124420) ((-333 . -107) 124358) ((-330 . -107) 124296) ((-322 . -107) 124234) ((-243 . -107) 124063) ((-227 . -107) 123892) ((-759 . -1130) 123871) ((-573 . -389) 123855) ((-43 . -21) T) ((-43 . -25) T) ((-757 . -588) 123763) ((-759 . -517) 123742) ((-230 . -967) 123571) ((-229 . -967) 123400) ((-122 . -115) 123384) ((-844 . -982) 123349) ((-641 . -983) T) ((-655 . -97) T) ((-321 . -160) T) ((-143 . -21) T) ((-143 . -25) T) ((-86 . -566) 123331) ((-844 . -107) 123287) ((-39 . -660) 123232) ((-804 . -1019) T) ((-305 . -567) 123193) ((-305 . -566) 123105) ((-1135 . -734) 123058) ((-1135 . -737) 123011) ((-230 . -355) 122981) ((-229 . -355) 122951) ((-600 . -37) 122921) ((-561 . -33) T) ((-458 . -1031) 122852) ((-452 . -33) T) 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NIL) ((-357 . -594) 121508) ((-804 . -660) 121495) ((-973 . -142) 121460) ((-39 . -160) T) ((-636 . -389) 121442) ((-655 . -288) 121429) ((-776 . -594) 121389) ((-769 . -594) 121363) ((-297 . -25) T) ((-297 . -21) T) ((-604 . -265) 121342) ((-537 . -1019) T) ((-525 . -1019) T) ((-468 . -1019) T) ((-225 . -267) 121319) ((-291 . -211) 121280) ((-1086 . -820) NIL) ((-1042 . -820) 121139) ((-125 . -789) T) ((-1086 . -967) 121021) ((-1042 . -967) 120906) ((-169 . -566) 120888) ((-793 . -967) 120786) ((-724 . -265) 120713) ((-759 . -1031) T) ((-964 . -669) T) ((-556 . -597) 120697) ((-973 . -908) 120626) ((-930 . -97) T) ((-759 . -23) T) ((-655 . -1066) 120604) ((-636 . -983) T) ((-556 . -351) 120588) ((-329 . -429) T) ((-321 . -269) T) ((-1173 . -1019) T) ((-377 . -97) T) ((-268 . -21) T) ((-268 . -25) T) ((-339 . -669) T) ((-653 . -1019) T) ((-641 . -1019) T) ((-339 . -450) T) ((-1121 . -566) 120570) ((-1086 . -355) 120554) ((-1042 . -355) 120538) ((-954 . -389) 120500) ((-132 . -209) 120482) ((-357 . -736) T) ((-357 . -733) T) ((-804 . -160) T) ((-357 . -669) T) ((-654 . -566) 120464) ((-655 . -37) 120293) ((-1172 . -1170) 120277) ((-329 . -380) T) ((-1172 . -1019) 120227) ((-537 . -660) 120214) ((-525 . -660) 120201) ((-468 . -660) 120166) ((-294 . -578) 120145) ((-776 . -669) T) ((-769 . -669) T) ((-592 . -1126) T) ((-1002 . -588) 120093) ((-1086 . -834) 120036) ((-1042 . -834) 120020) ((-608 . -982) 120004) ((-103 . -588) 119986) ((-458 . -126) 119857) ((-1092 . -1031) T) ((-886 . -46) 119826) ((-573 . -1019) T) ((-608 . -107) 119805) ((-305 . -267) 119782) ((-457 . -46) 119739) ((-1092 . -23) T) ((-113 . -1019) T) ((-98 . -97) 119717) ((-1182 . -1031) T) ((-980 . -126) T) ((-954 . -983) T) ((-761 . -967) 119701) ((-934 . -667) 119673) ((-1182 . -23) T) ((-641 . -660) 119638) ((-542 . -566) 119620) ((-364 . -967) 119604) ((-332 . -983) T) ((-363 . -126) T) ((-302 . -967) 119588) ((-205 . -820) 119570) ((-935 . -854) T) ((-89 . -33) T) ((-935 . -762) T) ((-848 . -854) T) ((-462 . -1130) T) ((-1107 . -566) 119552) ((-1024 . -1019) T) ((-198 . -1130) T) ((-930 . -288) 119517) ((-205 . -967) 119477) ((-39 . -269) T) ((-1002 . -21) T) ((-1002 . -25) T) ((-1037 . -770) T) ((-462 . -517) T) ((-337 . -25) T) ((-198 . -517) T) ((-337 . -21) T) ((-331 . -25) T) ((-331 . -21) T) ((-657 . -594) 119437) ((-323 . -25) T) ((-323 . -21) T) ((-103 . -25) T) ((-103 . -21) T) ((-47 . -983) T) ((-537 . -160) T) ((-525 . -160) T) ((-468 . -160) T) ((-604 . -566) 119419) ((-680 . -679) 119403) ((-314 . -566) 119385) ((-66 . -361) T) ((-66 . -373) T) ((-1021 . -102) 119369) ((-987 . -820) 119351) ((-886 . -820) 119276) ((-599 . -1031) T) ((-573 . -660) 119263) ((-457 . -820) NIL) ((-1061 . -97) T) ((-987 . -967) 119245) ((-92 . -566) 119227) ((-454 . -138) T) ((-886 . -967) 119109) ((-113 . -660) 119054) ((-599 . -23) T) ((-457 . -967) 118932) ((-1008 . -567) NIL) ((-1008 . -566) 118914) ((-724 . -567) NIL) ((-724 . -566) 118875) ((-722 . -567) 118510) ((-722 . -566) 118424) ((-1032 . -588) 118332) ((-438 . -566) 118314) ((-431 . -566) 118296) ((-431 . -567) 118157) ((-965 . -209) 118103) ((-122 . -33) T) ((-759 . -126) T) ((-806 . -843) 118082) ((-595 . -566) 118064) ((-333 . -1189) 118048) ((-330 . -1189) 118032) ((-322 . -1189) 118016) ((-123 . -486) 117949) ((-117 . -486) 117882) ((-483 . -734) T) ((-483 . -737) T) ((-482 . -736) T) ((-98 . -288) 117820) ((-202 . -97) 117798) ((-636 . -1019) T) ((-641 . -160) T) ((-806 . -594) 117750) ((-63 . -362) T) ((-254 . -566) 117732) ((-63 . -373) T) ((-886 . -355) 117716) ((-804 . -269) T) ((-49 . -566) 117698) ((-930 . -37) 117646) ((-538 . -566) 117628) ((-457 . -355) 117612) ((-538 . -567) 117594) ((-489 . -566) 117576) ((-844 . -1189) 117563) ((-805 . -1126) T) ((-643 . -429) T) ((-468 . -486) 117529) ((-462 . -341) T) ((-333 . -346) 117508) ((-330 . -346) 117487) ((-322 . -346) 117466) ((-198 . -341) T) ((-657 . -669) T) ((-112 . -429) T) ((-1193 . -1184) 117450) ((-805 . -818) 117427) ((-805 . -820) NIL) ((-897 . -789) 117326) ((-757 . -789) 117277) ((-600 . -602) 117261) ((-1113 . -33) T) ((-159 . -566) 117243) ((-1032 . -21) 117154) ((-1032 . -25) 117006) ((-805 . -967) 116983) ((-886 . -834) 116964) ((-1145 . -46) 116941) ((-844 . -346) T) ((-57 . -597) 116925) ((-488 . -597) 116909) ((-457 . -834) 116886) ((-69 . -418) T) ((-69 . -373) T) ((-469 . -597) 116870) ((-57 . -351) 116854) ((-573 . -160) T) ((-488 . -351) 116838) ((-469 . -351) 116822) ((-769 . -651) 116806) ((-1086 . -286) 116785) ((-1092 . -126) T) ((-113 . -160) T) ((-1061 . -288) 116723) ((-157 . -1126) T) ((-584 . -687) 116707) ((-560 . -687) 116691) ((-1182 . -126) T) ((-1157 . -854) 116670) ((-1136 . -854) 116649) ((-1136 . -762) NIL) ((-636 . -660) 116599) ((-1135 . -843) 116552) ((-954 . -1019) T) ((-805 . -355) 116529) ((-805 . -316) 116506) ((-839 . -1031) T) ((-157 . -818) 116490) ((-157 . -820) 116415) ((-462 . -1031) T) ((-332 . -1019) T) ((-198 . -1031) T) ((-74 . -418) T) ((-74 . -373) T) 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T) ((-1121 . -107) 114900) ((-451 . -594) 114797) ((-332 . -660) 114742) ((-157 . -834) 114701) ((-641 . -269) T) ((-636 . -160) T) ((-654 . -107) 114657) ((-1198 . -983) T) ((-1145 . -355) 114641) ((-396 . -1130) 114619) ((-291 . -787) NIL) ((-396 . -517) T) ((-205 . -286) T) ((-1135 . -733) 114572) ((-1135 . -736) 114525) ((-1156 . -669) T) ((-1135 . -669) T) ((-47 . -660) 114490) ((-205 . -952) T) ((-329 . -1179) 114467) ((-1158 . -389) 114433) ((-661 . -669) T) ((-1145 . -834) 114376) ((-108 . -566) 114358) ((-108 . -567) 114340) ((-661 . -450) T) ((-458 . -21) 114251) ((-123 . -464) 114235) ((-117 . -464) 114219) ((-458 . -25) 114071) ((-573 . -269) T) ((-542 . -982) 114046) ((-415 . -1019) T) ((-987 . -286) T) ((-113 . -269) T) ((-1023 . -97) T) ((-934 . -97) T) ((-542 . -107) 114014) ((-1057 . -288) 113952) ((-1121 . -976) T) ((-987 . -952) T) ((-64 . -1126) T) ((-980 . -25) T) ((-980 . -21) T) ((-654 . -976) T) ((-363 . -21) T) ((-363 . -25) T) ((-636 . -486) NIL) ((-954 . -160) T) ((-654 . -223) T) ((-987 . -510) T) ((-475 . -97) T) ((-332 . -160) T) ((-321 . -566) 113934) ((-372 . -566) 113916) ((-451 . -669) T) ((-1037 . -787) T) ((-826 . -967) 113884) ((-103 . -789) T) ((-604 . -982) 113868) ((-462 . -126) T) ((-1158 . -983) T) ((-198 . -126) T) ((-1071 . -97) 113846) ((-94 . -1019) T) ((-225 . -612) 113830) ((-225 . -597) 113814) ((-604 . -107) 113793) ((-294 . -389) 113777) ((-225 . -351) 113761) ((-1074 . -215) 113708) ((-930 . -211) 113692) ((-72 . -1126) T) ((-47 . -160) T) ((-643 . -365) T) ((-643 . -134) T) ((-1193 . -97) T) ((-1008 . -982) 113535) ((-243 . -843) 113514) ((-227 . -843) 113493) ((-724 . -982) 113316) ((-722 . -982) 113159) ((-561 . -1126) T) ((-1079 . -566) 113141) ((-1008 . -107) 112970) ((-973 . -97) T) ((-452 . -1126) T) ((-438 . -982) 112941) ((-431 . -982) 112784) ((-610 . -594) 112768) ((-805 . -286) T) ((-724 . -107) 112577) ((-722 . -107) 112406) ((-333 . -594) 112358) ((-330 . -594) 112310) ((-322 . -594) 112262) 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-566) 111126) ((-1100 . -33) T) ((-855 . -566) 111108) ((-1032 . -789) 111059) ((-713 . -566) 111041) ((-617 . -566) 111023) ((-1071 . -288) 110961) ((-455 . -33) T) ((-1012 . -1126) T) ((-454 . -429) T) ((-1008 . -976) T) ((-1056 . -33) T) ((-724 . -976) T) ((-722 . -976) T) ((-593 . -215) 110945) ((-581 . -215) 110891) ((-1145 . -286) 110870) ((-1008 . -304) 110831) ((-431 . -976) T) ((-1092 . -21) T) ((-1008 . -213) 110810) ((-724 . -304) 110787) ((-724 . -213) T) ((-722 . -304) 110759) ((-305 . -597) 110743) ((-674 . -1130) 110722) ((-1092 . -25) T) ((-57 . -33) T) ((-490 . -33) T) ((-488 . -33) T) ((-431 . -304) 110701) ((-305 . -351) 110685) ((-470 . -33) T) ((-469 . -33) T) ((-934 . -1066) NIL) ((-584 . -97) T) ((-560 . -97) T) ((-674 . -517) 110616) ((-333 . -669) T) ((-330 . -669) T) ((-322 . -669) T) ((-243 . -669) T) ((-227 . -669) T) ((-973 . -288) 110524) ((-835 . -1019) 110502) ((-49 . -976) T) ((-1182 . -21) T) ((-1182 . -25) T) ((-1088 . -517) 110481) ((-1087 . -1130) 110460) ((-538 . -976) T) ((-489 . -976) T) ((-1081 . -1130) 110439) ((-339 . -967) 110423) ((-300 . -967) 110407) ((-954 . -269) T) ((-357 . -820) 110389) ((-1087 . -517) 110340) ((-1081 . -517) 110291) ((-934 . -37) 110236) ((-741 . -1031) T) ((-844 . -669) T) ((-538 . -223) T) ((-538 . -213) T) ((-489 . -213) T) ((-489 . -223) T) ((-1043 . -517) 110215) ((-332 . -269) T) ((-593 . -637) 110199) ((-357 . -967) 110159) ((-1037 . -983) T) ((-98 . -121) 110143) ((-741 . -23) T) ((-1172 . -265) 110120) ((-385 . -288) 110085) ((-1192 . -1187) 110061) ((-1190 . -1187) 110040) ((-1158 . -1019) T) ((-804 . -566) 110022) ((-776 . -967) 109991) ((-185 . -729) T) ((-184 . -729) T) ((-183 . -729) T) ((-182 . -729) T) ((-181 . -729) T) ((-180 . -729) T) ((-179 . -729) T) ((-178 . -729) T) ((-177 . -729) T) ((-176 . -729) T) ((-468 . -933) T) ((-253 . -778) T) ((-252 . -778) T) ((-251 . -778) T) ((-250 . -778) T) ((-47 . -269) T) ((-249 . -778) T) ((-248 . -778) T) ((-247 . -778) T) ((-175 . -729) 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108279) ((-1172 . -567) 108240) ((-1158 . -160) T) ((-225 . -33) T) ((-860 . -906) T) ((-1113 . -1126) T) ((-608 . -733) 108219) ((-608 . -736) 108198) ((-376 . -373) T) ((-494 . -97) 108176) ((-965 . -1019) T) ((-202 . -926) 108160) ((-477 . -97) T) ((-573 . -566) 108142) ((-44 . -789) NIL) ((-573 . -567) 108119) ((-965 . -563) 108094) ((-835 . -486) 108027) ((-321 . -976) T) ((-113 . -567) NIL) ((-113 . -566) 108009) ((-806 . -1126) T) ((-616 . -395) 107993) ((-616 . -1040) 107938) ((-473 . -142) 107920) ((-321 . -213) T) ((-321 . -223) T) ((-39 . -982) 107865) ((-806 . -818) 107849) ((-806 . -820) 107774) ((-655 . -983) T) ((-636 . -933) NIL) ((-3 . |UnionCategory|) T) ((-1156 . -46) 107744) ((-1135 . -46) 107721) ((-1056 . -941) 107692) ((-205 . -854) T) ((-39 . -107) 107621) ((-806 . -967) 107488) ((-1037 . -660) 107475) ((-1024 . -566) 107457) ((-1002 . -138) 107436) ((-1002 . -136) 107387) ((-935 . -341) T) ((-297 . -1115) 107353) ((-357 . -286) T) ((-297 . -1112) 107319) ((-294 . -160) 107298) ((-291 . -160) T) ((-934 . -211) 107275) ((-848 . -341) T) ((-538 . -1189) 107262) ((-489 . -1189) 107239) ((-337 . -138) 107218) ((-337 . -136) 107169) ((-331 . -138) 107148) ((-331 . -136) 107099) ((-561 . -1103) 107075) ((-323 . -138) 107054) ((-323 . -136) 107005) ((-297 . -34) 106971) ((-452 . -1103) 106950) ((0 . |EnumerationCategory|) T) ((-297 . -91) 106916) ((-357 . -952) T) ((-103 . -138) T) ((-103 . -136) NIL) ((-44 . -215) 106866) ((-600 . -1019) T) ((-561 . -102) 106813) ((-460 . -126) T) ((-452 . -102) 106763) ((-220 . -1031) 106694) ((-806 . -355) 106678) ((-806 . -316) 106662) ((-220 . -23) 106533) ((-987 . -854) T) ((-987 . -762) T) ((-538 . -346) T) ((-489 . -346) T) ((-329 . -1066) T) ((-305 . -33) T) ((-43 . -395) 106517) ((-807 . -1126) T) ((-368 . -687) 106501) ((-1183 . -486) 106434) ((-674 . -126) T) ((-1164 . -517) 106413) ((-1157 . -1130) 106392) ((-1157 . -517) 106343) ((-680 . -486) 106276) ((-1136 . -1130) 106255) ((-1136 . -517) 106206) 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105153) ((-805 . -854) T) ((-805 . -762) NIL) ((-799 . -789) T) ((-1135 . -316) 105123) ((-1135 . -355) 105093) ((-202 . -1038) 105077) ((-1172 . -267) 105054) ((-1121 . -594) 104979) ((-896 . -21) T) ((-896 . -25) T) ((-678 . -21) T) ((-678 . -25) T) ((-658 . -21) T) ((-658 . -25) T) ((-654 . -594) 104944) ((-430 . -21) T) ((-430 . -25) T) ((-317 . -97) T) ((-161 . -97) T) ((-930 . -983) T) ((-804 . -976) T) ((-716 . -97) T) ((-1157 . -341) 104923) ((-1156 . -834) 104829) ((-1136 . -341) 104808) ((-1135 . -834) 104659) ((-954 . -566) 104641) ((-385 . -770) 104594) ((-1088 . -466) 104560) ((-157 . -854) 104491) ((-1087 . -466) 104457) ((-1081 . -466) 104423) ((-655 . -1019) T) ((-1043 . -466) 104389) ((-537 . -982) 104376) ((-525 . -982) 104363) ((-468 . -982) 104328) ((-294 . -269) 104307) ((-291 . -269) T) ((-332 . -566) 104289) ((-396 . -25) T) ((-396 . -21) T) ((-94 . -265) 104268) ((-537 . -107) 104253) ((-525 . -107) 104238) ((-468 . -107) 104194) ((-1090 . -820) 104161) ((-835 . 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101767) ((-57 . -1126) T) ((-490 . -1126) T) ((-488 . -1126) T) ((-470 . -1126) T) ((-469 . -1126) T) ((-415 . -566) 101749) ((-412 . -566) 101731) ((-3 . -97) T) ((-957 . -1120) 101700) ((-775 . -97) T) ((-632 . -55) 101658) ((-641 . -976) T) ((-49 . -594) 101632) ((-268 . -429) T) ((-453 . -1120) 101601) ((0 . -97) T) ((-538 . -594) 101566) ((-489 . -594) 101511) ((-48 . -97) T) ((-844 . -967) 101498) ((-641 . -223) T) ((-1002 . -387) 101477) ((-674 . -588) 101425) ((-930 . -1019) T) ((-655 . -160) 101316) ((-462 . -924) 101298) ((-243 . -355) 101282) ((-227 . -355) 101266) ((-377 . -1019) T) ((-317 . -37) 101250) ((-956 . -97) 101228) ((-198 . -924) 101210) ((-161 . -37) 101142) ((-1156 . -286) 101121) ((-1135 . -286) 101100) ((-604 . -669) T) ((-94 . -566) 101082) ((-1081 . -588) 101034) ((-460 . -25) T) ((-460 . -21) T) ((-1135 . -952) 100987) ((-573 . -976) T) ((-357 . -382) T) ((-368 . -97) T) ((-243 . -834) 100933) ((-227 . -834) 100910) ((-113 . -976) T) ((-758 . -1031) T) 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-341) 93146) ((-525 . -733) T) ((-525 . -669) T) ((-468 . -669) T) ((-1061 . -464) 93130) ((-1008 . -820) NIL) ((-805 . -1031) T) ((-113 . -843) NIL) ((-1192 . -1191) 93106) ((-1190 . -1191) 93085) ((-724 . -820) NIL) ((-722 . -820) 92944) ((-1185 . -25) T) ((-1185 . -21) T) ((-1124 . -97) 92922) ((-1025 . -373) T) ((-573 . -594) 92909) ((-431 . -820) NIL) ((-620 . -97) 92887) ((-1008 . -967) 92716) ((-805 . -23) T) ((-724 . -967) 92577) ((-722 . -967) 92436) ((-113 . -594) 92381) ((-431 . -967) 92259) ((-595 . -967) 92243) ((-576 . -97) T) ((-202 . -464) 92227) ((-1172 . -33) T) ((-584 . -660) 92211) ((-560 . -660) 92195) ((-616 . -37) 92155) ((-297 . -97) T) ((-83 . -566) 92137) ((-49 . -967) 92121) ((-1037 . -982) 92108) ((-1008 . -355) 92092) ((-58 . -55) 92054) ((-641 . -736) T) ((-641 . -733) T) ((-538 . -967) 92041) ((-489 . -967) 92018) ((-641 . -669) T) ((-294 . -976) 91909) ((-302 . -126) T) ((-291 . -976) T) ((-157 . -1031) T) ((-724 . -355) 91893) ((-722 . -355) 91877) 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T) ((-300 . -23) T) ((-877 . -789) 86702) ((-655 . -304) 86679) ((-457 . -588) 86627) ((-39 . -967) 86517) ((-643 . -660) 86504) ((-655 . -213) T) ((-317 . -1019) T) ((-161 . -1019) T) ((-309 . -789) T) ((-396 . -429) 86454) ((-357 . -23) T) ((-337 . -37) 86419) ((-331 . -37) 86384) ((-323 . -37) 86349) ((-78 . -418) T) ((-78 . -373) T) ((-205 . -25) T) ((-205 . -21) T) ((-776 . -1031) T) ((-103 . -37) 86299) ((-769 . -1031) T) ((-716 . -1019) T) ((-112 . -660) 86286) ((-617 . -967) 86270) ((-565 . -97) T) ((-776 . -23) T) ((-769 . -23) T) ((-1071 . -265) 86247) ((-1032 . -288) 86185) ((-1021 . -215) 86169) ((-62 . -374) T) ((-62 . -373) T) ((-106 . -97) T) ((-39 . -355) 86146) ((-599 . -791) 86130) ((-987 . -21) T) ((-987 . -25) T) ((-757 . -211) 86100) ((-886 . -25) T) ((-886 . -21) T) ((-571 . -983) T) ((-457 . -25) T) ((-457 . -21) T) ((-957 . -288) 86038) ((-823 . -566) 86020) ((-819 . -566) 86002) ((-230 . -789) 85953) ((-229 . -789) 85904) ((-494 . -486) 85837) ((-805 . -588) 85814) ((-453 . -288) 85752) ((-440 . -288) 85690) ((-329 . -269) T) ((-1071 . -1160) 85674) ((-1057 . -566) 85636) ((-1057 . -567) 85597) ((-1055 . -97) T) ((-930 . -982) 85493) ((-39 . -834) 85445) ((-1071 . -558) 85422) ((-1198 . -594) 85409) ((-988 . -142) 85355) ((-806 . -1130) T) ((-930 . -107) 85237) ((-317 . -660) 85221) ((-800 . -566) 85203) ((-161 . -660) 85135) ((-385 . -265) 85093) ((-806 . -517) T) ((-103 . -378) 85075) ((-82 . -362) T) ((-82 . -373) T) ((-643 . -160) T) ((-94 . -669) T) ((-458 . -97) 84886) ((-94 . -450) T) ((-112 . -160) T) ((-1032 . -37) 84856) ((-157 . -588) 84804) ((-980 . -97) T) ((-805 . -25) T) ((-757 . -218) 84783) ((-805 . -21) T) ((-760 . -97) T) ((-392 . -97) T) ((-363 . -97) T) ((-106 . -288) NIL) ((-207 . -97) 84761) ((-123 . -1126) T) ((-117 . -1126) T) ((-964 . -126) T) ((-616 . -345) 84745) ((-930 . -976) T) ((-1145 . -588) 84693) ((-1023 . -566) 84675) ((-934 . -566) 84657) ((-487 . -23) T) ((-482 . -23) T) ((-321 . -286) T) ((-480 . -23) 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-464) 82516) ((-680 . -33) T) ((-458 . -37) 82486) ((-132 . -33) T) ((-113 . -818) 82463) ((-113 . -820) NIL) ((-573 . -967) 82348) ((-592 . -789) 82327) ((-1182 . -97) T) ((-274 . -97) T) ((-655 . -346) 82306) ((-113 . -967) 82283) ((-368 . -660) 82267) ((-571 . -660) 82251) ((-44 . -288) 82055) ((-758 . -136) 82034) ((-758 . -138) 82013) ((-1193 . -360) 81992) ((-761 . -789) T) ((-1174 . -1019) T) ((-1074 . -209) 81939) ((-364 . -789) 81918) ((-1164 . -1115) 81884) ((-1164 . -1112) 81850) ((-1157 . -1112) 81816) ((-487 . -126) T) ((-1157 . -1115) 81782) ((-1136 . -1112) 81748) ((-1136 . -1115) 81714) ((-1164 . -34) 81680) ((-1164 . -91) 81646) ((-584 . -566) 81615) ((-560 . -566) 81584) ((-205 . -789) T) ((-1157 . -91) 81550) ((-1157 . -34) 81516) ((-1156 . -1031) T) ((-1037 . -594) 81503) ((-1136 . -91) 81469) ((-1135 . -1031) T) ((-548 . -142) 81451) ((-1002 . -327) 81430) ((-113 . -355) 81407) ((-113 . -316) 81384) ((-161 . -269) T) ((-1136 . -34) 81350) ((-804 . -286) T) ((-291 . 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. -1064) 72041) ((-112 . -107) 72026) ((-584 . -663) T) ((-560 . -663) T) ((-757 . -486) 71959) ((-965 . -1126) T) ((-877 . -142) 71943) ((-491 . -97) 71893) ((-1008 . -1130) 71872) ((-454 . -566) 71824) ((-454 . -567) 71746) ((-60 . -1126) T) ((-724 . -1130) 71725) ((-722 . -1130) 71704) ((-1086 . -429) 71635) ((-1073 . -1019) T) ((-1057 . -594) 71609) ((-1008 . -517) 71540) ((-458 . -389) 71509) ((-573 . -854) 71488) ((-431 . -1130) 71467) ((-1042 . -429) 71418) ((-376 . -566) 71400) ((-620 . -486) 71333) ((-724 . -517) 71244) ((-722 . -517) 71175) ((-674 . -288) 71162) ((-610 . -25) T) ((-610 . -21) T) ((-431 . -517) 71093) ((-113 . -854) T) ((-113 . -762) NIL) ((-333 . -25) T) ((-333 . -21) T) ((-330 . -25) T) ((-330 . -21) T) ((-322 . -25) T) ((-322 . -21) T) ((-243 . -25) T) ((-243 . -21) T) ((-81 . -362) T) ((-81 . -373) T) ((-227 . -25) T) ((-227 . -21) T) ((-1174 . -566) 71075) ((-1121 . -1031) T) ((-1121 . -23) T) ((-1081 . -288) 70960) ((-1043 . -288) 70947) ((-800 . -594) 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. -1019) T) ((-175 . -1019) T) ((-220 . -97) 70042) ((-157 . -34) 70020) ((-157 . -91) 69998) ((-600 . -967) 69896) ((-458 . -983) 69827) ((-1032 . -1019) 69638) ((-1057 . -33) T) ((-616 . -464) 69622) ((-71 . -1126) T) ((-100 . -566) 69604) ((-1194 . -566) 69586) ((-359 . -566) 69568) ((-532 . -1115) T) ((-532 . -1112) T) ((-674 . -37) 69417) ((-497 . -566) 69399) ((-491 . -288) 69337) ((-473 . -566) 69319) ((-473 . -567) 69301) ((-1081 . -1066) NIL) ((-957 . -995) 69270) ((-957 . -1019) T) ((-935 . -97) T) ((-903 . -97) T) ((-848 . -97) T) ((-827 . -967) 69247) ((-1057 . -669) T) ((-934 . -594) 69192) ((-453 . -1019) T) ((-440 . -1019) T) ((-542 . -23) T) ((-532 . -34) T) ((-532 . -91) T) ((-405 . -97) T) ((-988 . -209) 69138) ((-124 . -97) T) ((-1088 . -37) 69035) ((-800 . -669) T) ((-636 . -854) T) ((-483 . -25) T) ((-479 . -21) T) ((-479 . -25) T) ((-1087 . -37) 68876) ((-317 . -976) T) ((-1081 . -37) 68672) ((-1002 . -160) T) ((-161 . -976) T) ((-1043 . -37) 68569) ((-655 . -46) 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. -566) 36833) ((-511 . -567) NIL) ((-511 . -566) 36815) ((-1081 . -265) 36663) ((-462 . -982) 36613) ((-654 . -429) T) ((-483 . -481) 36592) ((-479 . -481) 36571) ((-198 . -982) 36521) ((-337 . -594) 36473) ((-331 . -594) 36425) ((-205 . -787) T) ((-323 . -594) 36377) ((-556 . -97) 36327) ((-458 . -346) 36306) ((-103 . -594) 36256) ((-462 . -107) 36190) ((-220 . -464) 36174) ((-321 . -138) 36156) ((-321 . -136) T) ((-157 . -348) 36127) ((-877 . -1170) 36111) ((-198 . -107) 36045) ((-806 . -288) 36010) ((-877 . -1019) 35960) ((-741 . -567) 35921) ((-741 . -566) 35903) ((-661 . -97) T) ((-309 . -1019) T) ((-1037 . -126) T) ((-657 . -37) 35873) ((-294 . -466) 35852) ((-473 . -1126) T) ((-1156 . -263) 35818) ((-1135 . -263) 35784) ((-305 . -142) 35768) ((-988 . -267) 35743) ((-1185 . -660) 35713) ((-1074 . -33) T) ((-1194 . -967) 35690) ((-445 . -566) 35672) ((-459 . -33) T) ((-359 . -967) 35656) ((-1086 . -983) T) ((-1042 . -983) T) ((-793 . -983) T) ((-987 . -787) T) ((-758 . -160) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 09609645..99fae7ea 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3419278778) +(30 . 3420122810) (4257 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -460,647 +460,650 @@ |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |expand| |fractRagits| |OMsupportsCD?| |lex| - |tableForDiscreteLogarithm| |Beta| |recur| |numberOfFractionalTerms| - |currentSubProgram| |third| |sumSquares| |jacobi| |highCommonTerms| - |dec| |filterWhile| |OMread| |PDESolve| |unit?| |infix| |lazyPquo| - |cExp| |setMinPoints3D| |choosemon| |internal?| |listRepresentation| - |airyAi| |quickSort| |setelt| - |solveLinearPolynomialEquationByFractions| |filterUntil| - |torsionIfCan| |lexGroebner| |subNodeOf?| |c05nbf| |viewDeltaXDefault| - |redPo| |expandLog| |cAcos| |rewriteIdealWithHeadRemainder| |const| - |qroot| |flatten| |e02bef| |has?| |triangSolve| |contains?| |select| - |iFTable| |OMsetEncoding| |computeInt| |outputMeasure| |ParCondList| - |diagonalProduct| |expandPower| |lquo| |extractPoint| |squareFree| - |min| |copy| |SFunction| |intermediateResultsIF| |nextIrreduciblePoly| - |complexExpand| |symmetricPower| |withPredicates| |roman| |pointColor| - |primintfldpoly| |position!| |parent| |mapExpon| |sequences| - |normInvertible?| |mindeg| |cubic| |closedCurve?| |charthRoot| |iicot| - |complexNumeric| |zag| |autoCoerce| |conical| |trunc| |lyndon?| - |collectQuasiMonic| |pointColorPalette| |exponents| |mpsode| |c05adf| - |stripCommentsAndBlanks| |insertBottom!| |implies?| |exp1| - |inverseColeman| |reverseLex| |makeSUP| - |rewriteSetByReducingWithParticularGenerators| |setMaxPoints| - |leftTraceMatrix| |minordet| |extractBottom!| |kernels| |deepExpand| - |df2fi| |reducedSystem| |tValues| |calcRanges| |check| - |linearAssociatedOrder| |fTable| |normFactors| |insertMatch| - |univariate| |solve1| |radicalRoots| |makeRecord| |algDsolve| - |hypergeometric0F1| |dmp2rfi| |compdegd| |atrapezoidal| |stirling1| - |round| |bag| |hconcat| |constantOperator| |moreAlgebraic?| |iiabs| - |OMmakeConn| |splitConstant| |roughSubIdeal?| |derivative| |birth| - |outerProduct| |modularGcdPrimitive| |FormatArabic| |iiasin| - |dequeue!| |fractionPart| |transpose| |datalist| - |integralMatrixAtInfinity| |hasTopPredicate?| |cSin| |coleman| |width| - |shuffle| |OMconnectTCP| |simplify| |setEmpty!| |addPointLast| - |iiperm| |factorset| |fixedPoint| |OMconnInDevice| |getCurve| - |OMgetEndError| |reducedDiscriminant| |connect| |setLabelValue| - |makeResult| |e01bgf| |adaptive?| |evenInfiniteProduct| - |fortranLogical| |intcompBasis| |extractClosed| |clearTheIFTable| - |ratDsolve| |unaryFunction| |removeZeroes| |polarCoordinates| - |OMputVariable| |leftRankPolynomial| |localUnquote| |coth2tanh| - |whileLoop| |formula| |cAsech| |minPol| |rightQuotient| |setPrologue!| - |cyclic| |edf2efi| |plus!| |cCot| |OMunhandledSymbol| |legendreP| - |eigenvector| |f02aef| |measure| |appendPoint| |viewSizeDefault| - |dflist| |optional| |e02bbf| |supersub| |logGamma| - |partialDenominators| |cyclotomic| |factorAndSplit| |plenaryPower| - |plotPolar| |Gamma| |karatsuba| |PollardSmallFactor| |null| - |derivationCoordinates| |algebraicDecompose| |pushucoef| |backOldPos| - |f02aaf| |exprHasWeightCosWXorSinWX| |checkForZero| |sPol| - |totalGroebner| |shanksDiscLogAlgorithm| |createNormalPoly| |id| - |antisymmetricTensors| |case| |OMgetAtp| |positiveSolve| - |squareFreePolynomial| |mathieu24| |commutativeEquality| - |toseLastSubResultant| |resetNew| |nrows| |monomial?| |transcendent?| - |nthCoef| |viewWriteAvailable| |Zero| |tanh2trigh| |curve?| |s17aff| - |merge| |isobaric?| |extractTop!| |hyperelliptic| |ncols| - |eigenvalues| |branchPointAtInfinity?| |complexIntegrate| |ceiling| - |One| |table| |gderiv| |rightDiscriminant| |countRealRootsMultiple| - |style| |fortranCarriageReturn| |sech2cosh| |trigs| |components| - |splitLinear| |LiePolyIfCan| |deriv| |typeList| - |generalizedEigenvectors| |overbar| |phiCoord| |fintegrate| |getOrder| - |null?| |rightPower| |padicallyExpand| |tab1| - |factorsOfCyclicGroupSize| |sort| |leadingCoefficientRicDE| |presuper| - |internalAugment| |bsolve| |superHeight| |bfEntry| |algintegrate| - |c02aff| |subResultantChain| |headReduced?| |coerceListOfPairs| - |sturmSequence| |degree| |resetBadValues| - |leftCharacteristicPolynomial| |c05pbf| |binaryTree| |sumOfSquares| - |rightCharacteristicPolynomial| |edf2df| |e02dff| |e01sef| |elt| - |mapSolve| |symmetricProduct| |interReduce| |diag| |computeCycleEntry| - |primeFactor| |lastSubResultant| |forLoop| |c06gbf| |mainVariable?| Y - |compBound| |multiEuclideanTree| |makeYoungTableau| |moebius| - |iflist2Result| |stopMusserTrials| |positiveRemainder| - |removeRedundantFactors| |exprToUPS| |genericRightMinimalPolynomial| - |d03edf| |tryFunctionalDecomposition| |internalInfRittWu?| |matrix| - |colorFunction| |OMreadStr| |resultantnaif| |UpTriBddDenomInv| |light| - |random| |selectFiniteRoutines| |flexibleArray| |generic?| - |groebnerFactorize| |changeBase| |aLinear| |prepareSubResAlgo| - |generalizedContinuumHypothesisAssumed?| |reduceBasisAtInfinity| - |factorials| |print| |extend| |frst| |mainDefiningPolynomial| |yellow| - |GospersMethod| |lfunc| |structuralConstants| |simpleBounds?| - |complexSolve| |iisinh| |optpair| |hMonic| |rk4qc| - |noncommutativeJordanAlgebra?| |list| |physicalLength| |f02aff| - |companionBlocks| |useSingleFactorBound?| |consnewpol| |red| - |lazyIrreducibleFactors| |comment| |varList| |rdregime| |complexForm| - |car| |leastAffineMultiple| |boundOfCauchy| |prinshINFO| |palglimint| - |restorePrecision| |getConstant| |explimitedint| |commutator| - |quadraticNorm| |cdr| |differentiate| |wordInGenerators| |Lazard| - |acothIfCan| |dot| |digit| |halfExtendedSubResultantGcd2| - |permutationRepresentation| |e02ddf| |monomials| |userOrdered?| - |setDifference| |OMencodingXML| |bezoutDiscriminant| |sparsityIF| - |purelyAlgebraic?| |unparse| |setStatus| ^ |curve| - |subscriptedVariables| |constantCoefficientRicDE| |hcrf| |subPolSet?| - |setIntersection| |leftFactor| - |removeRoughlyRedundantFactorsInContents| |showFortranOutputStack| - |inverseLaplace| |semiResultantEuclideannaif| |typeLists| - |beauzamyBound| |s18dcf| |gbasis| |clearFortranOutputStack| - |zeroDimensional?| |lineColorDefault| |block| |fill!| |setUnion| - |showTheIFTable| |subscript| |palgintegrate| |monomialIntegrate| - |createPrimitivePoly| |drawCurves| |chainSubResultants| - |euclideanGroebner| |complexEigenvectors| |coordinates| |reverse!| - |apply| |possiblyNewVariety?| |extension| |multiple?| - |lazyResidueClass| |htrigs| |interpolate| |create3Space| |elementary| - |merge!| |quartic| |tubePointsDefault| |s18acf| |remove!| - |viewPhiDefault| |lowerPolynomial| |octon| |minset| |recip| - |scalarTypeOf| |constantRight| |countRealRoots| |cartesian| - |normalDenom| |size| |rightMult| |create| |factor1| |bumptab1| - |denomRicDE| |numFunEvals3D| |realElementary| |meshPar1Var| |c06ekf| - |removeRedundantFactorsInPols| |e04gcf| |resetAttributeButtons| - |romberg| |s17acf| |s17dhf| |getMeasure| |biRank| |s18def| - |setScreenResolution3D| |super| |li| |tubePlot| |universe| |rational| - |buildSyntax| |constructorName| |createMultiplicationTable| - |rangeIsFinite| |freeOf?| |constDsolve| |getCode| |first| |d01gbf| - |quatern| |delay| |move| |mainKernel| |represents| |modulus| - |chebyshevT| |palgint0| |rest| |OMputEndBVar| |normalized?| |#| - |rootPoly| |cCsch| |lazy?| |sizeLess?| |lyndon| |commaSeparate| - |stoseInvertible?sqfreg| |substitute| |sts2stst| |iicsch| |latex| - |zerosOf| |leftRecip| |c06gqf| |reorder| |plus| |OMputFloat| - |rootDirectory| |label| |removeDuplicates| |quadraticForm| |e04ycf| - |showAll?| |unvectorise| |tanNa| |subCase?| |gradient| |sinIfCan| - |ScanArabic| |getPickedPoints| |smith| |pleskenSplit| - |compiledFunction| |bracket| |hasoln| |figureUnits| |s21baf| - |leftExactQuotient| |var2StepsDefault| |setsubMatrix!| |exponent| - |laguerreL| |semiDegreeSubResultantEuclidean| |clearTheSymbolTable| - |say| |integralDerivationMatrix| |crushedSet| |cyclicSubmodule| - |setStatus!| |redpps| |monic?| |binarySearchTree| |clipWithRanges| - |solveid| |divisors| |times| |wordsForStrongGenerators| LODO2FUN - |totalfract| |stoseIntegralLastSubResultant| |tab| |reify| |paren| - |setRow!| |exprToXXP| |associator| |Is| |cylindrical| |gethi| - |messagePrint| |conjugates| |iicsc| |inGroundField?| |option| |rk4f| - |nextPartition| |nand| |scaleRoots| |sturmVariationsOf| |topPredicate| - |patternMatchTimes| |deepestInitial| |rotatez| |complexNormalize| - |cRationalPower| |partialFraction| |balancedFactorisation| |monom| - |LazardQuotient2| |superscript| |numberOfNormalPoly| - |makeFloatFunction| |iisech| |d02cjf| |controlPanel| |stronglyReduce| - |getBadValues| |notOperand| |lhs| |OMputObject| |multisect| |getlo| - |mkPrim| |iicos| |taylorIfCan| |d02ejf| |initiallyReduce| |rhs| - |number?| |seriesSolve| |constantToUnaryFunction| |f01maf| - |linearPolynomials| |concat| |common| |rootOfIrreduciblePoly| - |relationsIdeal| |explicitlyEmpty?| |graphCurves| |ravel| |write!| - |implies| |prefix| |groebner| |nextLatticePermutation| |f04jgf| - |OMreceive| |rowEch| |dmpToHdmp| |infRittWu?| |iroot| - |reducedContinuedFraction| |xor| |swap| |att2Result| |matrixGcd| - |reshape| |fortranComplex| |cTanh| |physicalLength!| |symbol?| - |trace2PowMod| |limitedIntegrate| |diophantineSystem| |rotatey| - |rightOne| |subspace| |rootKerSimp| |unitsColorDefault| |iiacosh| - |genericRightDiscriminant| |lagrange| |e04naf| |isExpt| - |optAttributes| |expenseOfEvaluation| |graphState| |cup| |leftNorm| - |append| |polygamma| |closedCurve| |invmultisect| |swapRows!| - |completeEchelonBasis| |contractSolve| |genericLeftMinimalPolynomial| - |OMputApp| |maxrow| |UnVectorise| |lazyGintegrate| |lazyPrem| |e04jaf| - |power| |elem?| |normal?| |d01fcf| |update| |nodeOf?| - |infiniteProduct| |sh| |iitan| |generic| |delta| |level| RF2UTS - |member?| |parabolic| |operator| |imagj| |elliptic| - |listConjugateBases| |minGbasis| |lexico| |identity| |makeFR| - |unitNormal| |e02akf| |bandedJacobian| F |solveRetract| |list?| - |normalise| |trapezoidal| |setClosed| |lifting1| |f04faf| - |clearDenominator| |getExplanations| |pToDmp| |untab| |digit?| - |anticoord| |d01aqf| |rightMinimalPolynomial| |checkPrecision| |nthr| - |routines| |currentEnv| |f02xef| |lSpaceBasis| |uniform| |ParCond| - |integralBasis| |clipBoolean| |rightUnits| |isOp| |lintgcd| |pureLex| - |condition| |extensionDegree| |safeCeiling| |npcoef| |position| - |updatF| |solve| |moduloP| |uncouplingMatrices| |linear?| |numer| - |saturate| |reseed| |currentScope| |interpret| |e02agf| |real?| - |sort!| |factorPolynomial| |denom| |binding| |mergeFactors| - |factorSFBRlcUnit| |besselJ| |bringDown| |prime| |definingInequation| - |rightTraceMatrix| |middle| |numberOfFactors| |getRef| |sample| - |laplace| |rst| |firstNumer| |pi| |d01alf| |OMgetEndAtp| |properties| - |f02wef| |outlineRender| |localReal?| |infinity| |selectsecond| - |csubst| |OMgetInteger| |repeating?| |translate| |pseudoRemainder| - |graphs| |pascalTriangle| |palgRDE| |nextItem| |palgextint| - |OMcloseConn| |lowerCase?| |tubeRadius| GE |stop| |jordanAdmissible?| - |fractionFreeGauss!| |denominator| |e02baf| |getVariableOrder| D - |stoseLastSubResultant| GT |endOfFile?| |pushuconst| |realRoots| - |kernel| |lifting| |replaceKthElement| |tanIfCan| |rename| |leftMult| - |nsqfree| LE |term| |draw| |generalPosition| |fixedDivisor| - |cycleEntry| |addmod| |more?| |firstUncouplingMatrix| |lprop| LT - |doubleComplex?| |univariateSolve| |bernoulliB| |points| - |newSubProgram| |setright!| |chineseRemainder| |intersect| |safeFloor| - |generateIrredPoly| |entry?| |asechIfCan| - |semiIndiceSubResultantEuclidean| |nonSingularModel| - |dimensionOfIrreducibleRepresentation| |patternMatch| |index?| - |rotate| |FormatRoman| |match?| |tan2cot| |univariate?| |d03eef| - |halfExtendedResultant2| |llprop| |init| |makeObject| - |createNormalElement| |setelt!| |e01bhf| |Si| |viewWriteDefault| - |antiCommutative?| |element?| |push!| |tryFunctionalDecomposition?| - |s14baf| |crest| |OMReadError?| |abs| |isMult| |e01sbf| |rootPower| - |odd?| |removeSinSq| |coef| |critT| |defineProperty| |leftZero| - |qfactor| |oneDimensionalArray| |iifact| - |rewriteIdealWithQuasiMonicGenerators| |changeMeasure| |retract| - |prime?| |exQuo| |OMgetError| |equiv?| |printCode| |setVariableOrder| - |OMgetEndBVar| |and?| |getSyntaxFormsFromFile| |mapExponents| - |cycleTail| |rootRadius| |dihedral| |equivOperands| |deleteRoutine!| - |univariatePolynomial| |leftAlternative?| |child?| - |stiffnessAndStabilityOfODEIF| |localAbs| |qPot| |primlimitedint| - |plusInfinity| |nextsubResultant2| |fortran| |setProperty| |acosIfCan| - |infieldint| |remainder| |writeLine!| |minusInfinity| |coefficient| - |viewpoint| |elRow2!| |isQuotient| |mapmult| |changeNameToObjf| - |randnum| |equality| |countable?| |distFact| |Ei| |lookup| |maxIndex| - |orbit| |addPoint| |changeThreshhold| |pointColorDefault| - |nextSubsetGray| |setValue!| |mapDown!| |root?| |socf2socdf| |imagE| - |dAndcExp| |expintegrate| |autoReduced?| |zeroDim?| |bernoulli| - |unrankImproperPartitions0| |cycleSplit!| |palgRDE0| |function| - |rationalIfCan| |iibinom| |ScanFloatIgnoreSpaces| - |numberOfPrimitivePoly| |addBadValue| |invertIfCan| |height| - |showTheSymbolTable| |printingInfo?| |copies| |type| |OMputInteger| - |f04atf| |scanOneDimSubspaces| |f04asf| |weight| |leftPower| - |abelianGroup| |mesh| |s14aaf| |outputArgs| |cond| |max| - |computePowers| |f01brf| |fortranDouble| |order| |ricDsolve| - |gcdPolynomial| |localIntegralBasis| |badNum| |inconsistent?| - |leastPower| |rischDEsys| |constantOpIfCan| |leftUnit| |eval| |invmod| - |tubePoints| |expandTrigProducts| |e02dcf| |composite| - |setProperties!| |reduced?| |point?| |reciprocalPolynomial| - |subResultantsChain| |minIndex| |children| |critMonD1| |over| |keys| - |palgextint0| |chebyshevU| |geometric| |pomopo!| |tanh2coth| - |tanintegrate| |alternatingGroup| |arity| |setref| |setRealSteps| - |semiSubResultantGcdEuclidean2| |replace| |lp| |central?| |linGenPos| - |iiasech| |besselI| |leadingIndex| |solveInField| |f07fdf| - |listBranches| |finiteBasis| |fillPascalTriangle| |categoryFrame| - |whatInfinity| |integralMatrix| |OMopenFile| |s17dlf| |karatsubaOnce| - |primes| |numberOfVariables| |mapUnivariate| |setMaxPoints3D| - |doubleRank| |cycleElt| |definingEquations| |infinite?| |script| - |newReduc| |stoseInvertible?reg| |bipolarCylindrical| |scan| |lcm| - |times!| |systemCommand| |precision| |d02kef| |normalize| - |setTopPredicate| |clipParametric| |insert| - |indiceSubResultantEuclidean| |c06frf| |initializeGroupForWordProblem| - |algebraic?| |prevPrime| |noKaratsuba| |leader| |solid| |mantissa| - |OMgetApp| |symbolIfCan| |putGraph| |validExponential| |cn| |tower| - |tablePow| |fibonacci| |singRicDE| |tex| |makeSin| - |removeRoughlyRedundantFactorsInPol| |rightRecip| |discriminant| - |monomialIntPoly| |makeMulti| |s17ahf| |OMputEndBind| |gcd| |error| - |d01amf| |e02bcf| |OMParseError?| |parametric?| |e01baf| |f07adf| - |aromberg| |uniform01| |union| |d01asf| |assert| |transcendenceDegree| - |f04adf| |multiplyCoefficients| |false| |rightExtendedGcd| |sinhcosh| - |norm| |s20adf| |rectangularMatrix| |alphabetic| |atoms| - |exprHasLogarithmicWeights| |cosSinInfo| |shiftRoots| - |extractSplittingLeaf| |d01ajf| |upperCase!| |fullPartialFraction| - |increment| |quotedOperators| |unary?| |heap| |gcdcofactprim| |redmat| - |alphabetic?| |Ci| |bit?| |lighting| |expintfldpoly| - |characteristicSet| |OMputBind| |shallowCopy| |iiacsc| |rroot| |ipow| - |mathieu12| |zoom| |ksec| |integrate| |genericRightTrace| |bitCoef| - |dom| |df2st| |integral?| |primitivePart| |rdHack1| - |numberOfIrreduciblePoly| |monicDecomposeIfCan| |isList| - |quasiRegular?| |setvalue!| |tree| |/\\| |semicolonSeparate| - |degreeSubResultant| |makeEq| |cross| |changeName| |axesColorDefault| - |summation| |numFunEvals| |body| |\\/| |initials| |nthFactor| - |principalIdeal| |nil| |headReduce| |inRadical?| |leftOne| - |extendedEuclidean| |bipolar| |cycleRagits| |any| |sin2csc| |less?| - |logIfCan| |maxint| |innerSolve| |e02daf| |fprindINFO| |f04qaf| - |normal| |brillhartIrreducible?| |pdf2ef| |equation| |stFunc2| - |thetaCoord| |realEigenvectors| |asinhIfCan| |OMputEndError| |symFunc| - |title| |makeTerm| |startTableGcd!| |monicRightDivide| |approximate| - |nullity| |transcendentalDecompose| |dimension| |irreducible?| - |primitiveElement| |or| |inverseIntegralMatrixAtInfinity| |indices| - |sylvesterMatrix| |complex| |pushdterm| |lieAlgebra?| |rowEchelon| - |and| |fortranCompilerName| |coth2trigh| |factorsOfDegree| FG2F - |cAtan| |permanent| |charClass| |exponential| |e| |idealiser| - |algebraicVariables| |lflimitedint| |subset?| |normalizeIfCan| - |d02raf| |leaves| |anfactor| |prepareDecompose| |powerAssociative?| - |harmonic| |mapMatrixIfCan| |antiCommutator| |LazardQuotient| |scale| - |generalizedContinuumHypothesisAssumed| |blue| |log| - |matrixDimensions| |mirror| |maxPoints3D| |shrinkable| |coerceP| - |external?| |obj| |conditionP| |queue| ** |irreducibleRepresentation| - |univariatePolynomialsGcds| |SturmHabichtSequence| |possiblyInfinite?| - |pr2dmp| |normalizedAssociate| |overlabel| |cache| |normalElement| - |interpretString| |basisOfNucleus| |inspect| |nullary?| |setOfMinN| - |orthonormalBasis| |iisqrt3| |rur| |cyclotomicDecomposition| |trim| - |rationalPoints| |any?| |numberOfDivisors| |qinterval| EQ - |approxNthRoot| |scalarMatrix| |nextNormalPoly| |makeGraphImage| - |logpart| |removeRoughlyRedundantFactorsInPols| |OMwrite| - |radicalEigenvector| |concat!| |OMputEndAtp| |rightRemainder| - |primitivePart!| |rightRank| |fullDisplay| |sumOfDivisors| - |cyclePartition| |maxrank| |zero?| |stopTable!| |cyclicEntries| - |outputFixed| |findCycle| |exteriorDifferential| |primintegrate| - |bandedHessian| |difference| |floor| |twist| |stoseInvertible?| - |ffactor| |cCsc| |ord| |oblateSpheroidal| |infinityNorm| - |subResultantGcd| |eulerE| |OMputString| |collectUpper| |integers| - |polyPart| |maxRowIndex| |qelt| |someBasis| |makeCrit| |powmod| - |primPartElseUnitCanonical| |semiSubResultantGcdEuclidean1| - |bivariatePolynomials| |hasPredicate?| |s17aef| |maxdeg| - |fortranLiteralLine| |mkAnswer| |cAsin| |psolve| |characteristic| - |hdmpToP| |search| |complexZeros| |lambda| |one?| |xRange| |pattern| - |drawComplexVectorField| |f02axf| |movedPoints| |OMputAtp| - |cyclicParents| |tan2trig| |modifyPointData| |complex?| |removeCosSq| - |yRange| |length| |adaptive| |f01qdf| |rewriteIdealWithRemainder| - |oddlambert| |toseInvertible?| |dominantTerm| |gcdPrimitive| - |internalZeroSetSplit| |zRange| |scripts| - |stoseInternalLastSubResultant| |oddintegers| |BumInSepFFE| |lambert| - |hostPlatform| |OMgetFloat| |enterPointData| |linearPart| |rootOf| - |map!| |binomThmExpt| |ranges| |inHallBasis?| |zeroDimPrime?| - |acotIfCan| |setButtonValue| |rootBound| |indiceSubResultant| - |qsetelt!| |internalIntegrate0| |dimensionsOf| |seed| - |compactFraction| |rquo| |mainMonomial| |LyndonWordsList| |iExquo| - |s13adf| |computeCycleLength| |laplacian| |rotate!| - |leftRegularRepresentation| |copy!| |lazyIntegrate| |radix| - |maxPoints| |bat1| |trigs2explogs| |increase| - |squareFreeLexTriangular| |fracPart| |extendedResultant| |qqq| - |f02abf| |OMgetEndBind| |stronglyReduced?| |deepCopy| - |toseSquareFreePart| |removeSuperfluousQuasiComponents| |fglmIfCan| - |nthRoot| |mainMonomials| |size?| |leadingBasisTerm| |iidsum| |iicosh| - |LagrangeInterpolation| |OMgetBind| |exponential1| |composites| - |remove| |recolor| |setImagSteps| |omError| - |functionIsContinuousAtEndPoints| |normalDeriv| |laurentRep| - |absolutelyIrreducible?| |computeBasis| |f01ref| |direction| - |jacobian| |surface| |rightTrim| |minPoly| |cyclicGroup| |closed?| - |acsch| |unitCanonical| |selectSumOfSquaresRoutines| |groebgen| - |d01bbf| |cothIfCan| |setchildren!| |ref| |initiallyReduced?| - |leftTrim| |last| |mapCoef| |exists?| |divideIfCan| |basisOfCenter| - |nextPrimitiveNormalPoly| |linearlyDependent?| |repeatUntilLoop| - |powern| |hclf| |karatsubaDivide| |updatD| |prem| |assoc| - |nthRootIfCan| |multiplyExponents| |retractable?| |permutation| - |innerint| |vconcat| |genericRightNorm| |pointLists| |inc| |f01qef| - |stoseInvertibleSet| |rule| |e04mbf| |f04arf| - |zeroSetSplitIntoTriangularSystems| |getGraph| - |setAttributeButtonStep| |clip| |degreePartition| |cTan| |ddFact| - |weierstrass| |bright| |lazyPseudoDivide| |genericLeftNorm| |expPot| - |eigenMatrix| |divideIfCan!| |HenselLift| |minPoints3D| - |basisOfCentroid| |ode1| |monicLeftDivide| |coHeight| - |resultantEuclidean| |addPoint2| |rationalPower| |mathieu22| - |alphanumeric?| |cSec| |bezoutMatrix| |innerSolve1| |primlimintfrac| - |exquo| |minrank| |subNode?| |call| |members| |f02adf| |axes| |s17def| - |pseudoDivide| |perfectSqrt| |div| |lastSubResultantElseSplit| - |elRow1!| |tanSum| |insertRoot!| |OMUnknownSymbol?| |string?| |next| - UTS2UP |cSinh| |c06gcf| |select!| |delete| |normalizedDivide| |quo| - |nlde| |squareFreePart| |previous| |s21bcf| |Nul| |mainForm| |push| - |aQuadratic| |perspective| |invertibleElseSplit?| |cosh2sech| - |kroneckerDelta| |plot| |zeroSetSplit| |integer?| |viewport2D| - |createLowComplexityTable| |string| |e04ucf| |getMultiplicationMatrix| - |rem| |evenlambert| |iilog| |B1solve| |mapBivariate| |rowEchLocal| - |topFortranOutputStack| |printTypes| |basisOfMiddleNucleus| - |discreteLog| |rationalFunction| |expextendedint| |addMatchRestricted| - |prinpolINFO| |basis| |perfectSquare?| |bumprow| |c06ebf| |column| - |kmax| |selectNonFiniteRoutines| |leftRank| |prindINFO| |predicate| - |jacobiIdentity?| |in?| |solveLinearPolynomialEquation| - |deleteProperty!| |xCoord| |e04dgf| |extendIfCan| - |purelyAlgebraicLeadingMonomial?| |insertionSort!| - |exprHasAlgebraicWeight| |semiLastSubResultantEuclidean| |squareTop| - |pushdown| |generalLambert| |content| |acscIfCan| |integerIfCan| - |mainValue| |iiasec| |useEisensteinCriterion?| |transform| |froot| - |doubleFloatFormat| |setleaves!| UP2UTS |retractIfCan| |radPoly| - |mightHaveRoots| |trueEqual| |fmecg| |euler| |definingPolynomial| - |f2st| |status| |expr| |zCoord| |sign| |key?| |newLine| |vark| - |integralAtInfinity?| |indicialEquation| |OMputEndApp| |diagonals| - |linears| |complete| |rightAlternative?| |firstSubsetGray| |swap!| - |nextPrime| |explicitEntries?| |pade| |s15aef| |spherical| |gcdcofact| - |nextNormalPrimitivePoly| |minPoints| |stFuncN| |log10| |hdmpToDmp| - |diagonal?| |iisin| |viewZoomDefault| |badValues| |s13acf| |bitand| - |varselect| |s17adf| |c06eaf| |deepestTail| |oddInfiniteProduct| - |setPosition| |euclideanNormalForm| |e01bff| |variable| |parameters| - |bitior| |hspace| |mainCoefficients| |not| |euclideanSize| - |viewPosDefault| |factors| |f01qcf| |dihedralGroup| |imagJ| |randomLC| - |modifyPoint| |OMreadFile| |setAdaptive| |OMgetEndObject| |delete!| - |mainContent| |coerceImages| |associatedSystem| |cCosh| |exp| - |errorInfo| |cons| |cfirst| |makeprod| |optimize| |edf2fi| |df2mf| - |fortranCharacter| |sechIfCan| |nodes| - |solveLinearPolynomialEquationByRecursion| - |numberOfImproperPartitions| |range| |groebSolve| |symbol| |cycle| - |yCoord| |t| |ran| |branchPoint?| |solveLinear| |gramschmidt| - |setCondition!| |repSq| |applyRules| |createMultiplicationMatrix| - |characteristicPolynomial| |map| |option?| |groebnerIdeal| |power!| - |read!| |sqfrFactor| |totalDegree| |critpOrder| |integer| |quotient| - |unmakeSUP| |generalSqFr| |commutative?| |dimensions| |square?| - |splitNodeOf!| |quasiComponent| |denominators| |multMonom| - |putColorInfo| |leadingSupport| |generalTwoFactor| |nullary| - |setFieldInfo| |c06gsf| |s13aaf| |sayLength| |virtualDegree| |cap| - |coerceL| |adaptive3D?| |semiResultantEuclidean2| |completeEval| - |basicSet| |extendedint| |s21bbf| |selectIntegrationRoutines| - |associatedEquations| |selectPolynomials| |wordInStrongGenerators| - |iCompose| |e01sff| |selectPDERoutines| |OMputEndAttr| - |resetVariableOrder| |f04axf| |row| |fractRadix| |fortranLiteral| - |vspace| |complementaryBasis| |clikeUniv| |rischDE| |setOrder| - |unravel| |convert| |midpoints| |s19abf| |outputForm| |printInfo!| - |f07aef| |readIfCan!| |e02ahf| |setnext!| |pseudoQuotient| - |vertConcat| |roughBasicSet| |drawComplex| |semiDiscriminantEuclidean| - |double| |realZeros| |ridHack1| |ptree| |or?| |atom?| |setTex!| - |showClipRegion| |separant| |ocf2ocdf| |compile| |cotIfCan| |hue| - |front| |complexLimit| |lazyPseudoRemainder| |leftScalarTimes!| - |myDegree| |s14abf| SEGMENT |zero| |determinant| |result| |infLex?| - |factor| |numberOfChildren| |char| |OMbindTCP| |showTheRoutinesTable| - |stoseInvertibleSetsqfreg| |generalInfiniteProduct| |d01akf| |s19acf| - |enumerate| |hermiteH| |listOfLists| |positive?| |split!| |sqrt| - |viewThetaDefault| |reindex| |rootNormalize| |leftGcd| - |stoseInvertibleSetreg| |mkcomm| |seriesToOutputForm| |node?| - |midpoint| |getZechTable| |associative?| |removeDuplicates!| |And| - |idealSimplify| |SturmHabicht| |LyndonCoordinates| |real| |acoshIfCan| - |clearTable!| |monicDivide| |s17akf| |nary?| |setleft!| |reducedForm| - |Or| |getOperator| |f01rcf| |printHeader| |subtractIfCan| |imag| - |distdfact| |tracePowMod| |neglist| |legendre| |f04mbf| |usingTable?| - |brace| |mesh?| |ignore?| |sylvesterSequence| |fortranDoubleComplex| - |Not| |curveColorPalette| |component| |directProduct| |readable?| - |d02bbf| |particularSolution| |float| |reduceByQuasiMonic| - |alternative?| |hash| |baseRDE| |numberOfComponents| - |isAbsolutelyIrreducible?| |RemainderList| |quote| - |discriminantEuclidean| |quasiMonic?| |lllip| |iomode| |pdf2df| |int| - |comparison| |linkToFortran| |integerBound| |insertTop!| - |decreasePrecision| |findBinding| |declare!| |lazyPseudoQuotient| - |bivariate?| |resultant| |destruct| |explicitlyFinite?| |moduleSum| - |nthFlag| |count| |minColIndex| |conjug| |decrease| |interval| - |leviCivitaSymbol| |functionIsOscillatory| |leadingTerm| - |binaryFunction| |moebiusMu| |eq?| |makeViewport3D| - |primPartElseUnitCanonical!| |rightFactorCandidate| |value| - |ellipticCylindrical| |close!| |ef2edf| |internalIntegrate| - |removeConstantTerm| |c06fqf| |OMclose| |sin?| |lieAdmissible?| - |cot2tan| |constant?| |setlast!| |distribute| |ratpart| |bits| - |infieldIntegrate| |ptFunc| |clipSurface| |empty?| |ODESolve| - |integralLastSubResultant| |void| |iiasinh| |limitedint| |adjoint| - |e02ajf| |OMputBVar| |var1StepsDefault| |makeSketch| |monomial| - |identityMatrix| |completeHermite| |prolateSpheroidal| |iisec| - |specialTrigs| |argument| |symbolTable| |cyclic?| |twoFactor| - |groebner?| |simplifyExp| |partialQuotients| |multivariate| - |divergence| |OMgetSymbol| |morphism| |split| |drawStyle| - |degreeSubResultantEuclidean| |iisqrt2| |primextendedint| - |nthExponent| |cAtanh| |rischNormalize| |variables| |outputFloating| - |readLine!| |hexDigit| |pushFortranOutputStack| |d02gaf| |complement| - |bumptab| |meshPar2Var| |OMgetString| |d01anf| |satisfy?| |tail| - |rk4a| |graeffe| |BasicMethod| |chvar| |iiatan| |indicialEquations| - |popFortranOutputStack| |leftFactorIfCan| |perfectNthRoot| |opeval| - |pmintegrate| |trailingCoefficient| |schema| |s17ajf| - |numberOfOperations| |iiGamma| |lllp| |palgint| |outputAsFortran| - |hasSolution?| |hasHi| |digamma| |bombieriNorm| |aQuartic| - |numberOfComposites| |key| |scopes| |complexRoots| |listOfMonoms| - |iprint| |pile| |algebraicOf| |factorSquareFree| |modTree| |singular?| - |linSolve| |laguerre| |substring?| |options| |skewSFunction| - |exprToGenUPS| |extractIndex| |processTemplate| |partitions| - |explogs2trigs| |lazyPremWithDefault| |taylor| |child| - |extendedSubResultantGcd| |output| |cycleLength| - |genericLeftTraceForm| |top!| |build| |limit| |OMgetObject| - |symmetricSquare| |evaluateInverse| |subHeight| |inverse| |filename| - |increasePrecision| NOT |regularRepresentation| |laurent| |sqfree| - |stosePrepareSubResAlgo| |exactQuotient| |suffix?| |cCos| - |selectfirst| |subresultantSequence| |sup| |matrixConcat3D| - |maximumExponent| |bubbleSort!| |halfExtendedSubResultantGcd1| - |segment| |puiseux| |top| OR |selectOrPolynomials| |secIfCan| - |simplifyLog| |constant| |besselY| |rootSimp| |bitTruth| |pushup| - |bitLength| |areEquivalent?| |ratDenom| |subresultantVector| - |continue| AND |factorOfDegree| |cAcsc| |setMinPoints| - |lastSubResultantEuclidean| |not?| |prefix?| |getIdentifier| - |traverse| |SturmHabichtCoefficients| |symbolTableOf| - |singularitiesOf| |s18aff| |rationalPoint?| |inv| |color| - |internalSubPolSet?| |getGoodPrime| |parse| |new| |showTypeInOutput| - |quadratic?| |edf2ef| |OMUnknownCD?| |s19aaf| |startTable!| - |brillhartTrials| |ground?| |subMatrix| |generator| |makeop| |leaf?| - |setProperties| |modularGcd| |reverse| |debug3D| |lowerCase| |empty| - |ground| |slash| |probablyZeroDim?| |makeViewport2D| |iiacsch| |iiexp| - |sizePascalTriangle| |setScreenResolution| |monicCompleteDecompose| - |mindegTerm| |leadingMonomial| |getButtonValue| |palglimint0| - |enqueue!| |relativeApprox| |baseRDEsys| |compound?| |knownInfBasis| - |partialNumerators| |leadingCoefficient| |numberOfHues| - |minimumExponent| |argumentListOf| |externalList| |rootsOf| |product| - |outputSpacing| |regime| |primitiveMonomials| |getMultiplicationTable| - |intPatternMatch| |getProperty| |infix?| |shallowExpand| - |changeWeightLevel| |separate| |vector| |setErrorBound| - |sortConstraints| |reductum| |enterInCache| |repeating| |mask| - |showIntensityFunctions| |dioSolve| |genericRightTraceForm| |cos2sec| - |postfix| |mix| |subQuasiComponent?| |csch2sinh| |rotatex| |algint| - |equiv| |revert| |reducedQPowers| |signAround| * |lift| - |numberOfCycles| |resize| |rootSplit| |byte| |quasiMonicPolynomials| - |getMatch| |semiResultantEuclidean1| |f01mcf| |asinIfCan| |lo| - |reduce| |addiag| |splitDenominator| |asecIfCan| |safetyMargin| - |permutationGroup| |iiacot| |reopen!| |Lazard2| |tube| |iiacoth| - |left| |elColumn2!| |coercePreimagesImages| |vectorise| - |primeFrobenius| |prologue| |hexDigit?| |upDateBranches| |leftLcm| - |right| |stFunc1| |graphImage| |coefChoose| |radicalOfLeftTraceForm| - |normal01| |arguments| |basisOfCommutingElements| |roughBase?| - |ListOfTerms| |coerceS| |antiAssociative?| |setPredicates| |iicoth| - |listYoungTableaus| |genericLeftTrace| |polygon?| |flagFactor| - |rightLcm| |rombergo| |blankSeparate| |alternating| - |halfExtendedResultant1| |tanhIfCan| |nonQsign| |index| - |mainCharacterization| |intChoose| |pdct| |makingStats?| - |mapUnivariateIfCan| |lfintegrate| |returnType!| |cyclicCopy| - |wrregime| |principal?| |numericIfCan| |dmpToP| |squareFreeFactors| - |hex| |returns| |complexElementary| |var2Steps| |genus| - |OMgetVariable| |variable?| |singularAtInfinity?| |testModulus| - |lazyVariations| |createPrimitiveElement| |argscript| |OMgetAttr| - |pair| |s21bdf| |triangular?| |Vectorise| |triangularSystems| - |heapSort| |getDatabase| |headRemainder| |algSplitSimple| |ldf2vmf| - |ode2| |OMgetType| |nthFractionalTerm| |internalLastSubResultant| - |removeSinhSq| |terms| |rootProduct| |exptMod| - |resultantReduitEuclidean| |showAllElements| |quasiRegular| - |clearCache| |indicialEquationAtInfinity| |cyclotomicFactorization| - |e04fdf| |elliptic?| |mr| |cschIfCan| |recoverAfterFail| - |getProperties| |removeSuperfluousCases| |rank| |totalLex| - |setFormula!| |ode| |finite?| |factorial| |curryRight| |nthExpon| - |createGenericMatrix| |center| |polygon| |integral| |colorDef| - |makeSeries| |weights| |logical?| |eigenvectors| |getOperands| - |bfKeys| |currentCategoryFrame| |Frobenius| |expint| - |incrementKthElement| |pop!| |OMsupportsSymbol?| - |factorSquareFreeByRecursion| |depth| |isTimes| - |setLegalFortranSourceExtensions| |triangulate| |extendedIntegrate| - |printInfo| |mat| |patternVariable| |inrootof| |mathieu23| - |unprotectedRemoveRedundantFactors| |f02ajf| |open?| |double?| - |message| |high| |supDimElseRittWu?| |nextSublist| |nextColeman| - |goodPoint| |makeVariable| |shellSort| |contract| |imaginary| - |curveColor| |separateDegrees| |internalDecompose| |lists| |augment| - |setClipValue| |padicFraction| |nor| |rightTrace| |sinh2csch| - |createNormalPrimitivePoly| |cAsec| |approximants| |critBonD| |float?| - |numerators| |operation| |leftQuotient| |OMencodingSGML| - |roughEqualIdeals?| |invertibleSet| |unitVector| |wreath| - |horizConcat| |solveLinearlyOverQ| |preprocess| |name| - |startPolynomial| |d01gaf| |nil?| |bottom!| |mulmod| |endSubProgram| - |generalizedEigenvector| |LowTriBddDenomInv| |even?| |toScale| |prinb| - |setPoly| |pack!| |sub| |true| |dn| |createLowComplexityNormalBasis| - |minRowIndex| |loopPoints| |randomR| |monomRDEsys| |rightUnit| - |toseInvertibleSet| |genericPosition| |f02akf| |denomLODE| |pquo| - |irreducibleFactor| |s18aef| |complexNumericIfCan| |sec2cos| - |rightFactorIfCan| |reflect| |callForm?| |f01bsf| - |factorGroebnerBasis| |pair?| |zeroOf| |expressIdealMember| |debug| - |decimal| |rightZero| |rightRankPolynomial| |shade| |s15adf| - |internalSubQuasiComponent?| |primaryDecomp| |refine| |shiftLeft| - |janko2| |completeSmith| |createIrreduciblePoly| |OMputError| - |poisson| |redPol| |readLineIfCan!| |showSummary| - |resultantEuclideannaif| |nilFactor| |evaluate| |monomRDE| |notelem| - |nonLinearPart| |besselK| |credPol| |completeHensel| |alphanumeric| - |critB| |largest| |eyeDistance| |c06fuf| |flexible?| |writable?| - |variationOfParameters| |aCubic| |space| |showAttributes| - |zeroDimPrimary?| |generators| |sumOfKthPowerDivisors| |head| - |magnitude| |selectODEIVPRoutines| |branchIfCan| |zeroSquareMatrix| - |coord| |removeCoshSq| |unit| |checkRur| |partition| |eulerPhi| - |dictionary| |singleFactorBound| |leftUnits| |perfectNthPower?| |find| - |distance| |fortranReal| |changeVar| |module| |cLog| |cAcoth| - |innerEigenvectors| |reduceLODE| |taylorQuoByVar| |coordinate| - |OMlistSymbols| |dark| |corrPoly| |medialSet| |basisOfRightNucloid| - F2FG |factorList| |powers| |linear| |pointData| |mvar| |s17dcf| - |basisOfRightNucleus| |upperCase| |combineFeatureCompatibility| - |decomposeFunc| |arrayStack| |lfinfieldint| |f02bbf| |ramified?| - |showTheFTable| |cSech| |divisorCascade| |exponentialOrder| |iipow| - |paraboloidal| |polynomial| |rk4| |expIfCan| |outputGeneral| - |fixPredicate| |airyBi| |droot| |rightNorm| |s18adf| |e01daf| - |loadNativeModule| |setProperty!| |curry| |useEisensteinCriterion| - |po| |rightRegularRepresentation| |c06fpf| |printStatement| BY - |character?| |impliesOperands| |every?| |failed?| |close| |extract!| - |relerror| |wholeRadix| |scripted?| |duplicates| |newTypeLists| - |stirling2| |palgLODE| |drawToScale| |coefficients| - |numberOfMonomials| |cyclicEqual?| |pmComplexintegrate| |subSet| - |display| |subst| |basisOfRightAnnihilator| |squareFreePrim| - |multiEuclidean| |ideal| |curryLeft| |closeComponent| |bindings| - |identification| |node| |solid?| |erf| |imagI| |linearMatrix| - |radicalEigenvalues| |var1Steps| |primitive?| |critM| |youngGroup| - |differentialVariables| |f04maf| |extractProperty| |declare| - |nextsousResultant2| |fi2df| |belong?| |cardinality| |symmetric?| - |LyndonBasis| |splitSquarefree| |polyRDE| |outputAsTex| |f02bjf| - |OMconnOutDevice| |negative?| |rewriteSetWithReduction| |viewport3D| - |dilog| |factorSquareFreePolynomial| |subResultantGcdEuclidean| - |packageCall| |multiset| |binaryTournament| |aspFilename| |shufflein| - |ratPoly| |realEigenvalues| |input| |mkIntegral| |irreducibleFactors| - |sin| |binomial| |stoseSquareFreePart| |imagk| |addMatch| |taylorRep| - |cCoth| |semiResultantReduitEuclidean| |library| |sorted?| |objects| - |rational?| |cos| |critMTonD1| |d01apf| |powerSum| |ldf2lst| - |orOperands| |outputAsScript| |decompose| |noLinearFactor?| |base| - |accuracyIF| |tan| |iitanh| |minimumDegree| |pointPlot| |Aleph| - |LiePoly| |univariatePolynomials| |tRange| |selectAndPolynomials| - |functionIsFracPolynomial?| |normalizeAtInfinity| |cot| |e01saf| - |antisymmetric?| |leftDivide| |symmetricRemainder| |palginfieldint| - |listLoops| |shiftRight| |viewDefaults| |leadingExponent| |parts| - |polyRicDE| |sec| |OMgetBVar| |quotientByP| |predicates| |associates?| - |e02bdf| |elements| |listexp| |linearlyDependentOverZ?| |set| |mapUp!| - |initTable!| |csc| |numericalOptimization| |showScalarValues| |green| - |useNagFunctions| |minimalPolynomial| |cAsinh| |removeSquaresIfCan| ~ - |factorByRecursion| |raisePolynomial| |numeric| |e02zaf| |asin| - |cAcot| |tableau| |bezoutResultant| |univcase| |identitySquareMatrix| - |kovacic| |dim| |property| |lepol| |nativeModuleExtension| - |linearAssociatedLog| |radical| |f01rdf| |mainPrimitivePart| |acos| - |stack| |sncndn| |leftRemainder| |directory| |totalDifferential| - |divisor| |minus!| |f2df| |d02gbf| |s17agf| |weakBiRank| |pastel| - |atan| |f04mcf| |radicalSolve| |createZechTable| - |rationalApproximation| |minimize| |squareMatrix| |arg1| |fixedPoints| - |certainlySubVariety?| |modularFactor| |generalizedInverse| |acot| - |imagi| |lowerCase!| |linearAssociatedExp| |traceMatrix| |presub| - |invertible?| |units| |arg2| |overset?| |asimpson| |problemPoints| - |rightExactQuotient| |asec| |pow| |mainSquareFreePart| |open| - |approxSqrt| |cosIfCan| |contours| |s17dgf| |mainVariable| |inR?| - |OMlistCDs| |leftExtendedGcd| |acsc| |se2rfi| |purelyTranscendental?| - |sn| |firstDenom| |conditions| |radicalEigenvectors| |subTriSet?| - |fortranTypeOf| |box| |andOperands| |polar| |s19adf| |sinh| - |doublyTransitive?| |stopTableInvSet!| |doubleResultant| |sdf2lst| - |lazyEvaluate| |op| |symmetricDifference| |match| |bat| - |polynomialZeros| |permutations| |OMserve| = - |removeIrreducibleRedundantFactors| |cosh| |ramifiedAtInfinity?| - |term?| |simpsono| |mergeDifference| |coshIfCan| |divideExponents| - |charpol| |quoted?| |normDeriv2| |show| |sizeMultiplication| - |lyndonIfCan| |primextintfrac| |tanh| |simpson| |characteristicSerie| - |monicModulo| |code| |stopTableGcd!| |returnTypeOf| |region| |escape| - |meshFun2Var| |balancedBinaryTree| |toroidal| |f02agf| < |e02adf| - |coth| |log2| |pol| |expenseOfEvaluationIF| |reduction| - |constantIfCan| |Hausdorff| |f02awf| |mapdiv| |vedf2vef| |duplicates?| - |eq| |trace| |digits| > |quadratic| |sech| |compose| |truncate| - |yCoordinates| |setAdaptive3D| |pole?| |henselFact| |torsion?| - |quoByVar| |upperCase?| |iter| |hessian| |mdeg| <= |csch| |tanAn| - |ScanFloatIgnoreSpacesIfCan| |prod| |rubiksGroup| |homogeneous?| - |diff| |collect| |directSum| |rCoord| |multinomial| |exactQuotient!| - |laurentIfCan| >= |integralCoordinates| |asinh| |s01eaf| - |OMencodingBinary| |entry| |acschIfCan| |initial| |finiteBound| - |overlap| |prefixRagits| |monicRightFactorIfCan| - |linearDependenceOverZ| |lfextendedint| - |standardBasisOfCyclicSubmodule| |constantKernel| |acosh| |zeroVector| - |setEpilogue!| |rename!| |xn| |numericalIntegration| |setfirst!| - |hitherPlane| |screenResolution3D| |sincos| |eisensteinIrreducible?| - |argumentList!| |incr| |removeRedundantFactorsInContents| - |createRandomElement| |atanh| |totolex| |algebraicSort| |iidprod| - |chiSquare| |fortranInteger| |e02def| |parabolicCylindrical| |hermite| - |binary| |limitPlus| |hi| |collectUnder| + |acoth| |epilogue| - |ScanRoman| |inverseIntegralMatrix| |idealiserMatrix| - |selectOptimizationRoutines| |swapColumns!| |conjugate| |tanQ| - |unrankImproperPartitions1| ~= |outputList| |df2ef| |simplifyPower| - |algebraicCoefficients?| - |nextPrimitivePoly| |asech| |cscIfCan| - |trivialIdeal?| |copyInto!| |clearTheFTable| |polyred| |chiSquare1| - |rangePascalTriangle| |polCase| |coerce| |representationType| - |zeroMatrix| / |testDim| |unexpand| |setrest!| |gcdprim| |cAcsch| - |LyndonWordsList1| |comp| |numerator| |tubeRadiusDefault| |orbits| - |pointSizeDefault| |construct| |padecf| |basisOfLeftNucloid| - |jordanAlgebra?| |f07fef| |multiple| |submod| |c02agf| - |leftMinimalPolynomial| |allRootsOf| |wronskianMatrix| - |fixedPointExquo| |e02aef| |printStats!| |iiatanh| |OMsend| - |applyQuote| |bivariateSLPEBR| |rowEchelonLocal| |iiacos| |errorKind| - |lexTriangular| |failed| |resultantReduit| |meatAxe| |is?| |mathieu11| - |symmetricTensors| |leftDiscriminant| |f02fjf| |continuedFraction| - |test| |complexEigenvalues| |removeZero| |useSingleFactorBound| - |wholePart| |imagK| |leastMonomial| |genericLeftDiscriminant| - |isPower| |objectOf| |entries| |KrullNumber| |graphStates| |isPlus| - |OMputSymbol| |optional?| |makeUnit| |An| |screenResolution| - |intensity| |OMputEndObject| |expt| |convergents| |showArrayValues| - |dequeue| |OMencodingUnknown| |HermiteIntegrate| |OMgetEndApp| - |showRegion| |fortranLinkerArgs| |OMputAttr| |root| |strongGenerators| - |measure2Result| |integralBasisAtInfinity| |conditionsForIdempotents| - |pushNewContour| |normalForm| |ruleset| |csc2sin| |sinhIfCan| - |operators| |goto| |createPrimitiveNormalPoly| |inf| |symmetricGroup| - |integralRepresents| |d02bhf| |sum| |leftTrace| |linearDependence| - |numberOfComputedEntries| |cycles| |RittWuCompare| |ReduceOrder| - |getStream| |mapGen| |rightDivide| |slex| |factorFraction| |realSolve| - |nullSpace| |reset| |frobenius| |diagonalMatrix| |d03faf| - |quasiAlgebraicSet| |insert!| |supRittWu?| |schwerpunkt| |atanIfCan| - |UP2ifCan| |shift| |doubleDisc| |roughUnitIdeal?| |lfextlimint| - |cot2trig| |trapezoidalo| |stiffnessAndStabilityFactor| |suchThat| - |startStats!| |low| |commonDenominator| |weighted| |updateStatus!| - |basisOfLeftAnnihilator| |leadingIdeal| |musserTrials| - |selectMultiDimensionalRoutines| |OMgetEndAttr| |rightGcd| |diagonal| - |write| |point| |viewDeltaYDefault| |systemSizeIF| |c06ecf| |generate| - |goodnessOfFit| |createThreeSpace| GF2FG |atanhIfCan| |setprevious!| - |rarrow| |associatorDependence| |rules| |radicalSimplify| |deref| - |unitNormalize| |clipPointsDefault| |OMopenString| |constantLeft| - |rightScalarTimes!| |e02gaf| |divide| |s20acf| |assign| |domainOf| - |pToHdmp| |btwFact| |mainVariables| |tensorProduct| |iteratedInitials| - |save| |back| |startTableInvSet!| |basisOfLeftNucleus| |incrementBy| - |separateFactors| |rspace| |maxColIndex| |cAcosh| |e01bef| |palgLODE0| - |cPower| |wholeRagits| |SturmHabichtMultiple| |second| |setColumn!| - |extractIfCan| |parametersOf| |series| |dfRange| |makeCos| |exprex| + |Record| |Union| |makeFR| |byte| |clipParametric| |expr| |condition| + |gramschmidt| |ScanFloatIgnoreSpacesIfCan| F2FG |compactFraction| + |leadingMonomial| |extractIndex| |unitNormal| |suchThat| + |indiceSubResultantEuclidean| |quasiMonicPolynomials| |prod| + |setCondition!| |linearPolynomials| |lp| |deepExpand| |factorList| + |leadingCoefficient| |rquo| |processTemplate| |e02akf| |c06frf| + |getMatch| |repSq| |rubiksGroup| |mr| |rootOfIrreduciblePoly| + |primitiveMonomials| |powers| |mainMonomial| |partitions| + |bandedJacobian| |initializeGroupForWordProblem| + |semiResultantEuclidean1| |applyRules| |homogeneous?| |relationsIdeal| + |df2fi| |LyndonWordsList| |pointData| |reductum| |explogs2trigs| + |solveRetract| |f01mcf| |variable| |algebraic?| + |createMultiplicationMatrix| |diff| |explicitlyEmpty?| |iExquo| |mvar| + |lazyPremWithDefault| |list?| |characteristicPolynomial| |prevPrime| + |asinIfCan| |collect| |retractIfCan| |graphCurves| |s13adf| |s17dcf| + |box| |child| |normalise| |option?| |directSum| |addiag| |noKaratsuba| + |message| |moduloP| |basisOfRightNucleus| |computeCycleLength| + |extendedSubResultantGcd| |printInfo| |trapezoidal| + |uncouplingMatrices| |solid| |splitDenominator| |groebnerIdeal| + |rCoord| |write!| |laplacian| |upperCase| |cycleLength| |multinomial| + |OMgetApp| |asecIfCan| |power!| |linear?| |append| + |combineFeatureCompatibility| |rotate!| |genericLeftTraceForm| |read!| + |safetyMargin| |symbolIfCan| |numer| |saturate| |exactQuotient!| + |leftRegularRepresentation| |decomposeFunc| |top!| |sqfrFactor| |name| + |laurentIfCan| |denom| |permutationGroup| |putGraph| |and?| |reseed| + |flatten| |arrayStack| |copy!| |build| |iiacot| |validExponential| + |integralCoordinates| |totalDegree| |getSyntaxFormsFromFile| + |currentScope| |lfinfieldint| |lazyIntegrate| |limit| |or| + |mapExponents| |reopen!| |critpOrder| |tablePow| |pi| |e02agf| + |s01eaf| |quotient| |f02bbf| |radix| |and| |OMgetObject| |fibonacci| + |Si| |OMencodingBinary| F |infinity| |Lazard2| |real?| |cycleTail| + |ramified?| |precision| |e02bef| |maxPoints| |symmetricSquare| |sort!| + |viewWriteDefault| |singRicDE| |tube| |acschIfCan| |unmakeSUP| |has?| + |showTheFTable| |bat1| |evaluateInverse| |finiteBound| |iiacoth| + |makeSin| |generalSqFr| |map| |factorPolynomial| |cSech| + |trigs2explogs| |triangSolve| |subHeight| |binding| |kernel| + |elColumn2!| |removeRoughlyRedundantFactorsInPol| |commutative?| + |overlap| |increase| |zero| |divisorCascade| |contains?| |inverse| + |parameters| |ptree| |draw| |mergeFactors| |rightRecip| + |coercePreimagesImages| |prefixRagits| |dimensions| |exponentialOrder| + |squareFreeLexTriangular| |iFTable| |increasePrecision| |square?| + |discriminant| |vectorise| |monicRightFactorIfCan| |factorSFBRlcUnit| + SEGMENT |iipow| |And| |fracPart| |OMsetEncoding| + |regularRepresentation| |primeFrobenius| |monomialIntPoly| + |splitNodeOf!| |linearDependenceOverZ| |besselJ| |rdregime| + |paraboloidal| |Or| |computeInt| |extendedResultant| |sqfree| + |bringDown| |lfextendedint| |makeMulti| D |prologue| |quasiComponent| + |convert| |complexForm| |outputMeasure| |Not| |rk4| |qqq| + |stosePrepareSubResAlgo| |depth| |hexDigit?| |denominators| + |makeObject| |s17ahf| |standardBasisOfCyclicSubmodule| |prime| + |leastAffineMultiple| |f02abf| |ParCondList| |expIfCan| + |exactQuotient| |search| |antiCommutative?| |multMonom| + |constantKernel| |definingInequation| |rootRadius| |boundOfCauchy| + |outputGeneral| |diagonalProduct| |OMgetEndBind| |cCos| |palgRDE0| + |zeroVector| |coef| |rightTraceMatrix| |putColorInfo| |dihedral| + |prinshINFO| |expandPower| |fixPredicate| |stronglyReduced?| + |selectfirst| |rationalIfCan| |getPickedPoints| |leadingSupport| + |setEpilogue!| |middle| |palglimint| |equivOperands| |lquo| |airyBi| + |deepCopy| |subresultantSequence| |iibinom| |smith| |numberOfFactors| + |rename!| |generalTwoFactor| |restorePrecision| |deleteRoutine!| + |extractPoint| |sup| |pleskenSplit| |ScanFloatIgnoreSpaces| + |sparsityIF| |xn| |getRef| |nullary| |getConstant| + |univariatePolynomial| |rightUnit| |concat!| |any| |matrixConcat3D| + |numberOfPrimitivePoly| |compiledFunction| |setFieldInfo| + |purelyAlgebraic?| |numericalIntegration| |sample| |leftAlternative?| + |explimitedint| |OMputEndAtp| |toseInvertibleSet| |squareFree| + |maximumExponent| |dimensionOfIrreducibleRepresentation| |bracket| + |addBadValue| |unparse| |c06gsf| |setfirst!| |commutator| |child?| + |genericPosition| |rightRemainder| |SFunction| |bubbleSort!| + |patternMatch| |invertIfCan| |hasoln| |setStatus| |laplace| + |stiffnessAndStabilityOfODEIF| |quadraticNorm| |f02akf| + |primitivePart!| |intermediateResultsIF| + |halfExtendedSubResultantGcd1| |figureUnits| |overset?| + |showTheSymbolTable| |froot| |curve| |rst| |localAbs| + |wordInGenerators| |rightRank| |denomLODE| |nextIrreduciblePoly| + |subscriptedVariables| |selectOrPolynomials| |index?| |s21baf| + |printingInfo?| |rightTrim| |doubleFloatFormat| |asimpson| |element?| + |firstNumer| |qPot| |Lazard| |fullDisplay| |pquo| |complexExpand| + |setleaves!| |secIfCan| |copies| |leaves| |leftTrim| + |leftExactQuotient| |problemPoints| |constantCoefficientRicDE| + |d01alf| |push!| |primlimitedint| |irreducibleFactor| |sumOfDivisors| + |rightExactQuotient| |OMputInteger| |var2StepsDefault| UP2UTS |hcrf| + |OMgetEndAtp| |acothIfCan| |nextsubResultant2| |symmetricPower| + |s18aef| |cyclePartition| |ptFunc| |createThreeSpace| |radPoly| + |rotate| |setsubMatrix!| |f04atf| |pow| |subPolSet?| + |tryFunctionalDecomposition?| |setProperty| |dot| + |complexNumericIfCan| |maxrank| GF2FG |clipSurface| |exponent| + |FormatRoman| |mightHaveRoots| |scanOneDimSubspaces| + |mainSquareFreePart| |leftFactor| |f02wef| |digit| |acosIfCan| + |atanhIfCan| |output| |zero?| |sec2cos| |empty?| |tail| |trueEqual| + |tan2cot| |f04asf| |laguerreL| |approxSqrt| + |removeRoughlyRedundantFactorsInContents| |infieldint| + |halfExtendedSubResultantGcd2| |stopTable!| |rightFactorIfCan| + |setprevious!| |ODESolve| |univariate?| |weight| + |showFortranOutputStack| |cosIfCan| |fmecg| |remainder| + |permutationRepresentation| |reflect| |cyclicEntries| |rarrow| + |integralLastSubResultant| |inverseLaplace| |d03eef| |leftPower| + |semiDegreeSubResultantEuclidean| |euler| |contours| |writeLine!| + |callForm?| |outputFixed| |iiasinh| |associatorDependence| |top| + |halfExtendedResultant2| |abelianGroup| |clearTheSymbolTable| |s17dgf| + |definingPolynomial| |comment| |e02ddf| |coefficient| |f01bsf| + |findCycle| |limitedint| |radicalSimplify| |continue| |f2st| + |integralDerivationMatrix| |mesh| |mainVariable| + |semiResultantEuclideannaif| |viewpoint| |generator| + |exteriorDifferential| |factorGroebnerBasis| |adjoint| |deref| + |coth2tanh| |s14aaf| |inR?| |crushedSet| |zCoord| |typeLists| + |elRow2!| |primintegrate| |pair?| |unitNormalize| |e02ajf| |whileLoop| + |beauzamyBound| |outputArgs| |cyclicSubmodule| |OMlistCDs| |sign| + |outlineRender| |mapmult| |reverse| |zeroOf| |bandedHessian| + |clipPointsDefault| |OMputBVar| |cAsech| |key?| |computePowers| + |s18dcf| |leftExtendedGcd| |localReal?| |changeNameToObjf| + |expressIdealMember| |difference| |OMopenString| |var1StepsDefault| + |minPol| |newLine| |f01brf| |setStatus!| |gbasis| |se2rfi| + |selectsecond| |rightMult| |randnum| |makeSketch| |decimal| |floor| + |constantLeft| |length| |fortranDouble| |vark| |purelyTranscendental?| + |csubst| |equality| |create| |rightZero| |identityMatrix| |twist| + |exQuo| |rightScalarTimes!| |scripts| |rightQuotient| |sn| |order| + |integralAtInfinity?| |clearFortranOutputStack| |OMgetInteger| + |countable?| |factor1| |rightRankPolynomial| |OMgetError| + |stoseInvertible?| |e02gaf| |completeHermite| |setPrologue!| |edf2df| + |ricDsolve| |indicialEquation| |firstDenom| |repeating?| |distFact| + |bumptab1| |ffactor| |equiv?| |shade| |prolateSpheroidal| |divide| + |cyclic| |e02dff| |gcdPolynomial| |OMputEndApp| |radicalEigenvectors| + |pseudoRemainder| |Ei| |denomRicDE| |printCode| |cCsc| |s15adf| + |iisec| |s20acf| |edf2efi| |e01sef| |localIntegralBasis| |subTriSet?| + |diagonals| |graphs| |lookup| |ord| |internalSubQuasiComponent?| + |setVariableOrder| |specialTrigs| |assign| |plus!| |linears| |badNum| + |mapSolve| |fortranTypeOf| |pascalTriangle| |maxIndex| |numFunEvals3D| + |oblateSpheroidal| |primaryDecomp| |domainOf| |argument| + |symmetricProduct| |inconsistent?| |andOperands| |complete| |palgRDE| + |realElementary| |orbit| |infinityNorm| |resetNew| |OMgetEndBVar| + |refine| |pToHdmp| |cyclic?| |cCot| |polar| |leastPower| + |rightAlternative?| |interReduce| |nextItem| |meshPar1Var| |addPoint| + |monomial?| |subResultantGcd| |shiftLeft| |btwFact| |twoFactor| + |firstSubsetGray| |rischDEsys| |diag| |s19adf| |palgextint| |c06ekf| + |changeThreshhold| |transcendent?| |eulerE| |janko2| |groebner?| + |mainVariables| |li| |doublyTransitive?| |constantOpIfCan| + |computeCycleEntry| |swap!| |OMcloseConn| |symbol| + |removeRedundantFactorsInPols| |pointColorDefault| |nthCoef| + |OMputString| |completeSmith| |tensorProduct| |simplifyExp| |leftUnit| + |primeFactor| |zeroDimensional?| |nextPrime| |stopTableInvSet!| + |lowerCase?| |partialQuotients| |nextSubsetGray| + |createIrreduciblePoly| |viewWriteAvailable| |reducedSystem| + |collectUpper| |op| |iteratedInitials| |doubleResultant| |tubeRadius| + |invmod| |explicitEntries?| |lastSubResultant| |error| |integer| + |e04gcf| |setValue!| |divergence| |tanh2trigh| |OMputError| |integers| + |back| |tValues| |tubePoints| |sdf2lst| |eq| |second| + |lineColorDefault| |forLoop| |pade| |jordanAdmissible?| |mapDown!| + |assert| |polyPart| |curve?| |OMgetSymbol| |poisson| ~= + |startTableInvSet!| |block| |lazyEvaluate| |iter| |expandTrigProducts| + |third| |c06gbf| |s15aef| |fractionFreeGauss!| |root?| + |basisOfLeftNucleus| |redPol| |maxRowIndex| |morphism| |coerce| + |OMunhandledSymbol| |spherical| |fill!| |e02dcf| |mainVariable?| + |symmetricDifference| |denominator| |socf2socdf| |someBasis| |s17aff| + |separateFactors| |readLineIfCan!| |split| |construct| |legendreP| + 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|ramifiedAtInfinity?| |stopMusserTrials| + |subResultantsChain| |nil| |diagonal?| |bernoulli| |userOrdered?| + |nonLinearPart| |eigenvalues| |cAtanh| |hasPredicate?| |cPower| + |trunc| |dflist| |getMeasure| |iisin| |minIndex| |positiveRemainder| + |term?| |OMencodingXML| |unrankImproperPartitions0| |rischNormalize| + |s17aef| |besselK| |lyndon?| |wholeRagits| |biRank| |e02bbf| + |children| |simpsono| |removeRedundantFactors| |viewZoomDefault| + |bezoutDiscriminant| |parts| |cycleSplit!| |outputFloating| |credPol| + |maxdeg| |collectQuasiMonic| |SturmHabichtMultiple| |s18def| + |supersub| |exprToUPS| |critMonD1| |mergeDifference| |approximate| + |badValues| |setColumn!| |fortranLiteralLine| |completeHensel| + |pointColorPalette| |readLine!| |logGamma| |setScreenResolution3D| + |complex| |over| |s13acf| |coshIfCan| |alphanumeric| |hexDigit| + |mkAnswer| |s14baf| |exponents| |extractIfCan| |partialDenominators| + |super| |obj| |genericRightMinimalPolynomial| |palgextint0| + |varselect| |divideExponents| |critB| |cAsin| |d02gaf| |crest| + |mpsode| |parametersOf| |tubePlot| |cyclotomic| |charpol| |chebyshevU| + |cache| |d03edf| |s17adf| |dfRange| |level| |OMReadError?| |psolve| + |largest| |complement| |c05adf| |factorAndSplit| |universe| + |tryFunctionalDecomposition| |geometric| |c06eaf| |quoted?| |makeCos| + |log| |abs| |characteristic| |eyeDistance| |stripCommentsAndBlanks| + |bumptab| |plenaryPower| |rational| |pomopo!| |normDeriv2| + |deepestTail| |internalInfRittWu?| |insertBottom!| |isMult| + |meshPar2Var| |exprex| |c06fuf| |hdmpToP| |setelt| |redpps| + |plotPolar| |buildSyntax| |colorFunction| |tanh2coth| |result| + |sizeMultiplication| |oddInfiniteProduct| |complexZeros| + |createMultiplicationTable| |flexible?| |e01sbf| |double| |implies?| + |OMgetString| |monic?| |Gamma| |tanintegrate| |setPosition| + |lyndonIfCan| |rootPower| |binarySearchTree| |writable?| |one?| + |d01anf| |copy| |rangeIsFinite| |karatsuba| |euclideanNormalForm| + |alternatingGroup| |primextintfrac| |OMreadStr| |clipWithRanges| + |drawComplexVectorField| |odd?| |variationOfParameters| |exp1| + |satisfy?| |freeOf?| |PollardSmallFactor| |arity| |e01bff| |simpson| + |solveid| |f02axf| |inverseColeman| |removeSinSq| |aCubic| |rk4a| + |autoCoerce| |derivationCoordinates| |constDsolve| |setref| |hspace| + |characteristicSerie| |graeffe| |space| |critT| |movedPoints| + |getCode| |reverseLex| |divisors| |algebraicDecompose| |monicModulo| + |mainCoefficients| |zeroDimPrimary?| |BasicMethod| |defineProperty| + |OMputAtp| |pushucoef| |makeSUP| |d01gbf| |wordsForStrongGenerators| + |euclideanSize| |stopTableGcd!| |leftZero| |generators| + |cyclicParents| |chvar| |rewriteSetByReducingWithParticularGenerators| + LODO2FUN |quatern| |returnTypeOf| |viewPosDefault| |iiatan| |qfactor| + |sumOfKthPowerDivisors| |declare!| |tan2trig| |backOldPos| + |setMaxPoints| |totalfract| |delay| |factors| |region| + |leftTraceMatrix| |f02aaf| |indicialEquations| + |stoseIntegralLastSubResultant| |move| |escape| |f01qcf| |charClass| + |f02ajf| |oneDimensionalArray| |exprHasWeightCosWXorSinWX| |minordet| + |leftFactorIfCan| |mainKernel| |tab| |meshFun2Var| |dihedralGroup| + |exponential| |open?| |iifact| |checkForZero| |extractBottom!| + |perfectNthRoot| |reify| |represents| |balancedBinaryTree| |imagJ| + |double?| |idealiser| |rewriteIdealWithQuasiMonicGenerators| |sPol| + |opeval| |paren| |modulus| |rank| |high| |algebraicVariables| + |changeMeasure| |pmintegrate| |setRow!| |chebyshevT| |push| + |quotientByP| |lflimitedint| |supDimElseRittWu?| |prime?| |exprToXXP| + |trailingCoefficient| |palgint0| |totalGroebner| |predicates| + |aQuadratic| |nextSublist| |subset?| |schema| |associator| + |OMputEndBVar| |associates?| |perspective| |normalizeIfCan| + |nextColeman| |Is| |normalized?| |e02bdf| |invertibleElseSplit?| + |goodPoint| |declare| |d02raf| |remove| |conditionsForIdempotents| + |d02bbf| |rootPoly| |cylindrical| |elements| |init| |cosh2sech| |id| + |makeVariable| |anfactor| |pushNewContour| |particularSolution| + |gethi| |cCsch| |kroneckerDelta| |listexp| |lists| |shellSort| |last| + |prepareDecompose| |normalForm| |reduceByQuasiMonic| |lazy?| + |messagePrint| |plot| |linearlyDependentOverZ?| |assoc| + |powerAssociative?| |contract| |alternative?| |csc2sin| |sizeLess?| + |conjugates| |mapUp!| |zeroSetSplit| |stoseInvertible?sqfreg| + |imaginary| |harmonic| |sinhIfCan| |baseRDE| |segment| |iicsc| + |lyndon| |node| |integer?| |initTable!| |sts2stst| |curveColor| + |mapMatrixIfCan| |operators| |numberOfComponents| |inGroundField?| + |commaSeparate| |numericalOptimization| |viewport2D| |iicsch| + |separateDegrees| |antiCommutator| |goto| |isAbsolutelyIrreducible?| + |rk4f| |createLowComplexityTable| |showScalarValues| |latex| |exquo| + |LazardQuotient| |internalDecompose| |createPrimitiveNormalPoly| + |RemainderList| |nextPartition| |green| |e04ucf| |zerosOf| |div| + |augment| |scale| ~ |inf| |quote| |nand| |useNagFunctions| + |getMultiplicationMatrix| |quo| + |generalizedContinuumHypothesisAssumed| |setClipValue| + |symmetricGroup| |discriminantEuclidean| |scaleRoots| + |minimalPolynomial| |evenlambert| |leftRecip| |blue| |padicFraction| + |integralRepresents| |quasiMonic?| |sturmVariationsOf| |iilog| + |cAsinh| |c06gqf| |rem| |leadingCoefficientRicDE| |OMgetEndError| + |nor| |matrixDimensions| |d02bhf| |lllip| |topPredicate| |B1solve| + |removeSquaresIfCan| |reorder| |presuper| |reducedDiscriminant| + |rightTrace| |mirror| |iomode| |leftTrace| |patternMatchTimes| + |mapBivariate| |factorByRecursion| |OMputFloat| |internalAugment| + |connect| |open| |maxPoints3D| |sinh2csch| |pdf2df| |linearDependence| + |raisePolynomial| |rowEchLocal| |rootDirectory| |setLabelValue| + |bsolve| |createNormalPrimitivePoly| |shrinkable| + |numberOfComputedEntries| |int| |deepestInitial| + |topFortranOutputStack| |e02zaf| |superHeight| |makeResult| |coerceP| + |cAsec| |comparison| |cycles| |rotatez| |cAcot| |printTypes| |bfEntry| + |quadraticForm| |groebner| |e01bgf| |approximants| |external?| + |linkToFortran| |RittWuCompare| |complexNormalize| + |basisOfMiddleNucleus| |tableau| |algintegrate| + |nextLatticePermutation| |adaptive?| |critBonD| |arg1| |conditionP| + |integerBound| |ReduceOrder| |cRationalPower| |bezoutResultant| + |discreteLog| |compile| |c02aff| |linear| |f04jgf| + |evenInfiniteProduct| |arg2| |queue| |float?| |insertTop!| |getStream| + |partialFraction| |univcase| |rationalFunction| |fortranLogical| + |OMreceive| |subResultantChain| |numerators| + |irreducibleRepresentation| |decreasePrecision| |mapGen| + |identitySquareMatrix| |expextendedint| |intcompBasis| |polynomial| + |rowEch| |headReduced?| |leftQuotient| |univariatePolynomialsGcds| + |conditions| |rightDivide| |findBinding| |balancedFactorisation| + |branchPointAtInfinity?| |kovacic| |addMatchRestricted| |dmpToHdmp| + |not| |coerceListOfPairs| |extractClosed| |OMencodingSGML| + |SturmHabichtSequence| |match| |lazyPseudoQuotient| |slex| + |complexIntegrate| |lepol| |prinpolINFO| |infRittWu?| + |clearTheIFTable| |sturmSequence| |roughEqualIdeals?| + |possiblyInfinite?| |bivariate?| |factorFraction| |ceiling| |basis| + |nativeModuleExtension| |iroot| |ratDsolve| |lo| |pr2dmp| + |invertibleSet| |resultant| |realSolve| |gderiv| |linearAssociatedLog| + |perfectSquare?| |entry| |reducedContinuedFraction| |degree| |incr| + |normalizedAssociate| |unitVector| |nullSpace| |explicitlyFinite?| + |rightDiscriminant| |f01rdf| |bumprow| |swap| |unaryFunction| + |resetBadValues| |hi| |wreath| |overlabel| |moduleSum| |frobenius| + |countRealRootsMultiple| |test| |c06ebf| |mainPrimitivePart| + |att2Result| |leftCharacteristicPolynomial| |removeZeroes| + |normalElement| |horizConcat| |nthFlag| |diagonalMatrix| |style| + |sncndn| |column| |polarCoordinates| |matrixGcd| |c05pbf| |d03faf| + |interpretString| |solveLinearlyOverQ| |label| |minColIndex| + |fortranCarriageReturn| |debug| |kmax| |leftRemainder| |binaryTree| + |fortranComplex| |OMputVariable| |basisOfNucleus| |preprocess| + |conjug| |quasiAlgebraicSet| |center| |formula| |sech2cosh| + |totalDifferential| |selectNonFiniteRoutines| |leftRankPolynomial| + |cTanh| |inspect| |startPolynomial| |decrease| |insert!| |trigs| + |leftRank| |leader| |divisor| |sumOfSquares| |physicalLength!| |cn| + |nullary?| |d01gaf| |interval| |supRittWu?| |components| |prindINFO| + |minus!| |localUnquote| |symbol?| |constantOperator| |setOfMinN| + |nil?| |leviCivitaSymbol| |schwerpunkt| |splitLinear| |f2df| + |jacobiIdentity?| |trace2PowMod| |functionIsOscillatory| + |moreAlgebraic?| |bottom!| |orthonormalBasis| |setClosed| |atanIfCan| + |LiePolyIfCan| |nrows| |in?| |d02gbf| |showSummary| |option| + |limitedIntegrate| |iisqrt3| |iiabs| |leadingTerm| |mulmod| |UP2ifCan| + |lifting1| |ncols| |s17agf| |solveLinearPolynomialEquation| + |diophantineSystem| |binaryFunction| |OMmakeConn| |rur| + |endSubProgram| |f04faf| |doubleDisc| |deriv| |weakBiRank| + |deleteProperty!| |cyclotomicDecomposition| |generalizedEigenvector| + |splitConstant| |showAttributes| |moebiusMu| |clearDenominator| + |roughUnitIdeal?| |typeList| |pastel| |xCoord| |numeric| |eq?| + |roughSubIdeal?| ** |trim| |LowTriBddDenomInv| |lfextlimint| + |getExplanations| |generalizedEigenvectors| |e04dgf| |f04mcf| + |radical| |derivative| |rationalPoints| |generate| |even?| |pToDmp| + |cot2trig| |makeViewport3D| |dec| |overbar| |extendIfCan| |hash| + |concat| |radicalSolve| |toScale| |any?| |reset| |birth| |print| + |untab| |trapezoidalo| |primPartElseUnitCanonical!| |phiCoord| EQ + |fortran| |createZechTable| |purelyAlgebraicLeadingMonomial?| + |stiffnessAndStabilityFactor| |incrementBy| |modularGcdPrimitive| + |prinb| |numberOfDivisors| |anticoord| |rightFactorCandidate| |count| + |rationalApproximation| |insertionSort!| |ellipticCylindrical| + |qinterval| |FormatArabic| |expand| |setPoly| |write| |d01aqf| + |startStats!| |fintegrate| |exprHasAlgebraicWeight| |minimize| + |iiasin| |save| |close!| |filterWhile| |approxNthRoot| |pack!| + |rightMinimalPolynomial| |low| |htrigs| + |semiLastSubResultantEuclidean| |squareMatrix| |ef2edf| |dequeue!| + |filterUntil| |sub| |scalarMatrix| |nthr| |commonDenominator| + |interpolate| |squareTop| |fixedPoints| |dn| |structuralConstants| + |fractionPart| |select| |nextNormalPoly| |internalIntegrate| + |weighted| |routines| |create3Space| |certainlySubVariety?| |pushdown| + |simpleBounds?| |createLowComplexityNormalBasis| |transpose| + |makeGraphImage| |removeConstantTerm| |f02xef| |updateStatus!| + |elementary| |modularFactor| |generalLambert| |complexSolve| + |basisOfLeftAnnihilator| |integralMatrixAtInfinity| |logpart| + |minRowIndex| |lSpaceBasis| |c06fqf| |merge!| |generalizedInverse| + |content| |iisinh| |leadingIdeal| |hasTopPredicate?| + |removeRoughlyRedundantFactorsInPols| |loopPoints| |OMclose| |uniform| + |quartic| |getVariableOrder| |imagi| |acscIfCan| |optpair| |sin?| + |cSin| |OMwrite| |randomR| |musserTrials| |ParCond| + |tubePointsDefault| |stoseLastSubResultant| |integerIfCan| + |lowerCase!| |hMonic| |lieAdmissible?| |coleman| |monomRDEsys| + |radicalEigenvector| |selectMultiDimensionalRoutines| |integralBasis| + |s18acf| |endOfFile?| |linearAssociatedExp| |mainValue| |rk4qc| + |makeRecord| |shuffle| |clipBoolean| |OMgetEndAttr| |cot2tan| + |pushuconst| |remove!| |iiasec| |traceMatrix| + |noncommutativeJordanAlgebra?| |qelt| |getDatabase| |isList| + |OMconnectTCP| |rightUnits| |rightGcd| |constant?| |fractRagits| + |realRoots| |viewPhiDefault| |useEisensteinCriterion?| |presub| + |physicalLength| |headRemainder| |quasiRegular?| |simplify| |diagonal| + |setlast!| |OMsupportsCD?| |isOp| |lowerPolynomial| |lifting| + |transform| |invertible?| |algSplitSimple| |xRange| |setvalue!| + |stack| |setEmpty!| |distribute| |lintgcd| |viewDeltaYDefault| |lex| + |octon| |replaceKthElement| |retract| |f02aff| |yRange| |ldf2vmf| + |semicolonSeparate| |systemSizeIF| |tableForDiscreteLogarithm| + |ratpart| |symbolTable| |minset| |f01qef| |outputAsTex| |zRange| + |degreeSubResultant| |companionBlocks| |ode2| |addPointLast| |bits| + |c06ecf| |pureLex| |Beta| |tanIfCan| |f02bjf| |stoseInvertibleSet| + |iiperm| |useSingleFactorBound?| |map!| |makeEq| |OMgetType| |script| + |infieldIntegrate| |recur| |goodnessOfFit| |extensionDegree| + |pushFortranOutputStack| |recip| |rename| |e04mbf| |OMconnOutDevice| + |qsetelt!| |consnewpol| |nthFractionalTerm| |cross| |factorset| + |safeCeiling| |numberOfFractionalTerms| |property| + |popFortranOutputStack| |scalarTypeOf| |leftMult| |f04arf| |negative?| + |red| |changeName| |fixedPoint| |internalLastSubResultant| + |leftScalarTimes!| |c02agf| |npcoef| |currentSubProgram| + |outputAsFortran| |constantRight| |nsqfree| + |zeroSetSplitIntoTriangularSystems| |rewriteSetWithReduction| |tex| + |removeSinhSq| |axesColorDefault| |OMconnInDevice| + |leftMinimalPolynomial| |myDegree| |sumSquares| |updatF| + |countRealRoots| |term| |getGraph| |viewport3D| + |rightCharacteristicPolynomial| |lazyIrreducibleFactors| |summation| + |terms| |s14abf| |allRootsOf| |jacobi| |units| |cartesian| + |setAttributeButtonStep| |factorSquareFreePolynomial| |rootProduct| + |numFunEvals| |getCurve| |wronskianMatrix| |determinant| + |highCommonTerms| |solve| |generalPosition| |clip| + |subResultantGcdEuclidean| |acsch| |exptMod| |initials| |infLex?| + |fixedPointExquo| |OMread| |normalDenom| |degreePartition| + |packageCall| |nthFactor| |resultantReduitEuclidean| |e02aef| + |numberOfChildren| |PDESolve| |cTan| |multiset| |match?| + |principalIdeal| |showAllElements| |OMbindTCP| |printStats!| |unit?| + |binaryTournament| |ddFact| |iiatanh| |headReduce| |quasiRegular| + |showTheRoutinesTable| GE |code| |infix| |getOrder| |aspFilename| + |weierstrass| |inRadical?| |indicialEquationAtInfinity| |OMsend| + |stoseInvertibleSetsqfreg| GT |lazyPquo| |inc| |null?| |shufflein| + |lazyPseudoDivide| |cyclotomicFactorization| |leftOne| + |bivariateSLPEBR| |generalInfiniteProduct| LE |cExp| |rightPower| + |ratPoly| |genericLeftNorm| |extendedEuclidean| |rowEchelonLocal| + |e04fdf| |d01akf| LT |setMinPoints3D| |padicallyExpand| |expPot| + |realEigenvalues| |bipolar| |elliptic?| |iiacos| |s19acf| |choosemon| + |tab1| |mkIntegral| |eigenMatrix| |cschIfCan| |cycleRagits| + |errorKind| |enumerate| |internal?| |vector| + |factorsOfCyclicGroupSize| |divideIfCan!| |irreducibleFactors| + |recoverAfterFail| |sin2csc| |lexTriangular| |hermiteH| + |listRepresentation| |differentiate| |HenselLift| |binomial| + |getProperties| |less?| |resultantReduit| |listOfLists| |airyAi| + |minPoints3D| |stoseSquareFreePart| |logIfCan| + |removeSuperfluousCases| |meatAxe| |positive?| |quickSort| |implies| + |basisOfCentroid| |imagk| |solveLinearPolynomialEquationByFractions| + |maxint| |totalLex| |is?| |split!| |comp| |list| |xor| |addMatch| + |ode1| |setFormula!| |innerSolve| |mathieu11| |viewThetaDefault| + |torsionIfCan| |car| |monicLeftDivide| |taylorRep| |e02daf| |ode| + |reindex| |symmetricTensors| |lexGroebner| |cdr| |cCoth| |coHeight| + |fprindINFO| |finite?| |rootNormalize| |leftDiscriminant| + |setDifference| |subNodeOf?| |resultantEuclidean| + |semiResultantReduitEuclidean| |plusInfinity| |factorial| |f04qaf| + |f02fjf| |leftGcd| |setIntersection| |fixedDivisor| |sorted?| + |addPoint2| |minusInfinity| |brillhartIrreducible?| |curryRight| + |continuedFraction| |stoseInvertibleSetreg| |setUnion| |cycleEntry| + |rational?| |rationalPower| |pdf2ef| |nthExpon| |mkcomm| + |complexEigenvalues| |c05nbf| |apply| |addmod| |critMTonD1| + |mathieu22| |eval| |createGenericMatrix| |stFunc2| + |seriesToOutputForm| |removeZero| |shift| |viewDeltaXDefault| |common| + |more?| |alphanumeric?| |d01apf| |thetaCoord| |polygon| + |useSingleFactorBound| |node?| |size| |firstUncouplingMatrix| + |powerSum| |cSec| |function| |realEigenvectors| |integral| |midpoint| + |wholePart| |redPo| |lprop| |bezoutMatrix| |ldf2lst| |asinhIfCan| + |colorDef| |getZechTable| |imagK| |expandLog| |doubleComplex?| + |innerSolve1| |orOperands| |constructorName| |type| |makeSeries| + |OMputEndError| |associative?| |leastMonomial| |cAcos| |first| + |univariateSolve| |primlimintfrac| |outputAsScript| |tree| |weights| + |symFunc| |genericLeftDiscriminant| |removeDuplicates!| + |rewriteIdealWithHeadRemainder| |rest| |true| |bernoulliB| |minrank| + |decompose| |logical?| |makeTerm| |isPower| |idealSimplify| + |substitute| |const| |points| |noLinearFactor?| |subNode?| + |eigenvectors| |startTableGcd!| |objectOf| |SturmHabicht| + |removeDuplicates| |qroot| |accuracyIF| |newSubProgram| |insert| + |members| |monicRightDivide| |getOperands| |entries| + |LyndonCoordinates| |setright!| |iitanh| |f02adf| |bfKeys| |nullity| + |acoshIfCan| |KrullNumber| |chineseRemainder| |minimumDegree| |axes| + |currentCategoryFrame| |transcendentalDecompose| |clearTable!| + |graphStates| |intersect| |s17def| |pointPlot| |void| |dimension| + |Frobenius| |isPlus| |monicDivide| |Aleph| |pseudoDivide| + |irreducible?| |expint| |s17akf| |OMputSymbol| |safeFloor| |LiePoly| + |perfectSqrt| |rotatey| |primitiveElement| |incrementKthElement| + |nary?| |optional?| |generateIrredPoly| |univariatePolynomials| + |lastSubResultantElseSplit| |rightOne| |setleft!| + |inverseIntegralMatrixAtInfinity| |pop!| |lcm| |makeUnit| |entry?| + |elRow1!| |tRange| |subspace| |indices| |OMsupportsSymbol?| + |reducedForm| |An| |asechIfCan| |selectAndPolynomials| |tanSum| + |rootKerSimp| |optimize| |sylvesterMatrix| |screenResolution| + |factorSquareFreeByRecursion| |getOperator| |lhs| + |semiIndiceSubResultantEuclidean| |insertRoot!| + |functionIsFracPolynomial?| |dom| |unitsColorDefault| |pushdterm| + |f01rcf| |width| |gcd| |isTimes| |intensity| |rhs| + |normalizeAtInfinity| |OMUnknownSymbol?| |iiacosh| |lieAlgebra?| + |setLegalFortranSourceExtensions| |OMputEndObject| |union| + |printHeader| |nonSingularModel| |e01saf| |string?| + |genericRightDiscriminant| |false| |triangulate| |rowEchelon| + |subtractIfCan| |expt| |antisymmetric?| UTS2UP |lagrange| + |extendedIntegrate| |fortranCompilerName| |convergents| |distdfact| + |cSinh| |leftDivide| |e04naf| |llprop| |mat| |coth2trigh| + |tracePowMod| |showArrayValues| |symmetricRemainder| |c06gcf| |title| + |isExpt| |factorsOfDegree| |optional| |close| |patternVariable| + |dequeue| |neglist| |select!| |palginfieldint| |optAttributes| + |inrootof| FG2F |OMencodingUnknown| |legendre| |withPredicates| NOT + |normalizedDivide| |listLoops| |shanksDiscLogAlgorithm| |cAtan| + |display| |mathieu23| |HermiteIntegrate| |f04mbf| |outerProduct| + |roman| OR |nlde| |shiftRight| |e| |expenseOfEvaluation| + |createNormalPoly| |permanent| |unprotectedRemoveRedundantFactors| + |OMgetEndApp| |usingTable?| |pointColor| AND |squareFreePart| + |viewDefaults| |graphState| |antisymmetricTensors| |mesh?| + |showRegion| |sort| |primintfldpoly| |leadingExponent| |s21bcf| |cup| + |datalist| |OMputEndBind| |upDateBranches| |ignore?| + |fortranLinkerArgs| |OMgetAtp| |position!| |dim| |Nul| |polyRicDE| + |leftNorm| |d01amf| |leftLcm| |OMputAttr| |sylvesterSequence| + |positiveSolve| |parent| |OMgetBVar| |mainForm| |polygamma| |e02bcf| + |stFunc1| |input| |fortranDoubleComplex| |root| |squareFreePolynomial| + |mapExpon| |constant| |graphImage| |OMParseError?| |curveColorPalette| + |library| |strongGenerators| |mathieu24| |droot| |toseSquareFreePart| + |sequences| |closedCurve| |coefChoose| |parametric?| |measure2Result| + |component| |commutativeEquality| |random| |rightNorm| + |normInvertible?| |removeSuperfluousQuasiComponents| + |radicalOfLeftTraceForm| |e01baf| |substring?| + |integralBasisAtInfinity| |readable?| |toseLastSubResultant| + |fglmIfCan| |s18adf| |mindeg| |f07adf| |normal01| |e01daf| |nthRoot| + |basisOfCommutingElements| |erf| |s13aaf| |aromberg| |resultantnaif| + |suffix?| |hitherPlane| |set| |setProperty!| |mainMonomials| |cubic| * + |interpret| |roughBase?| |uniform01| |UpTriBddDenomInv| |sayLength| + |screenResolution3D| |size?| |curry| |closedCurve?| |d01asf| |light| + |ListOfTerms| |prefix?| |virtualDegree| |sincos| |leadingBasisTerm| + |useEisensteinCriterion| |charthRoot| |dilog| |coerceS| + |selectFiniteRoutines| |transcendenceDegree| |cap| + |eisensteinIrreducible?| |iidsum| |iicot| |po| |simplifyLog| + |antiAssociative?| |status| |sin| |flexibleArray| |f04adf| |coerceL| + |argumentList!| |iicosh| |rightRegularRepresentation| |zag| |besselY| + |setPredicates| |generic?| |multiplyCoefficients| |adaptive3D?| + |removeRedundantFactorsInContents| |initial| |c06fpf| + |LagrangeInterpolation| |point| |rootSimp| |iicoth| + |groebnerFactorize| |cos| |semiResultantEuclidean2| |rightExtendedGcd| + |createRandomElement| |calcRanges| |conical| |printStatement| + |OMgetBind| |bitTruth| |completeEval| ^ |changeBase| + |listYoungTableaus| |sinhcosh| |totolex| |check| |character?| + |exponential1| |pushup| |linearAssociatedOrder| |genericLeftTrace| + |infix?| |norm| |aLinear| |algebraicSort| |basicSet| |impliesOperands| + |composites| |series| |bitLength| |iidprod| |mask| |fTable| |s20adf| + |prepareSubResAlgo| |polygon?| |extendedint| |show| |recolor| |every?| + |areEquivalent?| |generalizedContinuumHypothesisAssumed?| |flagFactor| + |s21bbf| |rectangularMatrix| |normFactors| |chiSquare| |pattern| + |setImagSteps| |failed?| |ratDenom| |alphabetic| + |reduceBasisAtInfinity| |fortranInteger| |selectIntegrationRoutines| + |rightLcm| |insertMatch| |trace| |extract!| |omError| |matrix| + |subresultantVector| |associatedEquations| |factorials| |rombergo| + |atoms| |solve1| |e02def| |functionIsContinuousAtEndPoints| |relerror| + |min| |factorOfDegree| |parabolicCylindrical| + |exprHasLogarithmicWeights| |blankSeparate| |selectPolynomials| + |radicalRoots| |normalDeriv| |wholeRadix| |cAcsc| |alternating| + |wordInStrongGenerators| |cosSinInfo| |extend| |hermite| |algDsolve| + |sum| |scripted?| |laurentRep| |setMinPoints| |hypergeometric0F1| + |shiftRoots| |frst| |halfExtendedResultant1| |binary| |iCompose| + |isQuotient| |absolutelyIrreducible?| |duplicates| + |lastSubResultantEuclidean| |createNormalElement| |e01sff| |tanhIfCan| + |mainDefiningPolynomial| |extractSplittingLeaf| |limitPlus| |dmp2rfi| + |computeBasis| |newTypeLists| |getIdentifier| |yellow| |setelt!| + |compdegd| |d01ajf| |nonQsign| |collectUnder| |selectPDERoutines| + |stirling2| |f01ref| |traverse| |GospersMethod| |OMputEndAttr| + |mainCharacterization| |upperCase!| |epilogue| |atrapezoidal| + |palgLODE| |direction| |SturmHabichtCoefficients| |e01bhf| + |fullPartialFraction| |intChoose| |ScanRoman| |resetVariableOrder| + |drawToScale| |jacobian| |symbolTableOf| |stirling1| |lfunc| + |increment| |pdct| |inverseIntegralMatrix| |f04axf| |height| |surface| + |coefficients| |singularitiesOf| |cond| |idealiserMatrix| + |quotedOperators| |makingStats?| |row| |string| |round| |minPoly| + |numberOfMonomials| |s18aff| |bag| |unary?| |mapUnivariateIfCan| + |fractRadix| |selectOptimizationRoutines| |cyclicGroup| |cyclicEqual?| + |rationalPoint?| |bright| |fortranLiteral| |heap| |lfintegrate| + |swapColumns!| |hconcat| |delta| |pmComplexintegrate| |closed?| + |color| |max| |gcdcofactprim| |returnType!| |vspace| |conjugate| + |unitCanonical| |subSet| |internalSubPolSet?| |redmat| |cyclicCopy| + |tanQ| |complementaryBasis| |basisOfRightAnnihilator| + |selectSumOfSquaresRoutines| |getGoodPrime| |alphabetic?| |wrregime| + |outputList| |unrankImproperPartitions1| |clikeUniv| |groebgen| + |squareFreePrim| |showTypeInOutput| |delete| |principal?| |Ci| |df2ef| + |rischDE| |multiEuclidean| |d01bbf| |quadratic?| |ravel| |bit?| + |numericIfCan| |simplifyPower| |setOrder| |ideal| |cothIfCan| |edf2ef| + |reshape| |dmpToP| |lighting| |unravel| |algebraicCoefficients?| + |curryLeft| |setchildren!| |OMUnknownCD?| |expintfldpoly| + |squareFreeFactors| |nextPrimitivePoly| |midpoints| |lambda| |ref| + |closeComponent| |s19aaf| |hex| |characteristicSet| |s19abf| + |cscIfCan| |mantissa| |bindings| |initiallyReduced?| |startTable!| + |systemCommand| |returns| |OMputBind| |trivialIdeal?| |outputForm| + |mapCoef| |identification| |brillhartTrials| |shallowCopy| + |complexElementary| |copyInto!| |printInfo!| |solid?| |exists?| |cons| + |subMatrix| |update| |var2Steps| |iiacsc| |clearTheFTable| |f07aef| + |imagI| |divideIfCan| |makeop| |genus| |rroot| |polyred| |readIfCan!| + |basisOfCenter| |linearMatrix| |leaf?| |ipow| |OMgetVariable| |e02ahf| + |chiSquare1| |nextPrimitiveNormalPoly| |radicalEigenvalues| + |setProperties| |log10| |mathieu12| |variable?| |setnext!| + |rangePascalTriangle| |var1Steps| |linearlyDependent?| |bitand| + |modularGcd| |tower| |singularAtInfinity?| |zoom| |polCase| + |pseudoQuotient| |repeatUntilLoop| |primitive?| |bitior| |debug3D| + |representationType| |directory| |testModulus| |ksec| + |loadNativeModule| |vertConcat| |equation| |LazardQuotient2| + |operation| |critM| |prefix| |powern| |objects| |lowerCase| |position| + BY |lazyVariations| |integrate| |zeroMatrix| |roughBasicSet| + |superscript| |hclf| |youngGroup| |base| |empty| |lift| + |createPrimitiveElement| |genericRightTrace| |drawComplex| |testDim| + |numberOfNormalPoly| |differentialVariables| |karatsubaDivide| |slash| + |bitCoef| |argscript| |semiDiscriminantEuclidean| |unexpand| |t| + |updatD| |f04maf| |probablyZeroDim?| |/\\| |df2st| |OMgetAttr| + |realZeros| |setrest!| |makeFloatFunction| |prem| |extractProperty| + |makeViewport2D| |\\/| |integral?| |s21bdf| |gcdprim| |ridHack1| + |iisech| |e04ycf| |nextsousResultant2| |nthRootIfCan| |iiacsch| + |triangular?| |primitivePart| |cAcsch| |or?| |d02cjf| |fi2df| + |showAll?| |multiplyExponents| |iiexp| |Vectorise| |rdHack1| + |LyndonWordsList1| |atom?| |controlPanel| |belong?| |retractable?| + |unvectorise| |sizePascalTriangle| |numberOfIrreduciblePoly| + |triangularSystems| |numerator| |setTex!| |brace| |stronglyReduce| + |permutation| |cardinality| |tanNa| |normal| |setScreenResolution| + |heapSort| |monicDecomposeIfCan| |showClipRegion| |tubeRadiusDefault| + |innerint| |symmetric?| |subCase?| |monicCompleteDecompose| |separant| + |orbits| |getBadValues| |LyndonBasis| |null| |gradient| |vconcat| + |mindegTerm| |setRealSteps| |minimumExponent| |ocf2ocdf| + |pointSizeDefault| |digit?| |genericRightNorm| |splitSquarefree| + |checkPrecision| |sinIfCan| |case| |getButtonValue| + |semiSubResultantGcdEuclidean2| |argumentListOf| |char| |padecf| + |cotIfCan| |value| |pointLists| |ScanArabic| |polyRDE| |Zero| + |previous| |palglimint0| |central?| |externalList| + |basisOfLeftNucloid| |hue| |One| |enqueue!| |rootsOf| |linGenPos| + |jordanAlgebra?| |front| |head| |modifyPointData| |invmultisect| + |relativeApprox| |iiasech| |product| |complexLimit| |f07fef| + |complex?| |complexNumeric| |magnitude| |swapRows!| |baseRDEsys| + |outputSpacing| |besselI| |submod| |lazyPseudoRemainder| |float| + |selectODEIVPRoutines| |removeCosSq| |varList| |completeEchelonBasis| + |compound?| |tan| |leadingIndex| |regime| |kernels| |adaptive| + |branchIfCan| |knownInfBasis| |contractSolve| |cot| + |getMultiplicationTable| |solveInField| |toroidal| |randomLC| + |replace| |zeroSquareMatrix| |f01qdf| |univariate| |elt| + |partialNumerators| |genericLeftMinimalPolynomial| |sec| + |intPatternMatch| |f07fdf| |f02agf| |modifyPoint| |coord| + |rewriteIdealWithRemainder| Y |numberOfHues| |OMputApp| |getProperty| + |csc| |e02adf| |listBranches| |OMreadFile| |key| |removeCoshSq| + |oddlambert| |maxrow| |finiteBasis| |asin| |log2| |shallowExpand| + |setAdaptive| |options| |stop| |unit| |toseInvertible?| |factor| + |s17ajf| = |UnVectorise| |acos| |fillPascalTriangle| + |changeWeightLevel| |pol| |OMgetEndObject| |checkRur| |sqrt| + |dominantTerm| |numberOfOperations| |lazyGintegrate| + |expenseOfEvaluationIF| |atan| |categoryFrame| |separate| |delete!| + |filename| |gcdPrimitive| |partition| |real| |iiGamma| < |lazyPrem| + |acot| |setErrorBound| |whatInfinity| |reduction| |mainContent| + |properties| |eulerPhi| |internalZeroSetSplit| |imag| |lllp| > + |sortConstraints| |e04jaf| |integralMatrix| |asec| |constantIfCan| + |table| |coerceImages| |not?| |reduce| |keys| |dictionary| + |directProduct| |stoseInternalLastSubResultant| |palgint| <= |power| + |associatedSystem| |acsc| |OMopenFile| |enterInCache| |parse| + |Hausdorff| |new| |singleFactorBound| |monomialIntegrate| + |oddintegers| |translate| |hasSolution?| >= |elem?| |sinh| |s17dlf| + |repeating| |cCosh| |f02awf| |arguments| |createPrimitivePoly| + |leftUnits| |destruct| |BumInSepFFE| |hasHi| |normal?| |cosh| + |showIntensityFunctions| |karatsubaOnce| |errorInfo| |mapdiv| + |perfectNthPower?| |lambert| |drawCurves| |digamma| |d01fcf| + |predicate| |tanh| |dioSolve| |primes| |vedf2vef| |cfirst| |find| + |plus| |hostPlatform| |chainSubResultants| |bombieriNorm| + |nodeOf?| + |coth| |genericRightTraceForm| |numberOfVariables| |duplicates?| + |makeprod| |euclideanGroebner| |OMgetFloat| |distance| |aQuartic| - + |infiniteProduct| |sech| |mapUnivariate| |cos2sec| |edf2fi| |digits| + |fortranReal| |complexEigenvectors| |monomial| |enterPointData| + |numberOfComposites| / |sh| |csch| |postfix| |setMaxPoints3D| |df2mf| + |quadratic| |notOperand| |linearPart| |changeVar| |multivariate| + |coordinates| |scopes| |iitan| |asinh| |doubleRank| |mix| + |fortranCharacter| |compose| |module| |OMputObject| |reverse!| + |variables| |rootOf| |times| |complexRoots| |generic| |cycleElt| + |acosh| |subQuasiComponent?| |rule| |sechIfCan| |truncate| |multisect| + |binomThmExpt| |cLog| |possiblyNewVariety?| |listOfMonoms| RF2UTS + |atanh| |definingEquations| |csch2sinh| |yCoordinates| |nodes| + |failed| |getlo| |extension| |ranges| |cAcoth| |iprint| |member?| + |acoth| |rotatex| |infinite?| + |solveLinearPolynomialEquationByRecursion| |setAdaptive3D| |left| + |mkPrim| |#| |inHallBasis?| |innerEigenvectors| |multiple?| |pile| + |parabolic| |next| |asech| |newReduc| |algint| |pole?| + |numberOfImproperPartitions| |right| |iicos| |zeroDimPrime?| + |reduceLODE| |lazyResidueClass| |monom| |algebraicOf| |operator| + |equiv| |stoseInvertible?reg| |range| |henselFact| |taylorIfCan| + |taylorQuoByVar| |acotIfCan| |rules| |taylor| |factorSquareFree| + |imagj| |multiple| |bipolarCylindrical| |revert| |groebSolve| + |torsion?| |d02ejf| |setButtonValue| |coordinate| |laurent| |modTree| + |call| |elliptic| |reducedQPowers| |applyQuote| |index| |scan| |cycle| + |quoByVar| |initiallyReduce| |rootBound| |OMlistSymbols| |puiseux| + |singular?| |listConjugateBases| |signAround| |times!| |upperCase?| + |yCoord| |number?| |dark| |indiceSubResultant| |linSolve| |minGbasis| + |d02kef| |numberOfCycles| |ran| |hessian| |seriesSolve| + |internalIntegrate0| |corrPoly| |inv| |laguerre| |lexico| + |branchPoint?| |ruleset| |normalize| |resize| |pair| |mdeg| + |constantToUnaryFunction| |ground?| |dimensionsOf| |medialSet| + |skewSFunction| |identity| |rootSplit| |setTopPredicate| |solveLinear| + |tanAn| |f01maf| |basisOfRightNucloid| |ground| |seed| |exprToGenUPS| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 4326de1e..26bd0179 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,4911 +1,4911 @@ -(3145093 . 3419278800) -((-3746 (((-108) (-1 (-108) |#2| |#2|) $) 63) (((-108) $) NIL)) (-1943 (($ (-1 (-108) |#2| |#2|) $) 18) (($ $) NIL)) (-1230 ((|#2| $ (-525) |#2|) NIL) ((|#2| $ (-1139 (-525)) |#2|) 34)) (-1626 (($ $) 59)) (-3336 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 40) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 38) ((|#2| (-1 |#2| |#2| |#2|) $) 37)) (-1930 (((-525) (-1 (-108) |#2|) $) 22) (((-525) |#2| $) NIL) (((-525) |#2| $ (-525)) 73)) (-3781 (((-592 |#2|) $) 13)) (-1440 (($ (-1 (-108) |#2| |#2|) $ $) 48) (($ $ $) NIL)) 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|%noBranch|))) +(((-21) . T) ((-23) . T) ((-25) . T) ((-37 #0=(-385 (-525))) -3309 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-37 |#1|) . T) ((-37 $) -3309 (|has| |#1| (-517)) (|has| |#1| (-327)) (|has| |#1| (-341)) (|has| |#1| (-286))) ((-34) |has| |#1| (-1112)) ((-91) |has| |#1| (-1112)) ((-97) . T) ((-107 #0# #0#) -3309 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-107 |#1| |#1|) . T) ((-107 $ $) . T) ((-126) . T) ((-136) -3309 (|has| |#1| (-327)) (|has| |#1| (-136))) ((-138) |has| |#1| (-138)) ((-566 (-797)) . T) ((-160) . T) ((-567 (-157 (-205))) |has| |#1| (-952)) ((-567 (-157 (-357))) |has| |#1| (-952)) ((-567 (-501)) |has| |#1| (-567 (-501))) ((-567 (-826 (-357))) |has| |#1| (-567 (-826 (-357)))) ((-567 (-826 (-525))) |has| |#1| (-567 (-826 (-525)))) ((-567 #1=(-1086 |#1|)) . T) ((-211 |#1|) . T) ((-213) -3309 (|has| |#1| (-327)) (|has| |#1| (-213))) ((-223) -3309 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-263) |has| |#1| (-1112)) ((-265 |#1| $) |has| |#1| (-265 |#1| |#1|)) ((-269) -3309 (|has| |#1| (-517)) (|has| |#1| (-327)) (|has| |#1| (-341)) (|has| |#1| (-286))) ((-286) -3309 (|has| |#1| (-327)) (|has| |#1| (-341)) (|has| |#1| (-286))) ((-288 |#1|) |has| |#1| (-288 |#1|)) ((-341) -3309 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-380) |has| |#1| (-327)) ((-346) -3309 (|has| |#1| (-346)) (|has| |#1| (-327))) ((-327) |has| |#1| (-327)) ((-348 |#1| #1#) . T) ((-387 |#1| #1#) . T) ((-316 |#1|) . T) ((-355 |#1|) . T) ((-378 |#1|) . T) ((-389 |#1|) . T) ((-429) -3309 (|has| |#1| (-327)) (|has| |#1| (-341)) (|has| |#1| (-286))) ((-466) |has| |#1| (-1112)) ((-486 (-1090) |#1|) |has| |#1| (-486 (-1090) |#1|)) ((-486 |#1| |#1|) |has| |#1| (-288 |#1|)) ((-517) -3309 (|has| |#1| (-517)) (|has| |#1| (-327)) (|has| |#1| (-341)) (|has| |#1| (-286))) ((-594 #0#) -3309 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-594 |#1|) . T) ((-594 $) . T) ((-588 (-525)) |has| |#1| (-588 (-525))) ((-588 |#1|) . T) ((-660 #0#) -3309 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-660 |#1|) . T) ((-660 $) -3309 (|has| |#1| (-517)) (|has| |#1| (-327)) (|has| |#1| (-341)) (|has| |#1| (-286))) ((-667 |#1| #1#) . T) ((-669) . T) ((-789) |has| |#1| (-789)) ((-834 (-1090)) |has| |#1| (-834 (-1090))) ((-820 (-357)) |has| |#1| (-820 (-357))) ((-820 (-525)) |has| |#1| (-820 (-525))) ((-818 |#1|) . T) ((-843) -12 (|has| |#1| (-286)) (|has| |#1| (-843))) ((-854) -3309 (|has| |#1| (-327)) (|has| |#1| (-341)) (|has| |#1| (-286))) ((-933) -12 (|has| |#1| (-933)) (|has| |#1| (-1112))) ((-967 (-385 (-525))) |has| |#1| (-967 (-385 (-525)))) ((-967 (-525)) |has| |#1| (-967 (-525))) ((-967 |#1|) . T) ((-982 #0#) -3309 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-982 |#1|) . T) ((-982 $) . T) ((-976) . T) ((-983) . T) ((-1031) . T) ((-1019) . T) ((-1066) |has| |#1| (-327)) ((-1112) |has| |#1| (-1112)) ((-1115) |has| |#1| (-1112)) ((-1126) . 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T) ((-486 |#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) ((-594 |#2|) -3215 (|has| |#2| (-976)) (|has| |#2| (-341)) (|has| |#2| (-160))) ((-594 $) -3215 (|has| |#2| (-976)) (|has| |#2| (-787)) (|has| |#2| (-160))) ((-588 (-525)) -12 (|has| |#2| (-588 (-525))) (|has| |#2| (-976))) ((-588 |#2|) |has| |#2| (-976)) ((-660 |#2|) -3215 (|has| |#2| (-341)) (|has| |#2| (-160))) ((-669) -3215 (|has| |#2| (-976)) (|has| |#2| (-787)) (|has| |#2| (-160))) ((-733) |has| |#2| (-787)) ((-734) -3215 (|has| |#2| (-787)) (|has| |#2| (-735))) ((-735) |has| |#2| (-735)) ((-736) -3215 (|has| |#2| (-787)) (|has| |#2| (-735))) ((-737) -3215 (|has| |#2| (-787)) (|has| |#2| (-735))) ((-787) |has| |#2| (-787)) ((-789) -3215 (|has| |#2| (-787)) (|has| |#2| (-735))) ((-834 (-1090)) -12 (|has| |#2| (-834 (-1090))) (|has| |#2| (-976))) ((-967 (-385 (-525))) -12 (|has| |#2| (-967 (-385 (-525)))) (|has| |#2| (-1019))) ((-967 (-525)) -12 (|has| |#2| (-967 (-525))) (|has| |#2| (-1019))) ((-967 |#2|) |has| |#2| (-1019)) ((-982 |#2|) -3215 (|has| |#2| (-976)) (|has| |#2| (-341)) (|has| |#2| (-160))) ((-982 $) |has| |#2| (-160)) ((-976) -3215 (|has| |#2| (-976)) (|has| |#2| (-787)) (|has| |#2| (-160))) ((-983) -3215 (|has| |#2| (-976)) (|has| |#2| (-787)) (|has| |#2| (-160))) ((-1031) -3215 (|has| |#2| (-976)) (|has| |#2| (-787)) (|has| |#2| (-160))) ((-1019) -3215 (|has| |#2| (-1019)) (|has| |#2| (-976)) (|has| |#2| (-787)) (|has| |#2| (-735)) (|has| |#2| (-346)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-126)) (|has| |#2| (-25))) ((-1126) . T) ((-1179 |#2|) |has| |#2| (-341))) -((-2225 (((-220 |#1| |#3|) (-1 |#3| |#2| |#3|) (-220 |#1| |#2|) |#3|) 21)) (-3336 ((|#3| (-1 |#3| |#2| |#3|) (-220 |#1| |#2|) |#3|) 23)) (-2868 (((-220 |#1| |#3|) (-1 |#3| |#2|) (-220 |#1| |#2|)) 18))) -(((-219 |#1| |#2| |#3|) (-10 -7 (-15 -2225 ((-220 |#1| |#3|) (-1 |#3| |#2| |#3|) (-220 |#1| |#2|) |#3|)) (-15 -3336 (|#3| (-1 |#3| |#2| |#3|) (-220 |#1| |#2|) |#3|)) (-15 -2868 ((-220 |#1| |#3|) (-1 |#3| |#2|) (-220 |#1| |#2|)))) (-713) (-1126) (-1126)) (T -219)) -((-2868 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-220 *5 *6)) (-14 *5 (-713)) (-4 *6 (-1126)) (-4 *7 (-1126)) (-5 *2 (-220 *5 *7)) (-5 *1 (-219 *5 *6 *7)))) (-3336 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-220 *5 *6)) (-14 *5 (-713)) (-4 *6 (-1126)) (-4 *2 (-1126)) (-5 *1 (-219 *5 *6 *2)))) (-2225 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-220 *6 *7)) (-14 *6 (-713)) (-4 *7 (-1126)) (-4 *5 (-1126)) (-5 *2 (-220 *6 *5)) (-5 *1 (-219 *6 *7 *5))))) -(-10 -7 (-15 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|#2|)) NIL (|has| |#2| (-976)))) (-3053 (((-713) (-1 (-108) |#2|) $) NIL (|has| $ (-6 -4254))) (((-713) |#2| $) NIL (-12 (|has| $ (-6 -4254)) (|has| |#2| (-1019))))) (-1261 (($ $) NIL)) (-4044 (((-1172 |#2|) $) 10) (($ (-525)) NIL (-3215 (-12 (|has| |#2| (-967 (-525))) (|has| |#2| (-1019))) (|has| |#2| (-976)))) (($ (-385 (-525))) NIL (-12 (|has| |#2| (-967 (-385 (-525)))) (|has| |#2| (-1019)))) (($ |#2|) 13 (|has| |#2| (-1019))) (((-797) $) NIL (|has| |#2| (-566 (-797))))) (-2502 (((-713)) NIL (|has| |#2| (-976)))) (-2443 (((-108) (-1 (-108) |#2|) $) NIL (|has| $ (-6 -4254)))) (-2053 (($ $) NIL (|has| |#2| (-787)))) (-1594 (($ $ (-713)) NIL (|has| |#2| (-976))) (($ $ (-855)) NIL (|has| |#2| (-976)))) (-1436 (($) 35 (|has| |#2| (-126)) CONST)) (-1449 (($) 38 (|has| |#2| (-976)) CONST)) (-1990 (($ $) NIL (-12 (|has| |#2| (-213)) (|has| |#2| (-976)))) (($ $ (-713)) NIL (-12 (|has| |#2| (-213)) (|has| |#2| (-976)))) (($ $ (-1090)) NIL (-12 (|has| |#2| (-834 (-1090))) (|has| |#2| (-976)))) 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(-126)) (-6 (-126)) |%noBranch|) (IF (|has| |t#2| (-669)) (PROGN (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-346)) (-6 (-346)) |%noBranch|) (IF (|has| |t#2| (-160)) (PROGN (-6 (-37 |t#2|)) (-6 (-160))) |%noBranch|) (IF (|has| |t#2| (-6 -4251)) (-6 -4251) |%noBranch|) (IF (|has| |t#2| (-787)) (-6 (-787)) |%noBranch|) (IF (|has| |t#2| (-735)) (-6 (-735)) |%noBranch|) (IF (|has| |t#2| (-341)) (-6 (-1179 |t#2|)) |%noBranch|))) +(((-21) -3309 (|has| |#2| (-976)) (|has| |#2| (-787)) (|has| |#2| (-341)) (|has| |#2| (-160))) ((-23) -3309 (|has| |#2| (-976)) (|has| |#2| (-787)) (|has| |#2| (-735)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-126))) ((-25) -3309 (|has| |#2| (-976)) (|has| |#2| (-787)) (|has| |#2| (-735)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-126)) (|has| |#2| (-25))) ((-33) . T) ((-37 |#2|) |has| |#2| (-160)) ((-97) -3309 (|has| |#2| (-1019)) (|has| |#2| (-976)) (|has| |#2| (-787)) (|has| |#2| (-735)) (|has| |#2| (-346)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-126)) (|has| |#2| (-25))) ((-107 |#2| |#2|) -3309 (|has| |#2| (-976)) (|has| |#2| (-341)) (|has| |#2| (-160))) ((-107 $ $) |has| |#2| (-160)) ((-126) -3309 (|has| |#2| (-976)) (|has| |#2| (-787)) (|has| |#2| (-735)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-126))) ((-566 (-797)) -3309 (|has| |#2| (-1019)) (|has| |#2| (-976)) (|has| |#2| (-787)) (|has| |#2| (-735)) (|has| |#2| (-346)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-566 (-797))) (|has| |#2| (-126)) (|has| |#2| (-25))) ((-566 (-1172 |#2|)) . T) ((-160) |has| |#2| (-160)) ((-211 |#2|) |has| |#2| (-976)) ((-213) -12 (|has| |#2| (-213)) (|has| |#2| (-976))) ((-265 #0=(-525) |#2|) . T) ((-267 #0# |#2|) . T) ((-288 |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1019))) ((-346) |has| |#2| (-346)) ((-355 |#2|) |has| |#2| (-976)) ((-389 |#2|) |has| |#2| (-1019)) ((-464 |#2|) . T) ((-558 #0# |#2|) . 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T) ((-23) . T) ((-46 |#1| |#4|) . T) ((-25) . T) ((-37 #0=(-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((-37 |#1|) |has| |#1| (-160)) ((-37 $) -3215 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-97) . T) ((-107 #0# #0#) |has| |#1| (-37 (-385 (-525)))) ((-107 |#1| |#1|) . T) ((-107 $ $) -3215 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-160))) ((-126) . T) ((-136) |has| |#1| (-136)) ((-138) |has| |#1| (-138)) ((-566 (-797)) . T) ((-160) -3215 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-160))) ((-567 (-501)) -12 (|has| |#1| (-567 (-501))) (|has| |#3| (-567 (-501)))) ((-567 (-826 (-357))) -12 (|has| |#1| (-567 (-826 (-357)))) (|has| |#3| (-567 (-826 (-357))))) ((-567 (-826 (-525))) -12 (|has| |#1| (-567 (-826 (-525)))) (|has| |#3| (-567 (-826 (-525))))) ((-211 |#1|) . T) ((-213) |has| |#1| (-213)) ((-269) -3215 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-288 $) . T) ((-304 |#1| |#4|) . T) ((-355 |#1|) . T) ((-389 |#1|) . T) ((-429) -3215 (|has| |#1| (-843)) (|has| |#1| (-429))) ((-486 |#2| |#1|) |has| |#1| (-213)) ((-486 |#2| $) |has| |#1| (-213)) ((-486 |#3| |#1|) . T) ((-486 |#3| $) . T) ((-486 $ $) . T) ((-517) -3215 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-594 #0#) |has| |#1| (-37 (-385 (-525)))) ((-594 |#1|) . T) ((-594 $) . T) ((-588 (-525)) |has| |#1| (-588 (-525))) ((-588 |#1|) . T) ((-660 #0#) |has| |#1| (-37 (-385 (-525)))) ((-660 |#1|) |has| |#1| (-160)) ((-660 $) -3215 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-669) . T) ((-789) |has| |#1| (-789)) ((-834 (-1090)) |has| |#1| (-834 (-1090))) ((-834 |#3|) . T) ((-820 (-357)) -12 (|has| |#1| (-820 (-357))) (|has| |#3| (-820 (-357)))) ((-820 (-525)) -12 (|has| |#1| (-820 (-525))) (|has| |#3| (-820 (-525)))) ((-883 |#1| |#4| |#3|) . 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T) ((-23) . T) ((-46 |#1| |#4|) . T) ((-25) . T) ((-37 #0=(-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((-37 |#1|) |has| |#1| (-160)) ((-37 $) -3309 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-97) . T) ((-107 #0# #0#) |has| |#1| (-37 (-385 (-525)))) ((-107 |#1| |#1|) . T) ((-107 $ $) -3309 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-160))) ((-126) . T) ((-136) |has| |#1| (-136)) ((-138) |has| |#1| (-138)) ((-566 (-797)) . T) ((-160) -3309 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-160))) ((-567 (-501)) -12 (|has| |#1| (-567 (-501))) (|has| |#3| (-567 (-501)))) ((-567 (-826 (-357))) -12 (|has| |#1| (-567 (-826 (-357)))) (|has| |#3| (-567 (-826 (-357))))) ((-567 (-826 (-525))) -12 (|has| |#1| (-567 (-826 (-525)))) (|has| |#3| (-567 (-826 (-525))))) ((-211 |#1|) . T) ((-213) |has| |#1| (-213)) ((-269) -3309 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-288 $) . T) ((-304 |#1| |#4|) . T) ((-355 |#1|) . T) ((-389 |#1|) . T) ((-429) -3309 (|has| |#1| (-843)) (|has| |#1| (-429))) ((-486 |#2| |#1|) |has| |#1| (-213)) ((-486 |#2| $) |has| |#1| (-213)) ((-486 |#3| |#1|) . T) ((-486 |#3| $) . T) ((-486 $ $) . T) ((-517) -3309 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-594 #0#) |has| |#1| (-37 (-385 (-525)))) ((-594 |#1|) . T) ((-594 $) . T) ((-588 (-525)) |has| |#1| (-588 (-525))) ((-588 |#1|) . T) ((-660 #0#) |has| |#1| (-37 (-385 (-525)))) ((-660 |#1|) |has| |#1| (-160)) ((-660 $) -3309 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-669) . T) ((-789) |has| |#1| (-789)) ((-834 (-1090)) |has| |#1| (-834 (-1090))) ((-834 |#3|) . T) ((-820 (-357)) -12 (|has| |#1| (-820 (-357))) (|has| |#3| (-820 (-357)))) ((-820 (-525)) -12 (|has| |#1| (-820 (-525))) (|has| |#3| (-820 (-525)))) ((-883 |#1| |#4| |#3|) . T) ((-843) |has| |#1| (-843)) ((-967 (-385 (-525))) |has| |#1| (-967 (-385 (-525)))) ((-967 (-525)) |has| |#1| (-967 (-525))) ((-967 |#1|) . T) ((-967 |#2|) . T) ((-967 |#3|) . T) ((-982 #0#) |has| |#1| (-37 (-385 (-525)))) ((-982 |#1|) . T) ((-982 $) -3309 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-160))) ((-976) . T) ((-983) . T) ((-1031) . T) ((-1019) . 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T) ((-23) . T) ((-46 |#1| #0=(-713)) . T) ((-25) . T) ((-37 #1=(-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((-37 |#1|) |has| |#1| (-160)) ((-37 $) -3309 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-341))) ((-97) . T) ((-107 #1# #1#) |has| |#1| (-37 (-385 (-525)))) ((-107 |#1| |#1|) . T) ((-107 $ $) -3309 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-341)) (|has| |#1| (-160))) ((-126) . T) ((-136) |has| |#1| (-136)) ((-138) |has| |#1| (-138)) ((-566 (-797)) . T) ((-160) -3309 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-341)) (|has| |#1| (-160))) ((-567 (-501)) -12 (|has| (-1004) (-567 (-501))) (|has| |#1| (-567 (-501)))) ((-567 (-826 (-357))) -12 (|has| (-1004) (-567 (-826 (-357)))) (|has| |#1| (-567 (-826 (-357))))) ((-567 (-826 (-525))) -12 (|has| (-1004) (-567 (-826 (-525)))) (|has| |#1| (-567 (-826 (-525))))) ((-211 |#1|) . T) ((-213) . T) ((-265 (-385 $) (-385 $)) |has| |#1| (-517)) ((-265 |#1| |#1|) . T) ((-265 $ $) . T) ((-269) -3309 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-341))) ((-286) |has| |#1| (-341)) ((-288 $) . T) ((-304 |#1| #0#) . T) ((-355 |#1|) . T) ((-389 |#1|) . T) ((-429) -3309 (|has| |#1| (-843)) (|has| |#1| (-429)) (|has| |#1| (-341))) ((-486 #2=(-1004) |#1|) . T) ((-486 #2# $) . T) ((-486 $ $) . T) ((-517) -3309 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-341))) ((-594 #1#) |has| |#1| (-37 (-385 (-525)))) ((-594 |#1|) . T) ((-594 $) . T) ((-588 (-525)) |has| |#1| (-588 (-525))) ((-588 |#1|) . T) ((-660 #1#) |has| |#1| (-37 (-385 (-525)))) ((-660 |#1|) |has| |#1| (-160)) ((-660 $) -3309 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-341))) ((-669) . T) ((-789) |has| |#1| (-789)) ((-834 #2#) . T) ((-834 (-1090)) |has| |#1| (-834 (-1090))) ((-820 (-357)) -12 (|has| (-1004) (-820 (-357))) (|has| |#1| (-820 (-357)))) ((-820 (-525)) -12 (|has| (-1004) (-820 (-525))) (|has| |#1| (-820 (-525)))) ((-883 |#1| #0# #2#) . T) ((-843) |has| |#1| (-843)) ((-854) |has| |#1| (-341)) ((-967 (-385 (-525))) |has| |#1| (-967 (-385 (-525)))) ((-967 (-525)) |has| |#1| (-967 (-525))) ((-967 #2#) . T) ((-967 |#1|) . T) ((-982 #1#) |has| |#1| (-37 (-385 (-525)))) ((-982 |#1|) . T) ((-982 $) -3309 (|has| |#1| (-843)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-341)) (|has| |#1| (-160))) ((-976) . T) ((-983) . T) ((-1031) . T) ((-1019) . 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3054281 3054401 "VARIABLE" 3054545 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1167 3054044 3054049 3054079 "UTYPE" 3054084 T UTYPE (NIL) -9 NIL NIL) (-1166 3052879 3053033 3053294 "UTSODETL" 3053870 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1165 3050319 3050779 3051303 "UTSODE" 3052420 NIL UTSODE (NIL T T) -7 NIL NIL) (-1164 3042163 3047959 3048447 "UTS" 3049888 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1163 3033508 3038873 3038915 "UTSCAT" 3040016 NIL UTSCAT (NIL T) -9 NIL 3040773) (-1162 3030863 3031579 3032567 "UTSCAT-" 3032572 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1161 3030494 3030537 3030668 "UTS2" 3030814 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1160 3024770 3027335 3027378 "URAGG" 3029448 NIL URAGG (NIL T) -9 NIL 3030170) (-1159 3021709 3022572 3023695 "URAGG-" 3023700 NIL URAGG- (NIL T T) -8 NIL NIL) (-1158 3017395 3020326 3020797 "UPXSSING" 3021373 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1157 3009286 3016516 3016796 "UPXS" 3017172 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1156 3002315 3009191 3009262 "UPXSCONS" 3009267 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1155 2992604 2999434 2999495 "UPXSCCA" 3000144 NIL UPXSCCA (NIL T T) -9 NIL 3000385) (-1154 2992243 2992328 2992501 "UPXSCCA-" 2992506 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1153 2982454 2989057 2989099 "UPXSCAT" 2989742 NIL UPXSCAT (NIL T) -9 NIL 2990350) (-1152 2981888 2981967 2982144 "UPXS2" 2982369 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1151 2980542 2980795 2981146 "UPSQFREE" 2981631 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1150 2974433 2977488 2977542 "UPSCAT" 2978691 NIL UPSCAT (NIL T T) -9 NIL 2979465) (-1149 2973638 2973845 2974171 "UPSCAT-" 2974176 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1148 2959724 2967761 2967803 "UPOLYC" 2969881 NIL UPOLYC (NIL T) -9 NIL 2971102) (-1147 2951054 2953479 2956625 "UPOLYC-" 2956630 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1146 2950685 2950728 2950859 "UPOLYC2" 2951005 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1145 2942104 2950254 2950391 "UP" 2950595 NIL UP (NIL NIL T) -8 NIL NIL) (-1144 2941447 2941554 2941717 "UPMP" 2941993 NIL UPMP (NIL T T) -7 NIL NIL) (-1143 2941000 2941081 2941220 "UPDIVP" 2941360 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1142 2939568 2939817 2940133 "UPDECOMP" 2940749 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1141 2938803 2938915 2939100 "UPCDEN" 2939452 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1140 2938326 2938395 2938542 "UP2" 2938728 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1139 2936843 2937530 2937807 "UNISEG" 2938084 NIL UNISEG (NIL T) -8 NIL NIL) (-1138 2936058 2936185 2936390 "UNISEG2" 2936686 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1137 2935118 2935298 2935524 "UNIFACT" 2935874 NIL UNIFACT (NIL T) -7 NIL NIL) (-1136 2919014 2934299 2934549 "ULS" 2934925 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1135 2906979 2918919 2918990 "ULSCONS" 2918995 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1134 2889729 2901742 2901803 "ULSCCAT" 2902515 NIL ULSCCAT (NIL T T) -9 NIL 2902811) (-1133 2888780 2889025 2889412 "ULSCCAT-" 2889417 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1132 2878770 2885287 2885329 "ULSCAT" 2886185 NIL ULSCAT (NIL T) -9 NIL 2886915) (-1131 2878204 2878283 2878460 "ULS2" 2878685 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1130 2876602 2877569 2877599 "UFD" 2877811 T UFD (NIL) -9 NIL 2877925) (-1129 2876396 2876442 2876537 "UFD-" 2876542 NIL UFD- (NIL T) -8 NIL NIL) (-1128 2875478 2875661 2875877 "UDVO" 2876202 T UDVO (NIL) -7 NIL NIL) (-1127 2873294 2873703 2874174 "UDPO" 2875042 NIL UDPO (NIL T) -7 NIL NIL) (-1126 2873227 2873232 2873262 "TYPE" 2873267 T TYPE (NIL) -9 NIL NIL) (-1125 2872198 2872400 2872640 "TWOFACT" 2873021 NIL TWOFACT (NIL T) -7 NIL NIL) (-1124 2871136 2871473 2871736 "TUPLE" 2871970 NIL TUPLE (NIL T) -8 NIL NIL) (-1123 2868827 2869346 2869885 "TUBETOOL" 2870619 T TUBETOOL (NIL) -7 NIL NIL) (-1122 2867676 2867881 2868122 "TUBE" 2868620 NIL TUBE (NIL T) -8 NIL NIL) (-1121 2862400 2866654 2866936 "TS" 2867428 NIL TS (NIL T) -8 NIL NIL) (-1120 2851104 2855196 2855292 "TSETCAT" 2860526 NIL TSETCAT (NIL T T T T) -9 NIL 2862057) (-1119 2845839 2847437 2849327 "TSETCAT-" 2849332 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1118 2840102 2840948 2841890 "TRMANIP" 2844975 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1117 2839543 2839606 2839769 "TRIMAT" 2840034 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1116 2837349 2837586 2837949 "TRIGMNIP" 2839292 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1115 2836869 2836982 2837012 "TRIGCAT" 2837225 T TRIGCAT (NIL) -9 NIL NIL) (-1114 2836538 2836617 2836758 "TRIGCAT-" 2836763 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1113 2833437 2835398 2835678 "TREE" 2836293 NIL TREE (NIL T) -8 NIL NIL) (-1112 2832711 2833239 2833269 "TRANFUN" 2833304 T TRANFUN (NIL) -9 NIL 2833370) (-1111 2831990 2832181 2832461 "TRANFUN-" 2832466 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1110 2831794 2831826 2831887 "TOPSP" 2831951 T TOPSP (NIL) -7 NIL NIL) (-1109 2831146 2831261 2831414 "TOOLSIGN" 2831675 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1108 2829807 2830323 2830562 "TEXTFILE" 2830929 T TEXTFILE (NIL) -8 NIL NIL) (-1107 2827672 2828186 2828624 "TEX" 2829391 T TEX (NIL) -8 NIL NIL) (-1106 2827453 2827484 2827556 "TEX1" 2827635 NIL TEX1 (NIL T) -7 NIL NIL) (-1105 2827101 2827164 2827254 "TEMUTL" 2827385 T TEMUTL (NIL) -7 NIL NIL) (-1104 2825255 2825535 2825860 "TBCMPPK" 2826824 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1103 2817144 2823416 2823472 "TBAGG" 2823872 NIL TBAGG (NIL T T) -9 NIL 2824083) (-1102 2812214 2813702 2815456 "TBAGG-" 2815461 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1101 2811598 2811705 2811850 "TANEXP" 2812103 NIL TANEXP (NIL T) -7 NIL NIL) (-1100 2805099 2811455 2811548 "TABLE" 2811553 NIL TABLE (NIL T T) -8 NIL NIL) (-1099 2804511 2804610 2804748 "TABLEAU" 2804996 NIL TABLEAU (NIL T) -8 NIL NIL) (-1098 2799119 2800339 2801587 "TABLBUMP" 2803297 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1097 2798547 2798647 2798775 "SYSTEM" 2799013 T SYSTEM (NIL) -7 NIL NIL) (-1096 2795010 2795705 2796488 "SYSSOLP" 2797798 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1095 2791301 2792009 2792743 "SYNTAX" 2794298 T SYNTAX (NIL) -8 NIL NIL) (-1094 2788435 2789043 2789681 "SYMTAB" 2790685 T SYMTAB (NIL) -8 NIL NIL) (-1093 2783684 2784586 2785569 "SYMS" 2787474 T SYMS (NIL) -8 NIL NIL) (-1092 2780917 2783144 2783373 "SYMPOLY" 2783489 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1091 2780437 2780512 2780634 "SYMFUNC" 2780829 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1090 2776414 2777674 2778496 "SYMBOL" 2779637 T SYMBOL (NIL) -8 NIL NIL) (-1089 2769953 2771642 2773362 "SWITCH" 2774716 T SWITCH (NIL) -8 NIL NIL) (-1088 2763183 2768780 2769082 "SUTS" 2769708 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1087 2755073 2762304 2762584 "SUPXS" 2762960 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1086 2746565 2754694 2754819 "SUP" 2754982 NIL SUP (NIL T) -8 NIL NIL) (-1085 2745724 2745851 2746068 "SUPFRACF" 2746433 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1084 2745349 2745408 2745519 "SUP2" 2745659 NIL SUP2 (NIL T T) -7 NIL NIL) (-1083 2743767 2744041 2744403 "SUMRF" 2745048 NIL SUMRF (NIL T) -7 NIL NIL) (-1082 2743084 2743150 2743348 "SUMFS" 2743688 NIL SUMFS (NIL T T) -7 NIL NIL) (-1081 2727020 2742265 2742515 "SULS" 2742891 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1080 2726342 2726545 2726685 "SUCH" 2726928 NIL SUCH (NIL T T) -8 NIL NIL) (-1079 2720269 2721281 2722239 "SUBSPACE" 2725430 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1078 2719699 2719789 2719953 "SUBRESP" 2720157 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1077 2713068 2714364 2715675 "STTF" 2718435 NIL STTF (NIL T) -7 NIL NIL) (-1076 2707241 2708361 2709508 "STTFNC" 2711968 NIL STTFNC (NIL T) -7 NIL NIL) (-1075 2698592 2700459 2702252 "STTAYLOR" 2705482 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1074 2691836 2698456 2698539 "STRTBL" 2698544 NIL STRTBL (NIL T) -8 NIL NIL) (-1073 2687227 2691791 2691822 "STRING" 2691827 T STRING (NIL) -8 NIL NIL) (-1072 2682116 2686601 2686631 "STRICAT" 2686690 T STRICAT (NIL) -9 NIL 2686752) (-1071 2674832 2679639 2680259 "STREAM" 2681531 NIL STREAM (NIL T) -8 NIL NIL) (-1070 2674342 2674419 2674563 "STREAM3" 2674749 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1069 2673324 2673507 2673742 "STREAM2" 2674155 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1068 2673012 2673064 2673157 "STREAM1" 2673266 NIL STREAM1 (NIL T) -7 NIL NIL) (-1067 2672028 2672209 2672440 "STINPROD" 2672828 NIL STINPROD (NIL T) -7 NIL NIL) (-1066 2671607 2671791 2671821 "STEP" 2671901 T STEP (NIL) -9 NIL 2671979) (-1065 2665150 2671506 2671583 "STBL" 2671588 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1064 2660326 2664373 2664416 "STAGG" 2664569 NIL STAGG (NIL T) -9 NIL 2664658) (-1063 2658028 2658630 2659502 "STAGG-" 2659507 NIL STAGG- (NIL T T) -8 NIL NIL) (-1062 2656223 2657798 2657890 "STACK" 2657971 NIL STACK (NIL T) -8 NIL NIL) (-1061 2648954 2654370 2654825 "SREGSET" 2655853 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1060 2641394 2642762 2644274 "SRDCMPK" 2647560 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1059 2634362 2638835 2638865 "SRAGG" 2640168 T SRAGG (NIL) -9 NIL 2640776) (-1058 2633379 2633634 2634013 "SRAGG-" 2634018 NIL SRAGG- (NIL T) -8 NIL NIL) (-1057 2627828 2632298 2632725 "SQMATRIX" 2632998 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1056 2621580 2624548 2625274 "SPLTREE" 2627174 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1055 2617570 2618236 2618882 "SPLNODE" 2621006 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1054 2616617 2616850 2616880 "SPFCAT" 2617324 T SPFCAT (NIL) -9 NIL NIL) (-1053 2615354 2615564 2615828 "SPECOUT" 2616375 T SPECOUT (NIL) -7 NIL NIL) (-1052 2615115 2615155 2615224 "SPADPRSR" 2615307 T SPADPRSR (NIL) -7 NIL NIL) (-1051 2607138 2608885 2608927 "SPACEC" 2613250 NIL SPACEC (NIL T) -9 NIL 2615066) (-1050 2605309 2607071 2607119 "SPACE3" 2607124 NIL SPACE3 (NIL T) -8 NIL NIL) (-1049 2604061 2604232 2604523 "SORTPAK" 2605114 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1048 2602117 2602420 2602838 "SOLVETRA" 2603725 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1047 2601128 2601350 2601624 "SOLVESER" 2601890 NIL SOLVESER (NIL T) -7 NIL NIL) (-1046 2596348 2597229 2598231 "SOLVERAD" 2600180 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1045 2592163 2592772 2593501 "SOLVEFOR" 2595715 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1044 2586463 2591515 2591611 "SNTSCAT" 2591616 NIL SNTSCAT (NIL T T T T) -9 NIL 2591686) (-1043 2580567 2584794 2585184 "SMTS" 2586153 NIL SMTS (NIL T T T) -8 NIL NIL) (-1042 2574977 2580456 2580532 "SMP" 2580537 NIL SMP (NIL T T) -8 NIL NIL) (-1041 2573136 2573437 2573835 "SMITH" 2574674 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1040 2566101 2570297 2570399 "SMATCAT" 2571739 NIL SMATCAT (NIL NIL T T T) -9 NIL 2572288) (-1039 2563042 2563865 2565042 "SMATCAT-" 2565047 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1038 2560756 2562279 2562322 "SKAGG" 2562583 NIL SKAGG (NIL T) -9 NIL 2562718) (-1037 2556814 2559860 2560138 "SINT" 2560500 T SINT (NIL) -8 NIL NIL) (-1036 2556586 2556624 2556690 "SIMPAN" 2556770 T SIMPAN (NIL) -7 NIL NIL) (-1035 2555424 2555645 2555920 "SIGNRF" 2556345 NIL SIGNRF (NIL T) -7 NIL NIL) (-1034 2554233 2554384 2554674 "SIGNEF" 2555253 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1033 2551923 2552377 2552883 "SHP" 2553774 NIL SHP (NIL T NIL) -7 NIL NIL) (-1032 2545776 2551824 2551900 "SHDP" 2551905 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1031 2545266 2545458 2545488 "SGROUP" 2545640 T SGROUP (NIL) -9 NIL 2545727) (-1030 2545036 2545088 2545192 "SGROUP-" 2545197 NIL SGROUP- (NIL T) -8 NIL NIL) (-1029 2541872 2542569 2543292 "SGCF" 2544335 T SGCF (NIL) -7 NIL NIL) (-1028 2536271 2541323 2541419 "SFRTCAT" 2541424 NIL SFRTCAT (NIL T T T T) -9 NIL 2541462) (-1027 2529731 2530746 2531880 "SFRGCD" 2535254 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1026 2522897 2523968 2525152 "SFQCMPK" 2528664 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1025 2522519 2522608 2522718 "SFORT" 2522838 NIL SFORT (NIL T T) -8 NIL NIL) (-1024 2521664 2522359 2522480 "SEXOF" 2522485 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1023 2520798 2521545 2521613 "SEX" 2521618 T SEX (NIL) -8 NIL NIL) (-1022 2515575 2516264 2516359 "SEXCAT" 2520130 NIL SEXCAT (NIL T T T T T) -9 NIL 2520749) (-1021 2512755 2515509 2515557 "SET" 2515562 NIL SET (NIL T) -8 NIL NIL) (-1020 2511006 2511468 2511773 "SETMN" 2512496 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1019 2510614 2510740 2510770 "SETCAT" 2510887 T SETCAT (NIL) -9 NIL 2510971) (-1018 2510394 2510446 2510545 "SETCAT-" 2510550 NIL SETCAT- (NIL T) -8 NIL NIL) (-1017 2506782 2508856 2508899 "SETAGG" 2509769 NIL SETAGG (NIL T) -9 NIL 2510109) (-1016 2506240 2506356 2506593 "SETAGG-" 2506598 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1015 2505444 2505737 2505798 "SEGXCAT" 2506084 NIL SEGXCAT (NIL T T) -9 NIL 2506204) (-1014 2504500 2505110 2505292 "SEG" 2505297 NIL SEG (NIL T) -8 NIL NIL) (-1013 2503407 2503620 2503663 "SEGCAT" 2504245 NIL SEGCAT (NIL T) -9 NIL 2504483) (-1012 2502456 2502786 2502986 "SEGBIND" 2503242 NIL SEGBIND (NIL T) -8 NIL NIL) (-1011 2502077 2502136 2502249 "SEGBIND2" 2502391 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1010 2501296 2501422 2501626 "SEG2" 2501921 NIL SEG2 (NIL T T) -7 NIL NIL) (-1009 2500733 2501231 2501278 "SDVAR" 2501283 NIL SDVAR (NIL T) -8 NIL NIL) (-1008 2492985 2500506 2500634 "SDPOL" 2500639 NIL SDPOL (NIL T) -8 NIL NIL) (-1007 2491578 2491844 2492163 "SCPKG" 2492700 NIL SCPKG (NIL T) -7 NIL NIL) (-1006 2490715 2490894 2491094 "SCOPE" 2491400 T SCOPE (NIL) -8 NIL NIL) (-1005 2489936 2490069 2490248 "SCACHE" 2490570 NIL SCACHE (NIL T) -7 NIL NIL) (-1004 2489375 2489696 2489781 "SAOS" 2489873 T SAOS (NIL) -8 NIL NIL) (-1003 2488940 2488975 2489148 "SAERFFC" 2489334 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1002 2482834 2488837 2488917 "SAE" 2488922 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1001 2482427 2482462 2482621 "SAEFACT" 2482793 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1000 2480748 2481062 2481463 "RURPK" 2482093 NIL RURPK (NIL T NIL) -7 NIL NIL) (-999 2479401 2479678 2479985 "RULESET" 2480584 NIL RULESET (NIL T T T) -8 NIL NIL) (-998 2476609 2477112 2477573 "RULE" 2479083 NIL RULE (NIL T T T) -8 NIL NIL) (-997 2476251 2476406 2476487 "RULECOLD" 2476561 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-996 2471143 2471937 2472853 "RSETGCD" 2475450 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-995 2460458 2465510 2465604 "RSETCAT" 2469669 NIL RSETCAT (NIL T T T T) -9 NIL 2470766) (-994 2458389 2458928 2459748 "RSETCAT-" 2459753 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-993 2450819 2452194 2453710 "RSDCMPK" 2456988 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-992 2448837 2449278 2449350 "RRCC" 2450426 NIL RRCC (NIL T T) -9 NIL 2450770) (-991 2448191 2448365 2448641 "RRCC-" 2448646 NIL RRCC- (NIL T T T) -8 NIL NIL) (-990 2422558 2432183 2432247 "RPOLCAT" 2442749 NIL RPOLCAT (NIL T T T) -9 NIL 2445907) (-989 2414062 2416400 2419518 "RPOLCAT-" 2419523 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-988 2405128 2412292 2412772 "ROUTINE" 2413602 T ROUTINE (NIL) -8 NIL NIL) (-987 2401833 2404684 2404831 "ROMAN" 2405001 T ROMAN (NIL) -8 NIL NIL) (-986 2400119 2400704 2400961 "ROIRC" 2401639 NIL ROIRC (NIL T T) -8 NIL NIL) (-985 2396524 2398828 2398856 "RNS" 2399152 T RNS (NIL) -9 NIL 2399422) (-984 2395038 2395421 2395952 "RNS-" 2396025 NIL RNS- (NIL T) -8 NIL NIL) (-983 2394464 2394872 2394900 "RNG" 2394905 T RNG (NIL) -9 NIL 2394926) (-982 2393862 2394224 2394264 "RMODULE" 2394324 NIL RMODULE (NIL T) -9 NIL 2394366) (-981 2392714 2392808 2393138 "RMCAT2" 2393763 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-980 2389428 2391897 2392218 "RMATRIX" 2392449 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-979 2382425 2384659 2384771 "RMATCAT" 2388080 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2389062) (-978 2381804 2381951 2382254 "RMATCAT-" 2382259 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-977 2381374 2381449 2381575 "RINTERP" 2381723 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-976 2380425 2380989 2381017 "RING" 2381127 T RING (NIL) -9 NIL 2381221) (-975 2380220 2380264 2380358 "RING-" 2380363 NIL RING- (NIL T) -8 NIL NIL) (-974 2379068 2379305 2379561 "RIDIST" 2379984 T RIDIST (NIL) -7 NIL NIL) (-973 2370390 2378542 2378745 "RGCHAIN" 2378917 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-972 2367395 2368009 2368677 "RF" 2369754 NIL RF (NIL T) -7 NIL NIL) (-971 2367044 2367107 2367208 "RFFACTOR" 2367326 NIL RFFACTOR (NIL T) -7 NIL NIL) (-970 2366772 2366807 2366902 "RFFACT" 2367003 NIL RFFACT (NIL T) -7 NIL NIL) (-969 2364902 2365266 2365646 "RFDIST" 2366412 T RFDIST (NIL) -7 NIL NIL) (-968 2364360 2364452 2364612 "RETSOL" 2364804 NIL RETSOL (NIL T T) -7 NIL NIL) (-967 2363953 2364033 2364074 "RETRACT" 2364264 NIL RETRACT (NIL T) -9 NIL NIL) (-966 2363805 2363830 2363914 "RETRACT-" 2363919 NIL RETRACT- (NIL T T) -8 NIL NIL) (-965 2356663 2363462 2363587 "RESULT" 2363700 T RESULT (NIL) -8 NIL NIL) (-964 2355248 2355937 2356134 "RESRING" 2356566 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-963 2354888 2354937 2355033 "RESLATC" 2355185 NIL RESLATC (NIL T) -7 NIL NIL) (-962 2354597 2354631 2354736 "REPSQ" 2354847 NIL REPSQ (NIL T) -7 NIL NIL) (-961 2352028 2352608 2353208 "REP" 2354017 T REP (NIL) -7 NIL NIL) (-960 2351729 2351763 2351872 "REPDB" 2351987 NIL REPDB (NIL T) -7 NIL NIL) (-959 2345674 2347053 2348273 "REP2" 2350541 NIL REP2 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(-933 2282525 2282600 2282628 "RADCAT" 2282785 T RADCAT (NIL) -9 NIL NIL) (-932 2282310 2282358 2282455 "RADCAT-" 2282460 NIL RADCAT- (NIL T) -8 NIL NIL) (-931 2280461 2282085 2282174 "QUEUE" 2282254 NIL QUEUE (NIL T) -8 NIL NIL) (-930 2276958 2280398 2280443 "QUAT" 2280448 NIL QUAT (NIL T) -8 NIL NIL) (-929 2276596 2276639 2276766 "QUATCT2" 2276909 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-928 2270390 2273770 2273810 "QUATCAT" 2274589 NIL QUATCAT (NIL T) -9 NIL 2275354) (-927 2266534 2267571 2268958 "QUATCAT-" 2269052 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-926 2264055 2265619 2265660 "QUAGG" 2266035 NIL QUAGG (NIL T) -9 NIL 2266210) (-925 2262980 2263453 2263625 "QFORM" 2263927 NIL QFORM (NIL NIL T) -8 NIL NIL) (-924 2254277 2259535 2259575 "QFCAT" 2260233 NIL QFCAT (NIL T) -9 NIL 2261226) (-923 2249849 2251050 2252641 "QFCAT-" 2252735 NIL QFCAT- (NIL T T) -8 NIL NIL) (-922 2249487 2249530 2249657 "QFCAT2" 2249800 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-921 2248947 2249057 2249187 "QEQUAT" 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1991884 1992003 "PAN2EXPR" 1992179 T PAN2EXPR (NIL) -7 NIL NIL) (-808 1990604 1990919 1991147 "PALETTE" 1991590 T PALETTE (NIL) -8 NIL NIL) (-807 1989072 1989609 1989969 "PAIR" 1990290 NIL PAIR (NIL T T) -8 NIL NIL) (-806 1982922 1988331 1988525 "PADICRC" 1988927 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-805 1976130 1982268 1982452 "PADICRAT" 1982770 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-804 1974434 1976067 1976112 "PADIC" 1976117 NIL PADIC (NIL NIL) -8 NIL NIL) (-803 1971639 1973213 1973253 "PADICCT" 1973834 NIL PADICCT (NIL NIL) -9 NIL 1974116) (-802 1970596 1970796 1971064 "PADEPAC" 1971426 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-801 1969808 1969941 1970147 "PADE" 1970458 NIL PADE (NIL T T T) -7 NIL NIL) (-800 1967819 1968651 1968966 "OWP" 1969576 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-799 1966928 1967424 1967596 "OVAR" 1967687 NIL OVAR (NIL NIL) -8 NIL NIL) (-798 1966192 1966313 1966474 "OUT" 1966787 T OUT (NIL) -7 NIL NIL) (-797 1955246 1957417 1959587 "OUTFORM" 1964042 T OUTFORM 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1932253 1932400 1932595 "ORDFUNS" 1932940 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-783 1931765 1932124 1932152 "ORDFIN" 1932157 T ORDFIN (NIL) -9 NIL 1932178) (-782 1928277 1930351 1930760 "ORDCOMP" 1931389 NIL ORDCOMP (NIL T) -8 NIL NIL) (-781 1927543 1927670 1927856 "ORDCOMP2" 1928137 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-780 1924050 1924933 1925770 "OPTPROB" 1926726 T OPTPROB (NIL) -8 NIL NIL) (-779 1920892 1921521 1922215 "OPTPACK" 1923376 T OPTPACK (NIL) -7 NIL NIL) (-778 1918618 1919354 1919382 "OPTCAT" 1920197 T OPTCAT (NIL) -9 NIL 1920843) (-777 1918386 1918425 1918491 "OPQUERY" 1918572 T OPQUERY (NIL) -7 NIL NIL) (-776 1915522 1916713 1917213 "OP" 1917918 NIL OP (NIL T) -8 NIL NIL) (-775 1912287 1914319 1914688 "ONECOMP" 1915186 NIL ONECOMP (NIL T) -8 NIL NIL) (-774 1911592 1911707 1911881 "ONECOMP2" 1912159 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-773 1911011 1911117 1911247 "OMSERVER" 1911482 T OMSERVER (NIL) -7 NIL NIL) (-772 1907900 1910452 1910492 "OMSAGG" 1910553 NIL OMSAGG (NIL T) -9 NIL 1910617) (-771 1906523 1906786 1907068 "OMPKG" 1907638 T OMPKG (NIL) -7 NIL NIL) (-770 1905953 1906056 1906084 "OM" 1906383 T OM (NIL) -9 NIL NIL) (-769 1904492 1905505 1905673 "OMLO" 1905834 NIL OMLO (NIL T T) -8 NIL NIL) (-768 1903422 1903569 1903795 "OMEXPR" 1904318 NIL OMEXPR (NIL T) -7 NIL NIL) (-767 1902740 1902968 1903104 "OMERR" 1903306 T OMERR (NIL) -8 NIL NIL) (-766 1901918 1902161 1902321 "OMERRK" 1902600 T OMERRK (NIL) -8 NIL NIL) (-765 1901396 1901595 1901703 "OMENC" 1901830 T OMENC (NIL) -8 NIL NIL) (-764 1895291 1896476 1897647 "OMDEV" 1900245 T OMDEV (NIL) -8 NIL NIL) (-763 1894360 1894531 1894725 "OMCONN" 1895117 T OMCONN (NIL) -8 NIL NIL) (-762 1892976 1893962 1893990 "OINTDOM" 1893995 T OINTDOM (NIL) -9 NIL 1894016) (-761 1888738 1889968 1890683 "OFMONOID" 1892293 NIL OFMONOID (NIL T) -8 NIL NIL) (-760 1888176 1888675 1888720 "ODVAR" 1888725 NIL ODVAR (NIL T) -8 NIL NIL) (-759 1885301 1887673 1887858 "ODR" 1888051 NIL ODR (NIL T T NIL) -8 NIL NIL) (-758 1877607 1885080 1885204 "ODPOL" 1885209 NIL ODPOL (NIL T) -8 NIL NIL) (-757 1871430 1877479 1877584 "ODP" 1877589 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-756 1870196 1870411 1870686 "ODETOOLS" 1871204 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-755 1867165 1867821 1868537 "ODESYS" 1869529 NIL ODESYS (NIL T T) -7 NIL NIL) (-754 1862069 1862977 1864000 "ODERTRIC" 1866240 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-753 1861495 1861577 1861771 "ODERED" 1861981 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-752 1858397 1858945 1859620 "ODERAT" 1860918 NIL ODERAT (NIL T T) -7 NIL NIL) (-751 1855365 1855829 1856425 "ODEPRRIC" 1857926 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-750 1853234 1853803 1854312 "ODEPROB" 1854876 T ODEPROB (NIL) -8 NIL NIL) (-749 1849766 1850249 1850895 "ODEPRIM" 1852713 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-748 1849019 1849121 1849379 "ODEPAL" 1849658 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-747 1845221 1846002 1846856 "ODEPACK" 1848185 T ODEPACK (NIL) -7 NIL NIL) (-746 1844258 1844365 1844593 "ODEINT" 1845110 NIL ODEINT (NIL T T) -7 NIL NIL) (-745 1838359 1839784 1841231 "ODEIFTBL" 1842831 T ODEIFTBL (NIL) -8 NIL NIL) (-744 1833703 1834489 1835447 "ODEEF" 1837518 NIL ODEEF (NIL T T) -7 NIL NIL) (-743 1833040 1833129 1833358 "ODECONST" 1833608 NIL ODECONST (NIL T T T) -7 NIL NIL) (-742 1831198 1831831 1831859 "ODECAT" 1832462 T ODECAT (NIL) -9 NIL 1832991) (-741 1828070 1830910 1831029 "OCT" 1831111 NIL OCT (NIL T) -8 NIL NIL) (-740 1827708 1827751 1827878 "OCTCT2" 1828021 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-739 1822542 1824980 1825020 "OC" 1826116 NIL OC (NIL T) -9 NIL 1826973) (-738 1819769 1820517 1821507 "OC-" 1821601 NIL OC- (NIL T T) -8 NIL NIL) (-737 1819148 1819590 1819618 "OCAMON" 1819623 T OCAMON (NIL) -9 NIL 1819644) (-736 1818602 1819009 1819037 "OASGP" 1819042 T OASGP (NIL) -9 NIL 1819062) (-735 1817890 1818353 1818381 "OAMONS" 1818421 T OAMONS (NIL) -9 NIL 1818464) (-734 1817331 1817738 1817766 "OAMON" 1817771 T OAMON (NIL) -9 NIL 1817791) (-733 1816636 1817128 1817156 "OAGROUP" 1817161 T OAGROUP (NIL) -9 NIL 1817181) (-732 1816326 1816376 1816464 "NUMTUBE" 1816580 NIL NUMTUBE (NIL T) -7 NIL NIL) (-731 1809899 1811417 1812953 "NUMQUAD" 1814810 T NUMQUAD (NIL) -7 NIL NIL) (-730 1805655 1806643 1807668 "NUMODE" 1808894 T NUMODE (NIL) -7 NIL NIL) (-729 1803059 1803905 1803933 "NUMINT" 1804850 T NUMINT (NIL) -9 NIL 1805606) (-728 1802007 1802204 1802422 "NUMFMT" 1802861 T NUMFMT (NIL) -7 NIL NIL) (-727 1788389 1791323 1793853 "NUMERIC" 1799516 NIL NUMERIC (NIL T) -7 NIL NIL) (-726 1782790 1787842 1787936 "NTSCAT" 1787941 NIL NTSCAT (NIL T T T T) -9 NIL 1787979) (-725 1781984 1782149 1782342 "NTPOLFN" 1782629 NIL NTPOLFN (NIL T) -7 NIL NIL) (-724 1769800 1778826 1779636 "NSUP" 1781206 NIL NSUP (NIL T) -8 NIL NIL) (-723 1769436 1769493 1769600 "NSUP2" 1769737 NIL NSUP2 (NIL T T) -7 NIL NIL) (-722 1759398 1769215 1769345 "NSMP" 1769350 NIL NSMP (NIL T T) -8 NIL NIL) (-721 1757830 1758131 1758488 "NREP" 1759086 NIL NREP (NIL T) -7 NIL NIL) (-720 1756421 1756673 1757031 "NPCOEF" 1757573 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-719 1755487 1755602 1755818 "NORMRETR" 1756302 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-718 1753540 1753830 1754237 "NORMPK" 1755195 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-717 1753225 1753253 1753377 "NORMMA" 1753506 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-716 1753052 1753182 1753211 "NONE" 1753216 T NONE (NIL) -8 NIL NIL) (-715 1752841 1752870 1752939 "NONE1" 1753016 NIL NONE1 (NIL T) -7 NIL NIL) (-714 1752326 1752388 1752573 "NODE1" 1752773 NIL NODE1 (NIL T T) -7 NIL NIL) (-713 1750619 1751489 1751744 "NNI" 1752091 T NNI (NIL) -8 NIL NIL) (-712 1749039 1749352 1749716 "NLINSOL" 1750287 NIL NLINSOL (NIL T) -7 NIL NIL) (-711 1745206 1746174 1747096 "NIPROB" 1748137 T NIPROB (NIL) -8 NIL NIL) (-710 1743963 1744197 1744499 "NFINTBAS" 1744968 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-709 1742671 1742902 1743183 "NCODIV" 1743731 NIL NCODIV (NIL T T) -7 NIL NIL) (-708 1742433 1742470 1742545 "NCNTFRAC" 1742628 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-707 1740613 1740977 1741397 "NCEP" 1742058 NIL NCEP (NIL T) -7 NIL NIL) (-706 1739525 1740264 1740292 "NASRING" 1740402 T NASRING (NIL) -9 NIL 1740476) (-705 1739320 1739364 1739458 "NASRING-" 1739463 NIL NASRING- (NIL T) -8 NIL NIL) (-704 1738474 1738973 1739001 "NARNG" 1739118 T NARNG (NIL) -9 NIL 1739209) (-703 1738166 1738233 1738367 "NARNG-" 1738372 NIL NARNG- (NIL T) -8 NIL NIL) (-702 1737045 1737252 1737487 "NAGSP" 1737951 T NAGSP (NIL) -7 NIL NIL) (-701 1728469 1730115 1731750 "NAGS" 1735430 T NAGS (NIL) -7 NIL NIL) (-700 1727033 1727337 1727664 "NAGF07" 1728162 T NAGF07 (NIL) -7 NIL NIL) (-699 1721615 1722895 1724191 "NAGF04" 1725757 T NAGF04 (NIL) -7 NIL NIL) (-698 1714647 1716245 1717862 "NAGF02" 1720018 T NAGF02 (NIL) -7 NIL NIL) (-697 1709911 1711001 1712108 "NAGF01" 1713560 T NAGF01 (NIL) -7 NIL NIL) (-696 1703571 1705129 1706706 "NAGE04" 1708354 T NAGE04 (NIL) -7 NIL NIL) (-695 1694812 1696915 1699027 "NAGE02" 1701479 T NAGE02 (NIL) -7 NIL NIL) (-694 1690805 1691742 1692696 "NAGE01" 1693878 T NAGE01 (NIL) -7 NIL NIL) (-693 1688612 1689143 1689698 "NAGD03" 1690270 T NAGD03 (NIL) -7 NIL NIL) (-692 1680398 1682317 1684262 "NAGD02" 1686687 T NAGD02 (NIL) -7 NIL NIL) (-691 1674257 1675670 1677098 "NAGD01" 1678990 T NAGD01 (NIL) -7 NIL NIL) (-690 1670514 1671324 1672149 "NAGC06" 1673452 T NAGC06 (NIL) -7 NIL NIL) (-689 1668991 1669320 1669673 "NAGC05" 1670181 T NAGC05 (NIL) -7 NIL NIL) (-688 1668375 1668492 1668634 "NAGC02" 1668869 T NAGC02 (NIL) -7 NIL NIL) (-687 1667437 1667994 1668034 "NAALG" 1668113 NIL NAALG (NIL T) -9 NIL 1668174) (-686 1667272 1667301 1667391 "NAALG-" 1667396 NIL NAALG- (NIL T T) -8 NIL NIL) (-685 1661222 1662330 1663517 "MULTSQFR" 1666168 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-684 1660541 1660616 1660800 "MULTFACT" 1661134 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-683 1653735 1657646 1657698 "MTSCAT" 1658758 NIL MTSCAT (NIL T T) -9 NIL 1659272) (-682 1653447 1653501 1653593 "MTHING" 1653675 NIL MTHING (NIL T) -7 NIL NIL) (-681 1653239 1653272 1653332 "MSYSCMD" 1653407 T MSYSCMD (NIL) -7 NIL NIL) (-680 1649351 1651994 1652314 "MSET" 1652952 NIL MSET (NIL T) -8 NIL NIL) (-679 1646447 1648913 1648954 "MSETAGG" 1648959 NIL MSETAGG (NIL T) -9 NIL 1648993) (-678 1642303 1643845 1644586 "MRING" 1645750 NIL MRING (NIL T T) -8 NIL NIL) (-677 1641873 1641940 1642069 "MRF2" 1642230 NIL MRF2 (NIL T T T) -7 NIL NIL) (-676 1641491 1641526 1641670 "MRATFAC" 1641832 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-675 1639103 1639398 1639829 "MPRFF" 1641196 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-674 1633123 1638958 1639054 "MPOLY" 1639059 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-673 1632613 1632648 1632856 "MPCPF" 1633082 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-672 1632129 1632172 1632355 "MPC3" 1632564 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-671 1631330 1631411 1631630 "MPC2" 1632044 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-670 1629631 1629968 1630358 "MONOTOOL" 1630990 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-669 1628756 1629091 1629119 "MONOID" 1629396 T MONOID (NIL) -9 NIL 1629568) (-668 1628134 1628297 1628540 "MONOID-" 1628545 NIL MONOID- (NIL T) -8 NIL NIL) (-667 1619115 1625101 1625160 "MONOGEN" 1625834 NIL MONOGEN (NIL T T) -9 NIL 1626290) (-666 1616333 1617068 1618068 "MONOGEN-" 1618187 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-665 1615193 1615613 1615641 "MONADWU" 1616033 T MONADWU (NIL) -9 NIL 1616271) (-664 1614565 1614724 1614972 "MONADWU-" 1614977 NIL MONADWU- (NIL T) -8 NIL NIL) (-663 1613951 1614169 1614197 "MONAD" 1614404 T MONAD (NIL) -9 NIL 1614516) (-662 1613636 1613714 1613846 "MONAD-" 1613851 NIL MONAD- (NIL T) -8 NIL NIL) (-661 1611887 1612549 1612828 "MOEBIUS" 1613389 NIL MOEBIUS (NIL T) -8 NIL NIL) (-660 1611281 1611659 1611699 "MODULE" 1611704 NIL MODULE (NIL T) -9 NIL 1611730) (-659 1610849 1610945 1611135 "MODULE-" 1611140 NIL MODULE- (NIL T T) -8 NIL NIL) (-658 1608520 1609215 1609541 "MODRING" 1610674 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-657 1605476 1606641 1607158 "MODOP" 1608052 NIL MODOP (NIL T T) -8 NIL NIL) (-656 1603663 1604115 1604456 "MODMONOM" 1605275 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-655 1593342 1601867 1602289 "MODMON" 1603291 NIL MODMON (NIL T T) -8 NIL NIL) (-654 1590468 1592186 1592462 "MODFIELD" 1593217 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-653 1589472 1589749 1589939 "MMLFORM" 1590298 T MMLFORM (NIL) -8 NIL NIL) (-652 1588998 1589041 1589220 "MMAP" 1589423 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-651 1587235 1588012 1588052 "MLO" 1588469 NIL MLO (NIL T) -9 NIL 1588710) (-650 1584602 1585117 1585719 "MLIFT" 1586716 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-649 1583993 1584077 1584231 "MKUCFUNC" 1584513 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-648 1583592 1583662 1583785 "MKRECORD" 1583916 NIL MKRECORD (NIL T T) -7 NIL NIL) (-647 1582640 1582801 1583029 "MKFUNC" 1583403 NIL MKFUNC (NIL T) -7 NIL NIL) (-646 1582028 1582132 1582288 "MKFLCFN" 1582523 NIL MKFLCFN (NIL T) -7 NIL NIL) (-645 1581454 1581821 1581910 "MKCHSET" 1581972 NIL MKCHSET (NIL T) -8 NIL NIL) (-644 1580731 1580833 1581018 "MKBCFUNC" 1581347 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-643 1577415 1580285 1580421 "MINT" 1580615 T MINT (NIL) -8 NIL NIL) (-642 1576227 1576470 1576747 "MHROWRED" 1577170 NIL MHROWRED (NIL T) -7 NIL NIL) (-641 1571498 1574672 1575096 "MFLOAT" 1575823 T MFLOAT (NIL) -8 NIL NIL) (-640 1570855 1570931 1571102 "MFINFACT" 1571410 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-639 1567170 1568018 1568902 "MESH" 1569991 T MESH (NIL) -7 NIL NIL) (-638 1565560 1565872 1566225 "MDDFACT" 1566857 NIL MDDFACT (NIL T) -7 NIL NIL) (-637 1562403 1564720 1564761 "MDAGG" 1565016 NIL MDAGG (NIL T) -9 NIL 1565159) (-636 1552101 1561696 1561903 "MCMPLX" 1562216 T MCMPLX (NIL) -8 NIL NIL) (-635 1551242 1551388 1551588 "MCDEN" 1551950 NIL MCDEN (NIL T T) -7 NIL NIL) (-634 1549132 1549402 1549782 "MCALCFN" 1550972 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-633 1546754 1547277 1547838 "MATSTOR" 1548603 NIL MATSTOR (NIL T) -7 NIL NIL) (-632 1542763 1546129 1546376 "MATRIX" 1546539 NIL MATRIX (NIL T) -8 NIL NIL) (-631 1538532 1539236 1539972 "MATLIN" 1542120 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-630 1528730 1531868 1531944 "MATCAT" 1536782 NIL MATCAT (NIL T T T) -9 NIL 1538199) (-629 1525095 1526108 1527463 "MATCAT-" 1527468 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-628 1523697 1523850 1524181 "MATCAT2" 1524930 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-627 1521809 1522133 1522517 "MAPPKG3" 1523372 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-626 1520790 1520963 1521185 "MAPPKG2" 1521633 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-625 1519289 1519573 1519900 "MAPPKG1" 1520496 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-624 1518900 1518958 1519081 "MAPHACK3" 1519225 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-623 1518492 1518553 1518667 "MAPHACK2" 1518832 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-622 1517930 1518033 1518175 "MAPHACK1" 1518383 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-621 1516038 1516632 1516935 "MAGMA" 1517659 NIL MAGMA (NIL T) -8 NIL NIL) (-620 1512512 1514282 1514742 "M3D" 1515611 NIL M3D (NIL T) -8 NIL NIL) (-619 1506668 1510883 1510924 "LZSTAGG" 1511706 NIL LZSTAGG (NIL T) -9 NIL 1512001) (-618 1502641 1503799 1505256 "LZSTAGG-" 1505261 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-617 1499757 1500534 1501020 "LWORD" 1502187 NIL LWORD (NIL T) -8 NIL NIL) (-616 1492917 1499528 1499662 "LSQM" 1499667 NIL LSQM (NIL NIL T) -8 NIL NIL) (-615 1492141 1492280 1492508 "LSPP" 1492772 NIL LSPP (NIL T T T T) -7 NIL NIL) (-614 1489953 1490254 1490710 "LSMP" 1491830 NIL LSMP (NIL T T T T) -7 NIL NIL) (-613 1486732 1487406 1488136 "LSMP1" 1489255 NIL LSMP1 (NIL T) -7 NIL NIL) (-612 1480659 1485901 1485942 "LSAGG" 1486004 NIL LSAGG (NIL T) -9 NIL 1486082) (-611 1477354 1478278 1479491 "LSAGG-" 1479496 NIL LSAGG- (NIL T T) -8 NIL NIL) (-610 1474980 1476498 1476747 "LPOLY" 1477149 NIL LPOLY (NIL T T) -8 NIL NIL) (-609 1474562 1474647 1474770 "LPEFRAC" 1474889 NIL LPEFRAC (NIL T) -7 NIL NIL) (-608 1472909 1473656 1473909 "LO" 1474394 NIL LO (NIL T T T) -8 NIL NIL) (-607 1472563 1472675 1472703 "LOGIC" 1472814 T LOGIC (NIL) -9 NIL 1472894) (-606 1472425 1472448 1472519 "LOGIC-" 1472524 NIL LOGIC- (NIL T) -8 NIL NIL) (-605 1471618 1471758 1471951 "LODOOPS" 1472281 NIL LODOOPS (NIL T T) -7 NIL NIL) (-604 1469036 1471535 1471600 "LODO" 1471605 NIL LODO (NIL T NIL) -8 NIL NIL) (-603 1467582 1467817 1468168 "LODOF" 1468783 NIL LODOF (NIL T T) -7 NIL NIL) (-602 1464002 1466438 1466478 "LODOCAT" 1466910 NIL LODOCAT (NIL T) -9 NIL 1467121) (-601 1463736 1463794 1463920 "LODOCAT-" 1463925 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-600 1461050 1463577 1463695 "LODO2" 1463700 NIL LODO2 (NIL T T) -8 NIL NIL) (-599 1458479 1460987 1461032 "LODO1" 1461037 NIL LODO1 (NIL T) -8 NIL NIL) (-598 1457342 1457507 1457818 "LODEEF" 1458302 NIL LODEEF (NIL T T T) -7 NIL NIL) (-597 1452629 1455473 1455514 "LNAGG" 1456461 NIL LNAGG (NIL T) -9 NIL 1456905) (-596 1451776 1451990 1452332 "LNAGG-" 1452337 NIL LNAGG- (NIL T T) -8 NIL NIL) (-595 1447941 1448703 1449341 "LMOPS" 1451192 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-594 1447339 1447701 1447741 "LMODULE" 1447801 NIL LMODULE (NIL T) -9 NIL 1447843) (-593 1444585 1446984 1447107 "LMDICT" 1447249 NIL LMDICT (NIL T) -8 NIL NIL) (-592 1437812 1443531 1443829 "LIST" 1444320 NIL LIST (NIL T) -8 NIL NIL) (-591 1437337 1437411 1437550 "LIST3" 1437732 NIL LIST3 (NIL T T T) -7 NIL NIL) (-590 1436344 1436522 1436750 "LIST2" 1437155 NIL LIST2 (NIL T T) -7 NIL NIL) (-589 1434478 1434790 1435189 "LIST2MAP" 1435991 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-588 1433191 1433871 1433911 "LINEXP" 1434164 NIL LINEXP (NIL T) -9 NIL 1434312) (-587 1431838 1432098 1432395 "LINDEP" 1432943 NIL LINDEP (NIL T T) -7 NIL NIL) (-586 1428605 1429324 1430101 "LIMITRF" 1431093 NIL LIMITRF (NIL T) -7 NIL NIL) (-585 1426885 1427180 1427595 "LIMITPS" 1428300 NIL LIMITPS (NIL T T) -7 NIL NIL) (-584 1421340 1426396 1426624 "LIE" 1426706 NIL LIE (NIL T T) -8 NIL NIL) (-583 1420391 1420834 1420874 "LIECAT" 1421014 NIL LIECAT (NIL T) -9 NIL 1421165) (-582 1420232 1420259 1420347 "LIECAT-" 1420352 NIL LIECAT- (NIL T T) -8 NIL NIL) (-581 1412844 1419681 1419846 "LIB" 1420087 T LIB (NIL) -8 NIL NIL) (-580 1408481 1409362 1410297 "LGROBP" 1411961 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-579 1406347 1406621 1406983 "LF" 1408202 NIL LF (NIL T T) -7 NIL NIL) (-578 1405187 1405879 1405907 "LFCAT" 1406114 T LFCAT (NIL) -9 NIL 1406253) (-577 1402099 1402725 1403411 "LEXTRIPK" 1404553 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-576 1398805 1399669 1400172 "LEXP" 1401679 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-575 1397203 1397516 1397917 "LEADCDET" 1398487 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-574 1396399 1396473 1396700 "LAZM3PK" 1397124 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-573 1391316 1394478 1395015 "LAUPOL" 1395912 NIL LAUPOL (NIL T T) -8 NIL NIL) (-572 1390883 1390927 1391094 "LAPLACE" 1391266 NIL LAPLACE (NIL T T) -7 NIL NIL) (-571 1388811 1389984 1390235 "LA" 1390716 NIL LA (NIL T T T) -8 NIL NIL) (-570 1387874 1388468 1388508 "LALG" 1388569 NIL LALG (NIL T) -9 NIL 1388627) (-569 1387589 1387648 1387783 "LALG-" 1387788 NIL LALG- (NIL T T) -8 NIL NIL) (-568 1386499 1386686 1386983 "KOVACIC" 1387389 NIL KOVACIC (NIL T T) -7 NIL NIL) (-567 1386334 1386358 1386399 "KONVERT" 1386461 NIL KONVERT (NIL T) -9 NIL NIL) (-566 1386169 1386193 1386234 "KOERCE" 1386296 NIL KOERCE (NIL T) -9 NIL NIL) (-565 1383903 1384663 1385056 "KERNEL" 1385808 NIL KERNEL (NIL T) -8 NIL NIL) (-564 1383405 1383486 1383616 "KERNEL2" 1383817 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-563 1377257 1381945 1381999 "KDAGG" 1382376 NIL KDAGG (NIL T T) -9 NIL 1382582) (-562 1376786 1376910 1377115 "KDAGG-" 1377120 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-561 1369961 1376447 1376602 "KAFILE" 1376664 NIL KAFILE (NIL T) -8 NIL NIL) (-560 1364416 1369472 1369700 "JORDAN" 1369782 NIL JORDAN (NIL T T) -8 NIL NIL) (-559 1364145 1364204 1364291 "JAVACODE" 1364349 T JAVACODE (NIL) -8 NIL NIL) (-558 1360445 1362351 1362405 "IXAGG" 1363334 NIL IXAGG (NIL T T) -9 NIL 1363793) (-557 1359364 1359670 1360089 "IXAGG-" 1360094 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-556 1354949 1359286 1359345 "IVECTOR" 1359350 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-555 1353715 1353952 1354218 "ITUPLE" 1354716 NIL ITUPLE (NIL T) -8 NIL NIL) (-554 1352151 1352328 1352634 "ITRIGMNP" 1353537 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-553 1350896 1351100 1351383 "ITFUN3" 1351927 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-552 1350528 1350585 1350694 "ITFUN2" 1350833 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-551 1348330 1349401 1349698 "ITAYLOR" 1350263 NIL ITAYLOR (NIL T) -8 NIL NIL) (-550 1337318 1342516 1343675 "ISUPS" 1347203 NIL ISUPS (NIL T) -8 NIL NIL) (-549 1336422 1336562 1336798 "ISUMP" 1337165 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-548 1331686 1336223 1336302 "ISTRING" 1336375 NIL ISTRING (NIL NIL) -8 NIL NIL) (-547 1330899 1330980 1331195 "IRURPK" 1331600 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-546 1329835 1330036 1330276 "IRSN" 1330679 T IRSN (NIL) -7 NIL NIL) (-545 1327870 1328225 1328660 "IRRF2F" 1329473 NIL IRRF2F (NIL T) -7 NIL NIL) (-544 1327617 1327655 1327731 "IRREDFFX" 1327826 NIL IRREDFFX (NIL T) -7 NIL NIL) (-543 1326232 1326491 1326790 "IROOT" 1327350 NIL IROOT (NIL T) -7 NIL NIL) (-542 1322870 1323921 1324611 "IR" 1325574 NIL IR (NIL T) -8 NIL NIL) (-541 1320483 1320978 1321544 "IR2" 1322348 NIL IR2 (NIL T T) -7 NIL NIL) (-540 1319559 1319672 1319892 "IR2F" 1320366 NIL IR2F (NIL T T) -7 NIL NIL) (-539 1319350 1319384 1319444 "IPRNTPK" 1319519 T IPRNTPK (NIL) -7 NIL NIL) (-538 1315904 1319239 1319308 "IPF" 1319313 NIL IPF (NIL NIL) -8 NIL NIL) (-537 1314221 1315829 1315886 "IPADIC" 1315891 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-536 1313720 1313778 1313967 "INVLAPLA" 1314157 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-535 1303369 1305722 1308108 "INTTR" 1311384 NIL INTTR (NIL T T) -7 NIL NIL) (-534 1299717 1300458 1301321 "INTTOOLS" 1302555 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-533 1299303 1299394 1299511 "INTSLPE" 1299620 T INTSLPE (NIL) -7 NIL NIL) (-532 1297253 1299226 1299285 "INTRVL" 1299290 NIL INTRVL (NIL T) -8 NIL NIL) (-531 1294860 1295372 1295946 "INTRF" 1296738 NIL INTRF (NIL T) -7 NIL NIL) (-530 1294275 1294372 1294513 "INTRET" 1294758 NIL INTRET (NIL T) -7 NIL NIL) (-529 1292277 1292666 1293135 "INTRAT" 1293883 NIL INTRAT (NIL T T) -7 NIL NIL) (-528 1289510 1290093 1290718 "INTPM" 1291762 NIL INTPM (NIL T T) -7 NIL NIL) (-527 1286219 1286818 1287562 "INTPAF" 1288896 NIL INTPAF (NIL T T T) -7 NIL NIL) (-526 1281462 1282408 1283443 "INTPACK" 1285204 T INTPACK (NIL) -7 NIL NIL) (-525 1278316 1281191 1281318 "INT" 1281355 T INT (NIL) -8 NIL NIL) (-524 1277568 1277720 1277928 "INTHERTR" 1278158 NIL INTHERTR (NIL T T) -7 NIL NIL) (-523 1277007 1277087 1277275 "INTHERAL" 1277482 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-522 1274853 1275296 1275753 "INTHEORY" 1276570 T INTHEORY (NIL) -7 NIL NIL) (-521 1266175 1267796 1269574 "INTG0" 1273205 NIL INTG0 (NIL T T T) -7 NIL NIL) (-520 1246748 1251538 1256348 "INTFTBL" 1261385 T INTFTBL (NIL) -8 NIL NIL) (-519 1245997 1246135 1246308 "INTFACT" 1246607 NIL INTFACT (NIL T) -7 NIL NIL) (-518 1243388 1243834 1244397 "INTEF" 1245551 NIL INTEF (NIL T T) -7 NIL NIL) (-517 1241850 1242599 1242627 "INTDOM" 1242928 T INTDOM (NIL) -9 NIL 1243135) (-516 1241219 1241393 1241635 "INTDOM-" 1241640 NIL INTDOM- (NIL T) -8 NIL NIL) (-515 1237712 1239644 1239698 "INTCAT" 1240497 NIL INTCAT (NIL T) -9 NIL 1240816) (-514 1237185 1237287 1237415 "INTBIT" 1237604 T INTBIT (NIL) -7 NIL NIL) (-513 1235860 1236014 1236327 "INTALG" 1237030 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-512 1235317 1235407 1235577 "INTAF" 1235764 NIL INTAF (NIL T T) -7 NIL NIL) (-511 1228771 1235127 1235267 "INTABL" 1235272 NIL INTABL (NIL T T T) -8 NIL NIL) (-510 1223722 1226451 1226479 "INS" 1227447 T INS (NIL) -9 NIL 1228128) (-509 1220962 1221733 1222707 "INS-" 1222780 NIL INS- (NIL T) -8 NIL NIL) (-508 1219741 1219968 1220265 "INPSIGN" 1220715 NIL INPSIGN (NIL T T) -7 NIL NIL) (-507 1218859 1218976 1219173 "INPRODPF" 1219621 NIL INPRODPF (NIL T T) -7 NIL NIL) (-506 1217753 1217870 1218107 "INPRODFF" 1218739 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-505 1216753 1216905 1217165 "INNMFACT" 1217589 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-504 1215950 1216047 1216235 "INMODGCD" 1216652 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-503 1214459 1214703 1215027 "INFSP" 1215695 NIL INFSP (NIL T T T) -7 NIL NIL) (-502 1213643 1213760 1213943 "INFPROD0" 1214339 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-501 1210653 1211812 1212303 "INFORM" 1213160 T INFORM (NIL) -8 NIL NIL) (-500 1210263 1210323 1210421 "INFORM1" 1210588 NIL INFORM1 (NIL T) -7 NIL NIL) (-499 1209786 1209875 1209989 "INFINITY" 1210169 T INFINITY (NIL) -7 NIL NIL) (-498 1208403 1208652 1208973 "INEP" 1209534 NIL INEP (NIL T T T) -7 NIL NIL) (-497 1207679 1208300 1208365 "INDE" 1208370 NIL INDE (NIL T) -8 NIL NIL) (-496 1207243 1207311 1207428 "INCRMAPS" 1207606 NIL INCRMAPS (NIL T) -7 NIL NIL) (-495 1202554 1203479 1204423 "INBFF" 1206331 NIL INBFF (NIL T) -7 NIL NIL) (-494 1199049 1202399 1202502 "IMATRIX" 1202507 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-493 1197761 1197884 1198199 "IMATQF" 1198905 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-492 1195981 1196208 1196545 "IMATLIN" 1197517 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-491 1190607 1195905 1195963 "ILIST" 1195968 NIL ILIST (NIL T NIL) -8 NIL NIL) (-490 1188560 1190467 1190580 "IIARRAY2" 1190585 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-489 1183928 1188471 1188535 "IFF" 1188540 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-488 1178971 1183220 1183408 "IFARRAY" 1183785 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-487 1178178 1178875 1178948 "IFAMON" 1178953 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-486 1177762 1177827 1177881 "IEVALAB" 1178088 NIL IEVALAB (NIL T T) -9 NIL NIL) (-485 1177437 1177505 1177665 "IEVALAB-" 1177670 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-484 1177095 1177351 1177414 "IDPO" 1177419 NIL IDPO (NIL T T) -8 NIL NIL) (-483 1176372 1176984 1177059 "IDPOAMS" 1177064 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-482 1175706 1176261 1176336 "IDPOAM" 1176341 NIL IDPOAM (NIL T T) -8 NIL NIL) (-481 1174792 1175042 1175095 "IDPC" 1175508 NIL IDPC (NIL T T) -9 NIL 1175657) (-480 1174288 1174684 1174757 "IDPAM" 1174762 NIL IDPAM (NIL T T) -8 NIL NIL) (-479 1173691 1174180 1174253 "IDPAG" 1174258 NIL IDPAG (NIL T T) -8 NIL NIL) (-478 1169946 1170794 1171689 "IDECOMP" 1172848 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-477 1162819 1163869 1164916 "IDEAL" 1168982 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-476 1161983 1162095 1162294 "ICDEN" 1162703 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-475 1161082 1161463 1161610 "ICARD" 1161856 T ICARD (NIL) -8 NIL NIL) (-474 1159154 1159467 1159870 "IBPTOOLS" 1160759 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-473 1154768 1158774 1158887 "IBITS" 1159073 NIL IBITS (NIL NIL) -8 NIL NIL) (-472 1151491 1152067 1152762 "IBATOOL" 1154185 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-471 1149271 1149732 1150265 "IBACHIN" 1151026 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-470 1147148 1149117 1149220 "IARRAY2" 1149225 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-469 1143301 1147074 1147131 "IARRAY1" 1147136 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-468 1137239 1141719 1142197 "IAN" 1142843 T IAN (NIL) -8 NIL NIL) (-467 1136750 1136807 1136980 "IALGFACT" 1137176 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-466 1136278 1136391 1136419 "HYPCAT" 1136626 T HYPCAT (NIL) -9 NIL NIL) (-465 1135816 1135933 1136119 "HYPCAT-" 1136124 NIL HYPCAT- (NIL T) -8 NIL NIL) (-464 1132496 1133827 1133868 "HOAGG" 1134849 NIL HOAGG (NIL T) -9 NIL 1135528) (-463 1131090 1131489 1132015 "HOAGG-" 1132020 NIL HOAGG- (NIL T T) -8 NIL NIL) (-462 1124920 1130531 1130697 "HEXADEC" 1130944 T HEXADEC (NIL) -8 NIL NIL) (-461 1123668 1123890 1124153 "HEUGCD" 1124697 NIL HEUGCD (NIL T) -7 NIL NIL) (-460 1122771 1123505 1123635 "HELLFDIV" 1123640 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-459 1120999 1122548 1122636 "HEAP" 1122715 NIL HEAP (NIL T) -8 NIL NIL) (-458 1114866 1120914 1120976 "HDP" 1120981 NIL HDP (NIL NIL T) -8 NIL NIL) (-457 1108578 1114503 1114654 "HDMP" 1114767 NIL HDMP (NIL NIL T) -8 NIL NIL) (-456 1107903 1108042 1108206 "HB" 1108434 T HB (NIL) -7 NIL NIL) (-455 1101400 1107749 1107853 "HASHTBL" 1107858 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-454 1099153 1101028 1101207 "HACKPI" 1101241 T HACKPI (NIL) -8 NIL NIL) (-453 1094849 1099007 1099119 "GTSET" 1099124 NIL GTSET (NIL T T T T) -8 NIL NIL) (-452 1088375 1094727 1094825 "GSTBL" 1094830 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-451 1080608 1087411 1087675 "GSERIES" 1088166 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-450 1079631 1080084 1080112 "GROUP" 1080373 T GROUP (NIL) -9 NIL 1080532) (-449 1078747 1078970 1079314 "GROUP-" 1079319 NIL GROUP- (NIL T) -8 NIL NIL) (-448 1077116 1077435 1077822 "GROEBSOL" 1078424 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-447 1076057 1076319 1076370 "GRMOD" 1076899 NIL GRMOD (NIL T T) -9 NIL 1077067) (-446 1075825 1075861 1075989 "GRMOD-" 1075994 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-445 1071151 1072179 1073179 "GRIMAGE" 1074845 T GRIMAGE (NIL) -8 NIL NIL) (-444 1069618 1069878 1070202 "GRDEF" 1070847 T GRDEF (NIL) -7 NIL NIL) (-443 1069062 1069178 1069319 "GRAY" 1069497 T GRAY (NIL) -7 NIL NIL) (-442 1068296 1068676 1068727 "GRALG" 1068880 NIL GRALG (NIL T T) -9 NIL 1068972) (-441 1067957 1068030 1068193 "GRALG-" 1068198 NIL GRALG- (NIL T T T) -8 NIL NIL) (-440 1064765 1067546 1067722 "GPOLSET" 1067864 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-439 1064121 1064178 1064435 "GOSPER" 1064702 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-438 1059880 1060559 1061085 "GMODPOL" 1063820 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-437 1058885 1059069 1059307 "GHENSEL" 1059692 NIL GHENSEL (NIL T T) -7 NIL NIL) (-436 1052951 1053794 1054820 "GENUPS" 1057969 NIL GENUPS (NIL T T) -7 NIL NIL) (-435 1052648 1052699 1052788 "GENUFACT" 1052894 NIL GENUFACT (NIL T) -7 NIL NIL) (-434 1052060 1052137 1052302 "GENPGCD" 1052566 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-433 1051534 1051569 1051782 "GENMFACT" 1052019 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-432 1050102 1050357 1050664 "GENEEZ" 1051277 NIL GENEEZ (NIL T T) -7 NIL NIL) (-431 1043976 1049715 1049876 "GDMP" 1050025 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-430 1033356 1037747 1038853 "GCNAALG" 1042959 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-429 1031778 1032650 1032678 "GCDDOM" 1032933 T GCDDOM (NIL) -9 NIL 1033090) (-428 1031248 1031375 1031590 "GCDDOM-" 1031595 NIL GCDDOM- (NIL T) -8 NIL NIL) (-427 1029920 1030105 1030409 "GB" 1031027 NIL GB (NIL T T T T) -7 NIL NIL) (-426 1018540 1020866 1023258 "GBINTERN" 1027611 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-425 1016377 1016669 1017090 "GBF" 1018215 NIL GBF (NIL T T T T) -7 NIL NIL) (-424 1015158 1015323 1015590 "GBEUCLID" 1016193 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-423 1014507 1014632 1014781 "GAUSSFAC" 1015029 T GAUSSFAC (NIL) -7 NIL NIL) (-422 1012884 1013186 1013499 "GALUTIL" 1014226 NIL GALUTIL (NIL T) -7 NIL NIL) (-421 1011201 1011475 1011798 "GALPOLYU" 1012611 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-420 1008590 1008880 1009285 "GALFACTU" 1010898 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-419 1000396 1001895 1003503 "GALFACT" 1007022 NIL GALFACT (NIL T) -7 NIL NIL) (-418 997784 998442 998470 "FVFUN" 999626 T FVFUN (NIL) -9 NIL 1000346) (-417 997050 997232 997260 "FVC" 997551 T FVC (NIL) -9 NIL 997734) (-416 996692 996847 996928 "FUNCTION" 997002 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-415 994362 994913 995402 "FT" 996223 T FT (NIL) -8 NIL NIL) (-414 993180 993663 993866 "FTEM" 994179 T FTEM (NIL) -8 NIL NIL) (-413 991445 991733 992135 "FSUPFACT" 992872 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-412 989842 990131 990463 "FST" 991133 T FST (NIL) -8 NIL NIL) (-411 989017 989123 989317 "FSRED" 989724 NIL FSRED (NIL T T) -7 NIL NIL) (-410 987696 987951 988305 "FSPRMELT" 988732 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-409 984781 985219 985718 "FSPECF" 987259 NIL FSPECF (NIL T T) -7 NIL NIL) (-408 967155 975712 975752 "FS" 979590 NIL FS (NIL T) -9 NIL 981872) (-407 955805 958795 962851 "FS-" 963148 NIL FS- (NIL T T) -8 NIL NIL) (-406 955321 955375 955551 "FSINT" 955746 NIL FSINT (NIL T T) -7 NIL NIL) (-405 953602 954314 954617 "FSERIES" 955100 NIL FSERIES (NIL T T) -8 NIL NIL) (-404 952620 952736 952966 "FSCINT" 953482 NIL FSCINT (NIL T T) -7 NIL NIL) (-403 948855 951565 951606 "FSAGG" 951976 NIL FSAGG (NIL T) -9 NIL 952235) (-402 946617 947218 948014 "FSAGG-" 948109 NIL FSAGG- (NIL T T) -8 NIL NIL) (-401 945659 945802 946029 "FSAGG2" 946470 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-400 943318 943597 944150 "FS2UPS" 945377 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-399 942904 942947 943100 "FS2" 943269 NIL FS2 (NIL T T T T) -7 NIL NIL) (-398 941764 941935 942243 "FS2EXPXP" 942729 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-397 941190 941305 941457 "FRUTIL" 941644 NIL FRUTIL (NIL T) -7 NIL NIL) (-396 932610 936689 938045 "FR" 939866 NIL FR (NIL T) -8 NIL NIL) (-395 927687 930330 930370 "FRNAALG" 931766 NIL FRNAALG (NIL T) -9 NIL 932373) (-394 923365 924436 925711 "FRNAALG-" 926461 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-393 923003 923046 923173 "FRNAAF2" 923316 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-392 921368 921860 922154 "FRMOD" 922816 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-391 919090 919759 920075 "FRIDEAL" 921159 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-390 918289 918376 918663 "FRIDEAL2" 918997 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-389 917547 917955 917996 "FRETRCT" 918001 NIL FRETRCT (NIL T) -9 NIL 918172) (-388 916659 916890 917241 "FRETRCT-" 917246 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-387 913869 915089 915148 "FRAMALG" 916030 NIL FRAMALG (NIL T T) -9 NIL 916322) (-386 912002 912458 913088 "FRAMALG-" 913311 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-385 905904 911477 911753 "FRAC" 911758 NIL FRAC (NIL T) -8 NIL NIL) (-384 905540 905597 905704 "FRAC2" 905841 NIL FRAC2 (NIL T T) -7 NIL NIL) (-383 905176 905233 905340 "FR2" 905477 NIL FR2 (NIL T T) -7 NIL NIL) (-382 899850 902763 902791 "FPS" 903910 T FPS (NIL) -9 NIL 904466) (-381 899299 899408 899572 "FPS-" 899718 NIL FPS- (NIL T) -8 NIL NIL) (-380 896748 898445 898473 "FPC" 898698 T FPC (NIL) -9 NIL 898840) (-379 896541 896581 896678 "FPC-" 896683 NIL FPC- (NIL T) -8 NIL NIL) (-378 895420 896030 896071 "FPATMAB" 896076 NIL FPATMAB (NIL T) -9 NIL 896228) (-377 893120 893596 894022 "FPARFRAC" 895057 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-376 888513 889012 889694 "FORTRAN" 892552 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-375 886229 886729 887268 "FORT" 887994 T FORT (NIL) -7 NIL NIL) (-374 883905 884467 884495 "FORTFN" 885555 T FORTFN (NIL) -9 NIL 886179) (-373 883669 883719 883747 "FORTCAT" 883806 T FORTCAT (NIL) -9 NIL 883868) (-372 881729 882212 882611 "FORMULA" 883290 T FORMULA (NIL) -8 NIL NIL) (-371 881517 881547 881616 "FORMULA1" 881693 NIL FORMULA1 (NIL T) -7 NIL NIL) (-370 881040 881092 881265 "FORDER" 881459 NIL FORDER (NIL T T T T) -7 NIL NIL) (-369 880136 880300 880493 "FOP" 880867 T FOP (NIL) -7 NIL NIL) (-368 878744 879416 879590 "FNLA" 880018 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-367 877413 877802 877830 "FNCAT" 878402 T FNCAT (NIL) -9 NIL 878695) (-366 876979 877372 877400 "FNAME" 877405 T FNAME (NIL) -8 NIL NIL) (-365 875639 876612 876640 "FMTC" 876645 T FMTC (NIL) -9 NIL 876680) (-364 871957 873164 873792 "FMONOID" 875044 NIL FMONOID (NIL T) -8 NIL NIL) (-363 871177 871700 871848 "FM" 871853 NIL FM (NIL T T) -8 NIL NIL) (-362 868601 869247 869275 "FMFUN" 870419 T FMFUN (NIL) -9 NIL 871127) (-361 867870 868051 868079 "FMC" 868369 T FMC (NIL) -9 NIL 868551) (-360 865100 865934 865987 "FMCAT" 867169 NIL FMCAT (NIL T T) -9 NIL 867663) (-359 863995 864868 864967 "FM1" 865045 NIL FM1 (NIL T T) -8 NIL NIL) (-358 861769 862185 862679 "FLOATRP" 863546 NIL FLOATRP (NIL T) -7 NIL NIL) (-357 855255 859425 860055 "FLOAT" 861159 T FLOAT (NIL) -8 NIL NIL) (-356 852693 853193 853771 "FLOATCP" 854722 NIL FLOATCP (NIL T) -7 NIL NIL) (-355 851482 852330 852370 "FLINEXP" 852375 NIL FLINEXP (NIL T) -9 NIL 852468) (-354 850637 850872 851199 "FLINEXP-" 851204 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-353 849713 849857 850081 "FLASORT" 850489 NIL FLASORT (NIL T T) -7 NIL NIL) (-352 846932 847774 847826 "FLALG" 849053 NIL FLALG (NIL T T) -9 NIL 849520) (-351 840717 844419 844460 "FLAGG" 845722 NIL FLAGG (NIL T) -9 NIL 846374) (-350 839443 839782 840272 "FLAGG-" 840277 NIL FLAGG- (NIL T T) -8 NIL NIL) (-349 838485 838628 838855 "FLAGG2" 839296 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-348 835458 836476 836535 "FINRALG" 837663 NIL FINRALG (NIL T T) -9 NIL 838171) (-347 834618 834847 835186 "FINRALG-" 835191 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-346 834025 834238 834266 "FINITE" 834462 T FINITE (NIL) -9 NIL 834569) (-345 826485 828646 828686 "FINAALG" 832353 NIL FINAALG (NIL T) -9 NIL 833806) (-344 821826 822867 824011 "FINAALG-" 825390 NIL FINAALG- (NIL T T) -8 NIL NIL) (-343 821221 821581 821684 "FILE" 821756 NIL FILE (NIL T) -8 NIL NIL) (-342 819906 820218 820272 "FILECAT" 820956 NIL FILECAT (NIL T T) -9 NIL 821172) (-341 817769 819325 819353 "FIELD" 819393 T FIELD (NIL) -9 NIL 819473) (-340 816389 816774 817285 "FIELD-" 817290 NIL FIELD- (NIL T) -8 NIL NIL) (-339 814204 815026 815372 "FGROUP" 816076 NIL FGROUP (NIL T) -8 NIL NIL) (-338 813294 813458 813678 "FGLMICPK" 814036 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-337 809096 813219 813276 "FFX" 813281 NIL FFX (NIL T NIL) -8 NIL NIL) (-336 808697 808758 808893 "FFSLPE" 809029 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-335 804690 805469 806265 "FFPOLY" 807933 NIL FFPOLY (NIL T) -7 NIL NIL) (-334 804194 804230 804439 "FFPOLY2" 804648 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-333 800015 804113 804176 "FFP" 804181 NIL FFP (NIL T NIL) -8 NIL NIL) (-332 795383 799926 799990 "FF" 799995 NIL FF (NIL NIL NIL) -8 NIL NIL) (-331 790479 794726 794916 "FFNBX" 795237 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-330 785388 789614 789872 "FFNBP" 790333 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-329 779991 784672 784883 "FFNB" 785221 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-328 778823 779021 779336 "FFINTBAS" 779788 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-327 775047 777287 777315 "FFIELDC" 777935 T FFIELDC (NIL) -9 NIL 778311) (-326 773710 774080 774577 "FFIELDC-" 774582 NIL FFIELDC- (NIL T) -8 NIL NIL) (-325 773280 773325 773449 "FFHOM" 773652 NIL FFHOM (NIL T T T) -7 NIL NIL) (-324 770978 771462 771979 "FFF" 772795 NIL FFF (NIL T) -7 NIL NIL) (-323 766566 770720 770821 "FFCGX" 770921 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-322 762168 766298 766405 "FFCGP" 766509 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-321 757321 761895 762003 "FFCG" 762104 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-320 739267 748390 748476 "FFCAT" 753641 NIL FFCAT (NIL T T T) -9 NIL 755128) (-319 734465 735512 736826 "FFCAT-" 738056 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-318 733876 733919 734154 "FFCAT2" 734416 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-317 723076 726866 728083 "FEXPR" 732731 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-316 722076 722511 722552 "FEVALAB" 722636 NIL FEVALAB (NIL T) -9 NIL 722897) (-315 721235 721445 721783 "FEVALAB-" 721788 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-314 719828 720618 720821 "FDIV" 721134 NIL FDIV (NIL T T T T) -8 NIL NIL) (-313 716895 717610 717725 "FDIVCAT" 719293 NIL FDIVCAT (NIL T T T T) -9 NIL 719730) (-312 716657 716684 716854 "FDIVCAT-" 716859 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-311 715877 715964 716241 "FDIV2" 716564 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-310 714563 714822 715111 "FCPAK1" 715608 T FCPAK1 (NIL) -7 NIL NIL) (-309 713691 714063 714204 "FCOMP" 714454 NIL FCOMP (NIL T) -8 NIL NIL) (-308 697326 700740 704301 "FC" 710150 T FC (NIL) -8 NIL NIL) (-307 689922 693968 694008 "FAXF" 695810 NIL FAXF (NIL T) -9 NIL 696501) (-306 687201 687856 688681 "FAXF-" 689146 NIL FAXF- (NIL T T) -8 NIL NIL) (-305 682301 686577 686753 "FARRAY" 687058 NIL FARRAY (NIL T) -8 NIL NIL) (-304 677692 679763 679815 "FAMR" 680827 NIL FAMR (NIL T T) -9 NIL 681287) (-303 676583 676885 677319 "FAMR-" 677324 NIL FAMR- (NIL T T T) -8 NIL NIL) (-302 675779 676505 676558 "FAMONOID" 676563 NIL FAMONOID (NIL T) -8 NIL NIL) (-301 673612 674296 674349 "FAMONC" 675290 NIL FAMONC (NIL T T) -9 NIL 675675) (-300 672304 673366 673503 "FAGROUP" 673508 NIL FAGROUP (NIL T) -8 NIL NIL) (-299 670107 670426 670828 "FACUTIL" 671985 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-298 669206 669391 669613 "FACTFUNC" 669917 NIL FACTFUNC (NIL T) -7 NIL NIL) (-297 661526 668457 668669 "EXPUPXS" 669062 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-296 659009 659549 660135 "EXPRTUBE" 660960 T EXPRTUBE (NIL) -7 NIL NIL) (-295 655203 655795 656532 "EXPRODE" 658348 NIL EXPRODE (NIL T T) -7 NIL NIL) (-294 640362 653862 654288 "EXPR" 654809 NIL EXPR (NIL T) -8 NIL NIL) (-293 634790 635377 636189 "EXPR2UPS" 639660 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-292 634426 634483 634590 "EXPR2" 634727 NIL EXPR2 (NIL T T) -7 NIL NIL) (-291 625780 633563 633858 "EXPEXPAN" 634264 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-290 625607 625737 625766 "EXIT" 625771 T EXIT (NIL) -8 NIL NIL) (-289 625234 625296 625409 "EVALCYC" 625539 NIL EVALCYC (NIL T) -7 NIL NIL) (-288 624775 624893 624934 "EVALAB" 625104 NIL EVALAB (NIL T) -9 NIL 625208) (-287 624256 624378 624599 "EVALAB-" 624604 NIL EVALAB- (NIL T T) -8 NIL NIL) (-286 621719 623031 623059 "EUCDOM" 623614 T EUCDOM (NIL) -9 NIL 623964) (-285 620124 620566 621156 "EUCDOM-" 621161 NIL EUCDOM- (NIL T) -8 NIL NIL) (-284 607702 610450 613190 "ESTOOLS" 617404 T ESTOOLS (NIL) -7 NIL NIL) (-283 607338 607395 607502 "ESTOOLS2" 607639 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-282 607089 607131 607211 "ESTOOLS1" 607290 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-281 601027 602751 602779 "ES" 605543 T ES (NIL) -9 NIL 606949) (-280 595974 597261 599078 "ES-" 599242 NIL ES- (NIL T) -8 NIL NIL) (-279 592349 593109 593889 "ESCONT" 595214 T ESCONT (NIL) -7 NIL NIL) (-278 592094 592126 592208 "ESCONT1" 592311 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-277 591769 591819 591919 "ES2" 592038 NIL ES2 (NIL T T) -7 NIL NIL) (-276 591399 591457 591566 "ES1" 591705 NIL ES1 (NIL T T) -7 NIL NIL) (-275 590615 590744 590920 "ERROR" 591243 T ERROR (NIL) -7 NIL NIL) (-274 584118 590474 590565 "EQTBL" 590570 NIL EQTBL (NIL T T) -8 NIL NIL) (-273 576555 579436 580883 "EQ" 582704 NIL -2446 (NIL T) -8 NIL NIL) (-272 576187 576244 576353 "EQ2" 576492 NIL EQ2 (NIL T T) -7 NIL NIL) (-271 571479 572525 573618 "EP" 575126 NIL EP (NIL T) -7 NIL NIL) (-270 570062 570362 570679 "ENV" 571182 T ENV (NIL) -8 NIL NIL) (-269 569222 569786 569814 "ENTIRER" 569819 T ENTIRER (NIL) -9 NIL 569864) (-268 565678 567177 567547 "EMR" 569021 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-267 564822 565007 565061 "ELTAGG" 565441 NIL ELTAGG (NIL T T) -9 NIL 565652) (-266 564541 564603 564744 "ELTAGG-" 564749 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-265 564330 564359 564413 "ELTAB" 564497 NIL ELTAB (NIL T T) -9 NIL NIL) (-264 563456 563602 563801 "ELFUTS" 564181 NIL ELFUTS (NIL T T) -7 NIL NIL) (-263 563198 563254 563282 "ELEMFUN" 563387 T ELEMFUN (NIL) -9 NIL NIL) (-262 563068 563089 563157 "ELEMFUN-" 563162 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-261 557960 561169 561210 "ELAGG" 562150 NIL ELAGG (NIL T) -9 NIL 562613) (-260 556245 556679 557342 "ELAGG-" 557347 NIL ELAGG- (NIL T T) -8 NIL NIL) (-259 554902 555182 555477 "ELABEXPR" 555970 T ELABEXPR (NIL) -8 NIL NIL) (-258 547770 549569 550396 "EFUPXS" 554178 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-257 541220 543021 543831 "EFULS" 547046 NIL EFULS (NIL T T T) -8 NIL NIL) (-256 538651 539009 539487 "EFSTRUC" 540852 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-255 527723 529288 530848 "EF" 537166 NIL EF (NIL T T) -7 NIL NIL) (-254 526824 527208 527357 "EAB" 527594 T EAB (NIL) -8 NIL NIL) (-253 526037 526783 526811 "E04UCFA" 526816 T E04UCFA (NIL) -8 NIL NIL) (-252 525250 525996 526024 "E04NAFA" 526029 T E04NAFA (NIL) -8 NIL NIL) (-251 524463 525209 525237 "E04MBFA" 525242 T E04MBFA (NIL) -8 NIL NIL) (-250 523676 524422 524450 "E04JAFA" 524455 T E04JAFA (NIL) -8 NIL NIL) (-249 522891 523635 523663 "E04GCFA" 523668 T E04GCFA (NIL) -8 NIL NIL) (-248 522106 522850 522878 "E04FDFA" 522883 T E04FDFA (NIL) -8 NIL NIL) (-247 521319 522065 522093 "E04DGFA" 522098 T E04DGFA (NIL) -8 NIL NIL) (-246 515504 516849 518211 "E04AGNT" 519977 T E04AGNT (NIL) -7 NIL NIL) (-245 514231 514711 514751 "DVARCAT" 515226 NIL DVARCAT (NIL T) -9 NIL 515424) (-244 513435 513647 513961 "DVARCAT-" 513966 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-243 506297 513237 513364 "DSMP" 513369 NIL DSMP (NIL T T T) -8 NIL NIL) (-242 501107 502242 503310 "DROPT" 505249 T DROPT (NIL) -8 NIL NIL) (-241 500772 500831 500929 "DROPT1" 501042 NIL DROPT1 (NIL T) -7 NIL NIL) (-240 495887 497013 498150 "DROPT0" 499655 T DROPT0 (NIL) -7 NIL NIL) (-239 494232 494557 494943 "DRAWPT" 495521 T DRAWPT (NIL) -7 NIL NIL) (-238 488819 489742 490821 "DRAW" 493206 NIL DRAW (NIL T) -7 NIL NIL) (-237 488452 488505 488623 "DRAWHACK" 488760 NIL DRAWHACK (NIL T) -7 NIL NIL) (-236 487183 487452 487743 "DRAWCX" 488181 T DRAWCX (NIL) -7 NIL NIL) (-235 486701 486769 486919 "DRAWCURV" 487109 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-234 477172 479131 481246 "DRAWCFUN" 484606 T DRAWCFUN (NIL) -7 NIL NIL) (-233 473986 475868 475909 "DQAGG" 476538 NIL DQAGG (NIL T) -9 NIL 476811) (-232 462493 469231 469313 "DPOLCAT" 471151 NIL DPOLCAT (NIL T T T T) -9 NIL 471695) (-231 457333 458679 460636 "DPOLCAT-" 460641 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-230 451417 457195 457292 "DPMO" 457297 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-229 445404 451198 451364 "DPMM" 451369 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-228 444917 445015 445135 "DOMAIN" 445304 T DOMAIN (NIL) -8 NIL NIL) (-227 438629 444554 444705 "DMP" 444818 NIL DMP (NIL NIL T) -8 NIL NIL) (-226 438229 438285 438429 "DLP" 438567 NIL DLP (NIL T) -7 NIL NIL) (-225 431873 437330 437557 "DLIST" 438034 NIL DLIST (NIL T) -8 NIL NIL) (-224 428720 430729 430770 "DLAGG" 431320 NIL DLAGG (NIL T) -9 NIL 431549) (-223 427430 428122 428150 "DIVRING" 428300 T DIVRING (NIL) -9 NIL 428408) (-222 426418 426671 427064 "DIVRING-" 427069 NIL DIVRING- (NIL T) -8 NIL NIL) (-221 424520 424877 425283 "DISPLAY" 426032 T DISPLAY (NIL) -7 NIL NIL) (-220 418409 424434 424497 "DIRPROD" 424502 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-219 417257 417460 417725 "DIRPROD2" 418202 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-218 406888 412893 412946 "DIRPCAT" 413354 NIL DIRPCAT (NIL NIL T) -9 NIL 414181) (-217 404214 404856 405737 "DIRPCAT-" 406074 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-216 403501 403661 403847 "DIOSP" 404048 T DIOSP (NIL) -7 NIL NIL) (-215 400204 402414 402455 "DIOPS" 402889 NIL DIOPS (NIL T) -9 NIL 403118) (-214 399753 399867 400058 "DIOPS-" 400063 NIL DIOPS- (NIL T T) -8 NIL NIL) (-213 398625 399263 399291 "DIFRING" 399478 T DIFRING (NIL) -9 NIL 399587) (-212 398271 398348 398500 "DIFRING-" 398505 NIL DIFRING- (NIL T) -8 NIL NIL) (-211 396061 397343 397383 "DIFEXT" 397742 NIL DIFEXT (NIL T) -9 NIL 398035) (-210 394347 394775 395440 "DIFEXT-" 395445 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-209 391670 393880 393921 "DIAGG" 393926 NIL DIAGG (NIL T) -9 NIL 393946) (-208 391054 391211 391463 "DIAGG-" 391468 NIL DIAGG- (NIL T T) -8 NIL NIL) (-207 386519 390013 390290 "DHMATRIX" 390823 NIL DHMATRIX (NIL T) -8 NIL NIL) (-206 382131 383040 384050 "DFSFUN" 385529 T DFSFUN (NIL) -7 NIL NIL) (-205 376917 380845 381210 "DFLOAT" 381786 T DFLOAT (NIL) -8 NIL NIL) (-204 375150 375431 375826 "DFINTTLS" 376625 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-203 372183 373185 373583 "DERHAM" 374817 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-202 370032 371958 372047 "DEQUEUE" 372127 NIL DEQUEUE (NIL T) -8 NIL NIL) (-201 369250 369383 369578 "DEGRED" 369894 NIL DEGRED (NIL T T) -7 NIL NIL) (-200 365650 366395 367247 "DEFINTRF" 368478 NIL DEFINTRF (NIL T) -7 NIL NIL) (-199 363181 363650 364248 "DEFINTEF" 365169 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-198 357011 362622 362788 "DECIMAL" 363035 T DECIMAL (NIL) -8 NIL NIL) (-197 354523 354981 355487 "DDFACT" 356555 NIL DDFACT (NIL T T) -7 NIL NIL) (-196 354119 354162 354313 "DBLRESP" 354474 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-195 351829 352163 352532 "DBASE" 353877 NIL DBASE (NIL T) -8 NIL NIL) (-194 350964 351788 351816 "D03FAFA" 351821 T D03FAFA (NIL) -8 NIL NIL) (-193 350100 350923 350951 "D03EEFA" 350956 T D03EEFA (NIL) -8 NIL NIL) (-192 348050 348516 349005 "D03AGNT" 349631 T D03AGNT (NIL) -7 NIL NIL) (-191 347368 348009 348037 "D02EJFA" 348042 T D02EJFA (NIL) -8 NIL NIL) (-190 346686 347327 347355 "D02CJFA" 347360 T D02CJFA (NIL) -8 NIL NIL) (-189 346004 346645 346673 "D02BHFA" 346678 T D02BHFA (NIL) -8 NIL NIL) (-188 345322 345963 345991 "D02BBFA" 345996 T D02BBFA (NIL) -8 NIL NIL) (-187 338520 340108 341714 "D02AGNT" 343736 T D02AGNT (NIL) -7 NIL NIL) (-186 336289 336811 337357 "D01WGTS" 337994 T D01WGTS (NIL) -7 NIL NIL) (-185 335392 336248 336276 "D01TRNS" 336281 T D01TRNS (NIL) -8 NIL NIL) (-184 334495 335351 335379 "D01GBFA" 335384 T D01GBFA (NIL) -8 NIL NIL) (-183 333598 334454 334482 "D01FCFA" 334487 T D01FCFA (NIL) -8 NIL NIL) (-182 332701 333557 333585 "D01ASFA" 333590 T D01ASFA (NIL) -8 NIL NIL) (-181 331804 332660 332688 "D01AQFA" 332693 T D01AQFA (NIL) -8 NIL NIL) (-180 330907 331763 331791 "D01APFA" 331796 T D01APFA (NIL) -8 NIL NIL) (-179 330010 330866 330894 "D01ANFA" 330899 T D01ANFA (NIL) -8 NIL NIL) (-178 329113 329969 329997 "D01AMFA" 330002 T D01AMFA (NIL) -8 NIL NIL) (-177 328216 329072 329100 "D01ALFA" 329105 T D01ALFA (NIL) -8 NIL NIL) (-176 327319 328175 328203 "D01AKFA" 328208 T D01AKFA (NIL) -8 NIL NIL) (-175 326422 327278 327306 "D01AJFA" 327311 T D01AJFA (NIL) -8 NIL NIL) (-174 319726 321275 322834 "D01AGNT" 324883 T D01AGNT (NIL) -7 NIL NIL) (-173 319063 319191 319343 "CYCLOTOM" 319594 T CYCLOTOM (NIL) -7 NIL NIL) (-172 315798 316511 317238 "CYCLES" 318356 T CYCLES (NIL) -7 NIL NIL) (-171 315110 315244 315415 "CVMP" 315659 NIL CVMP (NIL T) -7 NIL NIL) (-170 312891 313149 313524 "CTRIGMNP" 314838 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-169 312496 312579 312684 "CTORCALL" 312806 T CTORCALL (NIL) -8 NIL NIL) (-168 311870 311969 312122 "CSTTOOLS" 312393 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-167 307669 308326 309084 "CRFP" 311182 NIL CRFP (NIL T T) -7 NIL NIL) (-166 306716 306901 307129 "CRAPACK" 307473 NIL CRAPACK (NIL T) -7 NIL NIL) (-165 306100 306201 306405 "CPMATCH" 306592 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-164 305825 305853 305959 "CPIMA" 306066 NIL CPIMA (NIL T T T) -7 NIL NIL) (-163 302189 302861 303579 "COORDSYS" 305160 NIL COORDSYS (NIL T) -7 NIL NIL) (-162 301573 301702 301852 "CONTOUR" 302059 T CONTOUR (NIL) -8 NIL NIL) (-161 297434 299576 300068 "CONTFRAC" 301113 NIL CONTFRAC (NIL T) -8 NIL NIL) (-160 296588 297152 297180 "COMRING" 297185 T COMRING (NIL) -9 NIL 297236) (-159 295669 295946 296130 "COMPPROP" 296424 T COMPPROP (NIL) -8 NIL NIL) (-158 295330 295365 295493 "COMPLPAT" 295628 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-157 285311 295139 295248 "COMPLEX" 295253 NIL COMPLEX (NIL T) -8 NIL NIL) (-156 284947 285004 285111 "COMPLEX2" 285248 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-155 284665 284700 284798 "COMPFACT" 284906 NIL COMPFACT (NIL T T) -7 NIL NIL) (-154 269000 279294 279334 "COMPCAT" 280336 NIL COMPCAT (NIL T) -9 NIL 281729) (-153 258515 261439 265066 "COMPCAT-" 265422 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-152 258246 258274 258376 "COMMUPC" 258481 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-151 258041 258074 258133 "COMMONOP" 258207 T COMMONOP (NIL) -7 NIL NIL) (-150 257624 257792 257879 "COMM" 257974 T COMM (NIL) -8 NIL NIL) (-149 256873 257067 257095 "COMBOPC" 257433 T COMBOPC (NIL) -9 NIL 257608) (-148 255769 255979 256221 "COMBINAT" 256663 NIL COMBINAT (NIL T) -7 NIL NIL) (-147 251967 252540 253180 "COMBF" 255191 NIL COMBF (NIL T T) -7 NIL NIL) (-146 250753 251083 251318 "COLOR" 251752 T COLOR (NIL) -8 NIL NIL) (-145 250393 250440 250565 "CMPLXRT" 250700 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-144 245895 246923 248003 "CLIP" 249333 T CLIP (NIL) -7 NIL NIL) (-143 244233 245003 245241 "CLIF" 245723 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-142 240456 242380 242421 "CLAGG" 243350 NIL CLAGG (NIL T) -9 NIL 243886) (-141 238878 239335 239918 "CLAGG-" 239923 NIL CLAGG- (NIL T T) -8 NIL NIL) (-140 238422 238507 238647 "CINTSLPE" 238787 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-139 235923 236394 236942 "CHVAR" 237950 NIL CHVAR (NIL T T T) -7 NIL NIL) (-138 235146 235710 235738 "CHARZ" 235743 T CHARZ (NIL) -9 NIL 235757) (-137 234900 234940 235018 "CHARPOL" 235100 NIL CHARPOL (NIL T) -7 NIL NIL) (-136 234007 234604 234632 "CHARNZ" 234679 T CHARNZ (NIL) -9 NIL 234734) (-135 232032 232697 233032 "CHAR" 233692 T CHAR (NIL) -8 NIL NIL) (-134 231758 231819 231847 "CFCAT" 231958 T CFCAT (NIL) -9 NIL NIL) (-133 231003 231114 231296 "CDEN" 231642 NIL CDEN (NIL T T T) -7 NIL NIL) (-132 226995 230156 230436 "CCLASS" 230743 T CCLASS (NIL) -8 NIL NIL) (-131 226914 226940 226975 "CATEGORY" 226980 T -10 (NIL) -8 NIL NIL) (-130 221966 222943 223696 "CARTEN" 226217 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-129 221074 221222 221443 "CARTEN2" 221813 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-128 219372 220226 220482 "CARD" 220838 T CARD (NIL) -8 NIL NIL) (-127 218745 219073 219101 "CACHSET" 219233 T CACHSET (NIL) -9 NIL 219310) (-126 218242 218538 218566 "CABMON" 218616 T CABMON (NIL) -9 NIL 218672) (-125 217410 217789 217932 "BYTE" 218119 T BYTE (NIL) -8 NIL NIL) (-124 213358 217357 217391 "BYTEARY" 217396 T BYTEARY (NIL) -8 NIL NIL) (-123 210915 213050 213157 "BTREE" 213284 NIL BTREE (NIL T) -8 NIL NIL) (-122 208413 210563 210685 "BTOURN" 210825 NIL BTOURN (NIL T) -8 NIL NIL) (-121 205832 207885 207926 "BTCAT" 207994 NIL BTCAT (NIL T) -9 NIL 208071) (-120 205499 205579 205728 "BTCAT-" 205733 NIL BTCAT- (NIL T T) -8 NIL NIL) (-119 200720 204591 204619 "BTAGG" 204875 T BTAGG (NIL) -9 NIL 205054) (-118 200143 200287 200517 "BTAGG-" 200522 NIL BTAGG- (NIL T) -8 NIL NIL) (-117 197187 199421 199636 "BSTREE" 199960 NIL BSTREE (NIL T) -8 NIL NIL) (-116 196325 196451 196635 "BRILL" 197043 NIL BRILL (NIL T) -7 NIL NIL) (-115 193027 195054 195095 "BRAGG" 195744 NIL BRAGG (NIL T) -9 NIL 196001) (-114 191556 191962 192517 "BRAGG-" 192522 NIL BRAGG- (NIL T T) -8 NIL NIL) (-113 184764 190902 191086 "BPADICRT" 191404 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-112 183068 184701 184746 "BPADIC" 184751 NIL BPADIC (NIL NIL) -8 NIL NIL) (-111 182768 182798 182911 "BOUNDZRO" 183032 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-110 178283 179374 180241 "BOP" 181921 T BOP (NIL) -8 NIL NIL) (-109 175904 176348 176868 "BOP1" 177796 NIL BOP1 (NIL T) -7 NIL NIL) (-108 174539 175244 175462 "BOOLEAN" 175706 T BOOLEAN (NIL) -8 NIL NIL) (-107 173906 174284 174336 "BMODULE" 174341 NIL BMODULE (NIL T T) -9 NIL 174405) (-106 169716 173704 173777 "BITS" 173853 T BITS (NIL) -8 NIL NIL) (-105 168813 169248 169400 "BINFILE" 169584 T BINFILE (NIL) -8 NIL NIL) (-104 168225 168347 168489 "BINDING" 168691 T BINDING (NIL) -8 NIL NIL) (-103 162059 167669 167834 "BINARY" 168080 T BINARY (NIL) -8 NIL NIL) (-102 159887 161315 161356 "BGAGG" 161616 NIL BGAGG (NIL T) -9 NIL 161753) (-101 159718 159750 159841 "BGAGG-" 159846 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 158816 159102 159307 "BFUNCT" 159533 T BFUNCT (NIL) -8 NIL NIL) (-99 157517 157695 157980 "BEZOUT" 158640 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 154042 156377 156705 "BBTREE" 157220 NIL BBTREE (NIL T) -8 NIL NIL) (-97 153780 153833 153859 "BASTYPE" 153976 T BASTYPE (NIL) -9 NIL NIL) (-96 153635 153664 153734 "BASTYPE-" 153739 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 153073 153149 153299 "BALFACT" 153546 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 151895 152492 152677 "AUTOMOR" 152918 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151621 151626 151652 "ATTREG" 151657 T ATTREG (NIL) -9 NIL NIL) (-92 149900 150318 150670 "ATTRBUT" 151287 T ATTRBUT (NIL) -8 NIL NIL) (-91 149436 149549 149575 "ATRIG" 149776 T ATRIG (NIL) -9 NIL NIL) (-90 149245 149286 149373 "ATRIG-" 149378 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147442 149021 149109 "ASTACK" 149188 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145947 146244 146609 "ASSOCEQ" 147124 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144979 145606 145730 "ASP9" 145854 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144743 144927 144966 "ASP8" 144971 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143612 144348 144490 "ASP80" 144632 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142511 143247 143379 "ASP7" 143511 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141465 142188 142306 "ASP78" 142424 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140434 141145 141262 "ASP77" 141379 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139346 140072 140203 "ASP74" 140334 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 138246 138981 139113 "ASP73" 139245 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 137201 137923 138041 "ASP6" 138159 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136149 136878 136996 "ASP55" 137114 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135099 135823 135942 "ASP50" 136061 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134187 134800 134910 "ASP4" 135020 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 133275 133888 133998 "ASP49" 134108 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 132060 132814 132982 "ASP42" 133164 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130837 131593 131763 "ASP41" 131947 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129787 130514 130632 "ASP35" 130750 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129552 129735 129774 "ASP34" 129779 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 129289 129356 129432 "ASP33" 129507 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 128184 128924 129056 "ASP31" 129188 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127949 128132 128171 "ASP30" 128176 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127684 127753 127829 "ASP29" 127904 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127449 127632 127671 "ASP28" 127676 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 127214 127397 127436 "ASP27" 127441 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 126298 126912 127023 "ASP24" 127134 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 125214 125939 126069 "ASP20" 126199 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124302 124915 125025 "ASP1" 125135 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 123246 123976 124095 "ASP19" 124214 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122983 123050 123126 "ASP12" 123201 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121835 122582 122726 "ASP10" 122870 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119734 121679 121770 "ARRAY2" 121775 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115550 119382 119496 "ARRAY1" 119651 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114582 114755 114976 "ARRAY12" 115373 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108942 110813 110888 "ARR2CAT" 113518 NIL ARR2CAT (NIL T T T) -9 NIL 114276) (-54 106376 107120 108074 "ARR2CAT-" 108079 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 105136 105286 105589 "APPRULE" 106214 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 104789 104837 104955 "APPLYORE" 105082 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 103763 104054 104249 "ANY" 104612 T ANY (NIL) -8 NIL NIL) (-50 103041 103164 103321 "ANY1" 103637 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100573 101491 101816 "ANTISYM" 102766 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100088 100277 100374 "ANON" 100494 T ANON (NIL) -8 NIL NIL) (-47 94165 98633 99084 "AN" 99655 T AN (NIL) -8 NIL NIL) (-46 90519 91917 91967 "AMR" 92706 NIL AMR (NIL T T) -9 NIL 93305) (-45 89632 89853 90215 "AMR-" 90220 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74182 89549 89610 "ALIST" 89615 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71019 73776 73945 "ALGSC" 74100 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 67575 68129 68736 "ALGPKG" 70459 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 66852 66953 67137 "ALGMFACT" 67461 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 62602 63282 63936 "ALGMANIP" 66376 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 53921 62228 62378 "ALGFF" 62535 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53117 53248 53427 "ALGFACT" 53779 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52108 52718 52756 "ALGEBRA" 52816 NIL ALGEBRA (NIL T) -9 NIL 52874) (-36 51826 51885 52017 "ALGEBRA-" 52022 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34087 49830 49882 "ALAGG" 50018 NIL ALAGG (NIL T T) -9 NIL 50179) (-34 33623 33736 33762 "AHYP" 33963 T AHYP (NIL) -9 NIL NIL) (-33 32554 32802 32828 "AGG" 33327 T AGG (NIL) -9 NIL 33606) (-32 31988 32150 32364 "AGG-" 32369 NIL AGG- (NIL T) -8 NIL NIL) (-31 29675 30093 30510 "AF" 31631 NIL AF (NIL T T) -7 NIL NIL) (-30 28944 29202 29358 "ACPLOT" 29537 T ACPLOT (NIL) -8 NIL NIL) (-29 18411 26357 26408 "ACFS" 27119 NIL ACFS (NIL T) -9 NIL 27358) (-28 16425 16915 17690 "ACFS-" 17695 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12693 14649 14675 "ACF" 15554 T ACF (NIL) -9 NIL 15966) (-26 11397 11731 12224 "ACF-" 12229 NIL ACF- (NIL T) -8 NIL NIL) (-25 10996 11165 11191 "ABELSG" 11283 T ABELSG (NIL) -9 NIL 11348) (-24 10863 10888 10954 "ABELSG-" 10959 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10233 10494 10520 "ABELMON" 10690 T ABELMON (NIL) -9 NIL 10802) (-22 9897 9981 10119 "ABELMON-" 10124 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9232 9578 9604 "ABELGRP" 9729 T ABELGRP (NIL) -9 NIL 9811) (-20 8695 8824 9040 "ABELGRP-" 9045 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
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NIL NIL) (-1189 3115280 3117593 3117635 "XF" 3118256 NIL XF (NIL T) -9 NIL 3118655) (-1188 3114901 3114989 3115158 "XF-" 3115163 NIL XF- (NIL T T) -8 NIL NIL) (-1187 3110281 3111580 3111634 "XFALG" 3113782 NIL XFALG (NIL T T) -9 NIL 3114569) (-1186 3109418 3109522 3109726 "XEXPPKG" 3110173 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1185 3107517 3109269 3109364 "XDPOLY" 3109369 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1184 3106396 3107006 3107048 "XALG" 3107110 NIL XALG (NIL T) -9 NIL 3107229) (-1183 3099872 3104380 3104873 "WUTSET" 3105988 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1182 3097676 3098483 3098834 "WP" 3099654 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1181 3096562 3096760 3097055 "WFFINTBS" 3097473 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1180 3094442 3094869 3095331 "WEIER" 3096134 NIL WEIER (NIL T) -7 NIL NIL) (-1179 3093591 3094015 3094057 "VSPACE" 3094193 NIL VSPACE (NIL T) -9 NIL 3094267) (-1178 3093429 3093456 3093547 "VSPACE-" 3093552 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1177 3093175 3093218 3093289 "VOID" 3093380 T VOID (NIL) -8 NIL NIL) (-1176 3091311 3091670 3092076 "VIEW" 3092791 T VIEW (NIL) -7 NIL NIL) (-1175 3087736 3088374 3089111 "VIEWDEF" 3090596 T VIEWDEF (NIL) -7 NIL NIL) (-1174 3077074 3079284 3081457 "VIEW3D" 3085585 T VIEW3D (NIL) -8 NIL NIL) (-1173 3069356 3070985 3072564 "VIEW2D" 3075517 T VIEW2D (NIL) -8 NIL NIL) (-1172 3064765 3069126 3069218 "VECTOR" 3069299 NIL VECTOR (NIL T) -8 NIL NIL) (-1171 3063342 3063601 3063919 "VECTOR2" 3064495 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1170 3056882 3061134 3061177 "VECTCAT" 3062165 NIL VECTCAT (NIL T) -9 NIL 3062749) (-1169 3055896 3056150 3056540 "VECTCAT-" 3056545 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1168 3055367 3055537 3055657 "VARIABLE" 3055811 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1167 3055300 3055305 3055335 "UTYPE" 3055340 T UTYPE (NIL) -9 NIL NIL) (-1166 3054135 3054289 3054550 "UTSODETL" 3055126 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1165 3051575 3052035 3052559 "UTSODE" 3053676 NIL UTSODE (NIL T T) -7 NIL NIL) (-1164 3043419 3049215 3049703 "UTS" 3051144 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1163 3034754 3040119 3040161 "UTSCAT" 3041272 NIL UTSCAT (NIL T) -9 NIL 3042029) (-1162 3032109 3032825 3033813 "UTSCAT-" 3033818 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1161 3031740 3031783 3031914 "UTS2" 3032060 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1160 3026016 3028581 3028624 "URAGG" 3030694 NIL URAGG (NIL T) -9 NIL 3031416) (-1159 3022955 3023818 3024941 "URAGG-" 3024946 NIL URAGG- (NIL T T) -8 NIL NIL) (-1158 3018641 3021572 3022043 "UPXSSING" 3022619 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1157 3010532 3017762 3018042 "UPXS" 3018418 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1156 3003561 3010437 3010508 "UPXSCONS" 3010513 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1155 2993850 3000680 3000741 "UPXSCCA" 3001390 NIL UPXSCCA (NIL T T) -9 NIL 3001631) (-1154 2993489 2993574 2993747 "UPXSCCA-" 2993752 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1153 2983690 2990293 2990335 "UPXSCAT" 2990988 NIL UPXSCAT (NIL T) -9 NIL 2991596) (-1152 2983124 2983203 2983380 "UPXS2" 2983605 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1151 2981778 2982031 2982382 "UPSQFREE" 2982867 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1150 2975669 2978724 2978778 "UPSCAT" 2979927 NIL UPSCAT (NIL T T) -9 NIL 2980701) (-1149 2974874 2975081 2975407 "UPSCAT-" 2975412 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1148 2960960 2968997 2969039 "UPOLYC" 2971117 NIL UPOLYC (NIL T) -9 NIL 2972338) (-1147 2952290 2954715 2957861 "UPOLYC-" 2957866 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1146 2951921 2951964 2952095 "UPOLYC2" 2952241 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1145 2943340 2951490 2951627 "UP" 2951831 NIL UP (NIL NIL T) -8 NIL NIL) (-1144 2942683 2942790 2942953 "UPMP" 2943229 NIL UPMP (NIL T T) -7 NIL NIL) (-1143 2942236 2942317 2942456 "UPDIVP" 2942596 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1142 2940804 2941053 2941369 "UPDECOMP" 2941985 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1141 2940039 2940151 2940336 "UPCDEN" 2940688 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1140 2939562 2939631 2939778 "UP2" 2939964 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1139 2938079 2938766 2939043 "UNISEG" 2939320 NIL UNISEG (NIL T) -8 NIL NIL) (-1138 2937294 2937421 2937626 "UNISEG2" 2937922 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1137 2936354 2936534 2936760 "UNIFACT" 2937110 NIL UNIFACT (NIL T) -7 NIL NIL) (-1136 2920250 2935535 2935785 "ULS" 2936161 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1135 2908215 2920155 2920226 "ULSCONS" 2920231 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1134 2890965 2902978 2903039 "ULSCCAT" 2903751 NIL ULSCCAT (NIL T T) -9 NIL 2904047) (-1133 2890016 2890261 2890648 "ULSCCAT-" 2890653 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1132 2879996 2886513 2886555 "ULSCAT" 2887421 NIL ULSCAT (NIL T) -9 NIL 2888151) (-1131 2879430 2879509 2879686 "ULS2" 2879911 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1130 2877828 2878795 2878825 "UFD" 2879037 T UFD (NIL) -9 NIL 2879151) (-1129 2877622 2877668 2877763 "UFD-" 2877768 NIL UFD- (NIL T) -8 NIL NIL) (-1128 2876704 2876887 2877103 "UDVO" 2877428 T UDVO (NIL) -7 NIL NIL) (-1127 2874520 2874929 2875400 "UDPO" 2876268 NIL UDPO (NIL T) -7 NIL NIL) (-1126 2874453 2874458 2874488 "TYPE" 2874493 T TYPE (NIL) -9 NIL NIL) (-1125 2873424 2873626 2873866 "TWOFACT" 2874247 NIL TWOFACT (NIL T) -7 NIL NIL) (-1124 2872362 2872699 2872962 "TUPLE" 2873196 NIL TUPLE (NIL T) -8 NIL NIL) (-1123 2870053 2870572 2871111 "TUBETOOL" 2871845 T TUBETOOL (NIL) -7 NIL NIL) (-1122 2868902 2869107 2869348 "TUBE" 2869846 NIL TUBE (NIL T) -8 NIL NIL) (-1121 2863626 2867880 2868162 "TS" 2868654 NIL TS (NIL T) -8 NIL NIL) (-1120 2852330 2856422 2856518 "TSETCAT" 2861752 NIL TSETCAT (NIL T T T T) -9 NIL 2863283) (-1119 2847065 2848663 2850553 "TSETCAT-" 2850558 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1118 2841328 2842174 2843116 "TRMANIP" 2846201 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1117 2840769 2840832 2840995 "TRIMAT" 2841260 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1116 2838575 2838812 2839175 "TRIGMNIP" 2840518 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1115 2838095 2838208 2838238 "TRIGCAT" 2838451 T TRIGCAT (NIL) -9 NIL NIL) (-1114 2837764 2837843 2837984 "TRIGCAT-" 2837989 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1113 2834663 2836624 2836904 "TREE" 2837519 NIL TREE (NIL T) -8 NIL NIL) (-1112 2833937 2834465 2834495 "TRANFUN" 2834530 T TRANFUN (NIL) -9 NIL 2834596) (-1111 2833216 2833407 2833687 "TRANFUN-" 2833692 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1110 2833020 2833052 2833113 "TOPSP" 2833177 T TOPSP (NIL) -7 NIL NIL) (-1109 2832372 2832487 2832640 "TOOLSIGN" 2832901 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1108 2831033 2831549 2831788 "TEXTFILE" 2832155 T TEXTFILE (NIL) -8 NIL NIL) (-1107 2828898 2829412 2829850 "TEX" 2830617 T TEX (NIL) -8 NIL NIL) (-1106 2828679 2828710 2828782 "TEX1" 2828861 NIL TEX1 (NIL T) -7 NIL NIL) (-1105 2828327 2828390 2828480 "TEMUTL" 2828611 T TEMUTL (NIL) -7 NIL NIL) (-1104 2826481 2826761 2827086 "TBCMPPK" 2828050 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1103 2818370 2824642 2824698 "TBAGG" 2825098 NIL TBAGG (NIL T T) -9 NIL 2825309) (-1102 2813440 2814928 2816682 "TBAGG-" 2816687 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1101 2812824 2812931 2813076 "TANEXP" 2813329 NIL TANEXP (NIL T) -7 NIL NIL) (-1100 2806325 2812681 2812774 "TABLE" 2812779 NIL TABLE (NIL T T) -8 NIL NIL) (-1099 2805737 2805836 2805974 "TABLEAU" 2806222 NIL TABLEAU (NIL T) -8 NIL NIL) (-1098 2800310 2801530 2802778 "TABLBUMP" 2804523 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1097 2799738 2799838 2799966 "SYSTEM" 2800204 T SYSTEM (NIL) -7 NIL NIL) (-1096 2796201 2796896 2797679 "SYSSOLP" 2798989 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1095 2792492 2793200 2793934 "SYNTAX" 2795489 T SYNTAX (NIL) -8 NIL NIL) (-1094 2789626 2790234 2790872 "SYMTAB" 2791876 T SYMTAB (NIL) -8 NIL NIL) (-1093 2784875 2785777 2786760 "SYMS" 2788665 T SYMS (NIL) -8 NIL NIL) (-1092 2782104 2784331 2784560 "SYMPOLY" 2784680 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1091 2781624 2781699 2781821 "SYMFUNC" 2782016 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1090 2777601 2778861 2779683 "SYMBOL" 2780824 T SYMBOL (NIL) -8 NIL NIL) (-1089 2771140 2772829 2774549 "SWITCH" 2775903 T SWITCH (NIL) -8 NIL NIL) (-1088 2764370 2769967 2770269 "SUTS" 2770895 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1087 2756260 2763491 2763771 "SUPXS" 2764147 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1086 2747752 2755881 2756006 "SUP" 2756169 NIL SUP (NIL T) -8 NIL NIL) (-1085 2746911 2747038 2747255 "SUPFRACF" 2747620 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1084 2746536 2746595 2746706 "SUP2" 2746846 NIL SUP2 (NIL T T) -7 NIL NIL) (-1083 2744933 2745207 2745569 "SUMRF" 2746235 NIL SUMRF (NIL T) -7 NIL NIL) (-1082 2744250 2744316 2744514 "SUMFS" 2744854 NIL SUMFS (NIL T T) -7 NIL NIL) (-1081 2728186 2743431 2743681 "SULS" 2744057 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1080 2727508 2727711 2727851 "SUCH" 2728094 NIL SUCH (NIL T T) -8 NIL NIL) (-1079 2721435 2722447 2723405 "SUBSPACE" 2726596 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1078 2720865 2720955 2721119 "SUBRESP" 2721323 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1077 2714234 2715530 2716841 "STTF" 2719601 NIL STTF (NIL T) -7 NIL NIL) (-1076 2708407 2709527 2710674 "STTFNC" 2713134 NIL STTFNC (NIL T) -7 NIL NIL) (-1075 2699747 2701614 2703407 "STTAYLOR" 2706648 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1074 2692991 2699611 2699694 "STRTBL" 2699699 NIL STRTBL (NIL T) -8 NIL NIL) (-1073 2688382 2692946 2692977 "STRING" 2692982 T STRING (NIL) -8 NIL NIL) (-1072 2683271 2687756 2687786 "STRICAT" 2687845 T STRICAT (NIL) -9 NIL 2687907) (-1071 2675985 2680794 2681414 "STREAM" 2682686 NIL STREAM (NIL T) -8 NIL NIL) (-1070 2675495 2675572 2675716 "STREAM3" 2675902 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1069 2674477 2674660 2674895 "STREAM2" 2675308 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1068 2674165 2674217 2674310 "STREAM1" 2674419 NIL STREAM1 (NIL T) -7 NIL NIL) (-1067 2673181 2673362 2673593 "STINPROD" 2673981 NIL STINPROD (NIL T) -7 NIL NIL) (-1066 2672760 2672944 2672974 "STEP" 2673054 T STEP (NIL) -9 NIL 2673132) (-1065 2666303 2672659 2672736 "STBL" 2672741 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1064 2661479 2665526 2665569 "STAGG" 2665722 NIL STAGG (NIL T) -9 NIL 2665811) (-1063 2659181 2659783 2660655 "STAGG-" 2660660 NIL STAGG- (NIL T T) -8 NIL NIL) (-1062 2657376 2658951 2659043 "STACK" 2659124 NIL STACK (NIL T) -8 NIL NIL) (-1061 2650107 2655523 2655978 "SREGSET" 2657006 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1060 2642539 2643907 2645419 "SRDCMPK" 2648713 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1059 2635507 2639980 2640010 "SRAGG" 2641313 T SRAGG (NIL) -9 NIL 2641921) (-1058 2634524 2634779 2635158 "SRAGG-" 2635163 NIL SRAGG- (NIL T) -8 NIL NIL) (-1057 2628973 2633443 2633870 "SQMATRIX" 2634143 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1056 2622725 2625693 2626419 "SPLTREE" 2628319 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1055 2618715 2619381 2620027 "SPLNODE" 2622151 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1054 2617762 2617995 2618025 "SPFCAT" 2618469 T SPFCAT (NIL) -9 NIL NIL) (-1053 2616499 2616709 2616973 "SPECOUT" 2617520 T SPECOUT (NIL) -7 NIL NIL) (-1052 2616260 2616300 2616369 "SPADPRSR" 2616452 T SPADPRSR (NIL) -7 NIL NIL) (-1051 2608283 2610030 2610072 "SPACEC" 2614395 NIL SPACEC (NIL T) -9 NIL 2616211) (-1050 2606454 2608216 2608264 "SPACE3" 2608269 NIL SPACE3 (NIL T) -8 NIL NIL) (-1049 2605206 2605377 2605668 "SORTPAK" 2606259 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1048 2603262 2603565 2603983 "SOLVETRA" 2604870 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1047 2602273 2602495 2602769 "SOLVESER" 2603035 NIL SOLVESER (NIL T) -7 NIL NIL) (-1046 2597493 2598374 2599376 "SOLVERAD" 2601325 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1045 2593308 2593917 2594646 "SOLVEFOR" 2596860 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1044 2587608 2592660 2592756 "SNTSCAT" 2592761 NIL SNTSCAT (NIL T T T T) -9 NIL 2592831) (-1043 2581712 2585939 2586329 "SMTS" 2587298 NIL SMTS (NIL T T T) -8 NIL NIL) (-1042 2576122 2581601 2581677 "SMP" 2581682 NIL SMP (NIL T T) -8 NIL NIL) (-1041 2574281 2574582 2574980 "SMITH" 2575819 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1040 2567246 2571442 2571544 "SMATCAT" 2572884 NIL SMATCAT (NIL NIL T T T) -9 NIL 2573433) (-1039 2564187 2565010 2566187 "SMATCAT-" 2566192 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1038 2561901 2563424 2563467 "SKAGG" 2563728 NIL SKAGG (NIL T) -9 NIL 2563863) (-1037 2557959 2561005 2561283 "SINT" 2561645 T SINT (NIL) -8 NIL NIL) (-1036 2557731 2557769 2557835 "SIMPAN" 2557915 T SIMPAN (NIL) -7 NIL NIL) (-1035 2556569 2556790 2557065 "SIGNRF" 2557490 NIL SIGNRF (NIL T) -7 NIL NIL) (-1034 2555354 2555505 2555795 "SIGNEF" 2556398 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1033 2553044 2553498 2554004 "SHP" 2554895 NIL SHP (NIL T NIL) -7 NIL NIL) (-1032 2546897 2552945 2553021 "SHDP" 2553026 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1031 2546387 2546579 2546609 "SGROUP" 2546761 T SGROUP (NIL) -9 NIL 2546848) (-1030 2546157 2546209 2546313 "SGROUP-" 2546318 NIL SGROUP- (NIL T) -8 NIL NIL) (-1029 2542993 2543690 2544413 "SGCF" 2545456 T SGCF (NIL) -7 NIL NIL) (-1028 2537392 2542444 2542540 "SFRTCAT" 2542545 NIL SFRTCAT (NIL T T T T) -9 NIL 2542583) (-1027 2530852 2531867 2533001 "SFRGCD" 2536375 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1026 2524018 2525089 2526273 "SFQCMPK" 2529785 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1025 2523640 2523729 2523839 "SFORT" 2523959 NIL SFORT (NIL T T) -8 NIL NIL) (-1024 2522785 2523480 2523601 "SEXOF" 2523606 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1023 2521919 2522666 2522734 "SEX" 2522739 T SEX (NIL) -8 NIL NIL) (-1022 2516696 2517385 2517480 "SEXCAT" 2521251 NIL SEXCAT (NIL T T T T T) -9 NIL 2521870) (-1021 2513876 2516630 2516678 "SET" 2516683 NIL SET (NIL T) -8 NIL NIL) (-1020 2512095 2512557 2512862 "SETMN" 2513617 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1019 2511703 2511829 2511859 "SETCAT" 2511976 T SETCAT (NIL) -9 NIL 2512060) (-1018 2511483 2511535 2511634 "SETCAT-" 2511639 NIL SETCAT- (NIL T) -8 NIL NIL) (-1017 2507871 2509945 2509988 "SETAGG" 2510858 NIL SETAGG (NIL T) -9 NIL 2511198) (-1016 2507329 2507445 2507682 "SETAGG-" 2507687 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1015 2506533 2506826 2506887 "SEGXCAT" 2507173 NIL SEGXCAT (NIL T T) -9 NIL 2507293) (-1014 2505589 2506199 2506381 "SEG" 2506386 NIL SEG (NIL T) -8 NIL NIL) (-1013 2504496 2504709 2504752 "SEGCAT" 2505334 NIL SEGCAT (NIL T) -9 NIL 2505572) (-1012 2503545 2503875 2504075 "SEGBIND" 2504331 NIL SEGBIND (NIL T) -8 NIL NIL) (-1011 2503166 2503225 2503338 "SEGBIND2" 2503480 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1010 2502385 2502511 2502715 "SEG2" 2503010 NIL SEG2 (NIL T T) -7 NIL NIL) (-1009 2501822 2502320 2502367 "SDVAR" 2502372 NIL SDVAR (NIL T) -8 NIL NIL) (-1008 2494074 2501595 2501723 "SDPOL" 2501728 NIL SDPOL (NIL T) -8 NIL NIL) (-1007 2492667 2492933 2493252 "SCPKG" 2493789 NIL SCPKG (NIL T) -7 NIL NIL) (-1006 2491804 2491983 2492183 "SCOPE" 2492489 T SCOPE (NIL) -8 NIL NIL) (-1005 2491025 2491158 2491337 "SCACHE" 2491659 NIL SCACHE (NIL T) -7 NIL NIL) (-1004 2490464 2490785 2490870 "SAOS" 2490962 T SAOS (NIL) -8 NIL NIL) (-1003 2490029 2490064 2490237 "SAERFFC" 2490423 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1002 2483923 2489926 2490006 "SAE" 2490011 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1001 2483516 2483551 2483710 "SAEFACT" 2483882 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1000 2481837 2482151 2482552 "RURPK" 2483182 NIL RURPK (NIL T NIL) -7 NIL NIL) (-999 2480490 2480767 2481074 "RULESET" 2481673 NIL RULESET (NIL T T T) -8 NIL NIL) (-998 2477684 2478187 2478648 "RULE" 2480172 NIL RULE (NIL T T T) -8 NIL NIL) (-997 2477321 2477476 2477557 "RULECOLD" 2477636 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-996 2472213 2473007 2473923 "RSETGCD" 2476520 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-995 2461528 2466580 2466674 "RSETCAT" 2470739 NIL RSETCAT (NIL T T T T) -9 NIL 2471836) (-994 2459459 2459998 2460818 "RSETCAT-" 2460823 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-993 2451881 2453256 2454772 "RSDCMPK" 2458058 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-992 2449899 2450340 2450412 "RRCC" 2451488 NIL RRCC (NIL T T) -9 NIL 2451832) (-991 2449253 2449427 2449703 "RRCC-" 2449708 NIL RRCC- (NIL T T T) -8 NIL NIL) (-990 2423620 2433245 2433309 "RPOLCAT" 2443811 NIL RPOLCAT (NIL T T T) -9 NIL 2446969) (-989 2415124 2417462 2420580 "RPOLCAT-" 2420585 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-988 2406190 2413354 2413834 "ROUTINE" 2414664 T ROUTINE (NIL) -8 NIL NIL) (-987 2402895 2405746 2405893 "ROMAN" 2406063 T ROMAN (NIL) -8 NIL NIL) (-986 2401181 2401766 2402023 "ROIRC" 2402701 NIL ROIRC (NIL T T) -8 NIL NIL) (-985 2397586 2399890 2399918 "RNS" 2400214 T RNS (NIL) -9 NIL 2400484) (-984 2396100 2396483 2397014 "RNS-" 2397087 NIL RNS- (NIL T) -8 NIL NIL) (-983 2395526 2395934 2395962 "RNG" 2395967 T RNG (NIL) -9 NIL 2395988) (-982 2394924 2395286 2395326 "RMODULE" 2395386 NIL RMODULE (NIL T) -9 NIL 2395428) (-981 2393776 2393870 2394200 "RMCAT2" 2394825 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-980 2390490 2392959 2393280 "RMATRIX" 2393511 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-979 2383487 2385721 2385833 "RMATCAT" 2389142 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2390124) (-978 2382866 2383013 2383316 "RMATCAT-" 2383321 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-977 2382436 2382511 2382637 "RINTERP" 2382785 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-976 2381487 2382051 2382079 "RING" 2382189 T RING (NIL) -9 NIL 2382283) (-975 2381282 2381326 2381420 "RING-" 2381425 NIL RING- (NIL T) -8 NIL NIL) (-974 2380130 2380367 2380623 "RIDIST" 2381046 T RIDIST (NIL) -7 NIL NIL) (-973 2371452 2379604 2379807 "RGCHAIN" 2379979 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-972 2368457 2369071 2369739 "RF" 2370816 NIL RF (NIL T) -7 NIL NIL) (-971 2368106 2368169 2368270 "RFFACTOR" 2368388 NIL RFFACTOR (NIL T) -7 NIL NIL) (-970 2367834 2367869 2367964 "RFFACT" 2368065 NIL RFFACT (NIL T) -7 NIL NIL) (-969 2365964 2366328 2366708 "RFDIST" 2367474 T RFDIST (NIL) -7 NIL NIL) (-968 2365422 2365514 2365674 "RETSOL" 2365866 NIL RETSOL (NIL T T) -7 NIL NIL) (-967 2365015 2365095 2365136 "RETRACT" 2365326 NIL RETRACT (NIL T) -9 NIL NIL) (-966 2364867 2364892 2364976 "RETRACT-" 2364981 NIL RETRACT- (NIL T T) -8 NIL NIL) (-965 2357725 2364524 2364649 "RESULT" 2364762 T RESULT (NIL) -8 NIL NIL) (-964 2356310 2356999 2357196 "RESRING" 2357628 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-963 2355950 2355999 2356095 "RESLATC" 2356247 NIL RESLATC (NIL T) -7 NIL NIL) (-962 2355659 2355693 2355798 "REPSQ" 2355909 NIL REPSQ (NIL T) -7 NIL NIL) (-961 2353090 2353670 2354270 "REP" 2355079 T REP (NIL) -7 NIL NIL) (-960 2352791 2352825 2352934 "REPDB" 2353049 NIL REPDB (NIL T) -7 NIL NIL) (-959 2346736 2348115 2349335 "REP2" 2351603 NIL REP2 (NIL T) -7 NIL NIL) (-958 2343142 2343823 2344628 "REP1" 2345963 NIL REP1 (NIL T) -7 NIL NIL) (-957 2335888 2341303 2341755 "REGSET" 2342773 NIL REGSET (NIL T T T T) -8 NIL NIL) (-956 2334709 2335044 2335292 "REF" 2335673 NIL REF (NIL T) -8 NIL NIL) (-955 2334090 2334193 2334358 "REDORDER" 2334593 NIL REDORDER (NIL T T) -7 NIL NIL) (-954 2330059 2333324 2333545 "RECLOS" 2333921 NIL RECLOS (NIL T) -8 NIL NIL) (-953 2329116 2329297 2329510 "REALSOLV" 2329866 T REALSOLV (NIL) -7 NIL NIL) (-952 2328964 2329005 2329033 "REAL" 2329038 T REAL (NIL) -9 NIL 2329073) (-951 2325400 2326202 2327084 "REAL0Q" 2328129 NIL REAL0Q (NIL T) -7 NIL NIL) (-950 2321011 2321999 2323058 "REAL0" 2324381 NIL REAL0 (NIL T) -7 NIL NIL) (-949 2320419 2320491 2320696 "RDIV" 2320933 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-948 2319492 2319666 2319877 "RDIST" 2320241 NIL RDIST (NIL T) -7 NIL NIL) (-947 2318096 2318383 2318752 "RDETRS" 2319200 NIL RDETRS (NIL T T) -7 NIL NIL) (-946 2315909 2316363 2316898 "RDETR" 2317638 NIL RDETR (NIL T T) -7 NIL NIL) (-945 2314517 2314795 2315196 "RDEEFS" 2315625 NIL RDEEFS (NIL T T) -7 NIL NIL) (-944 2313009 2313315 2313744 "RDEEF" 2314205 NIL RDEEF (NIL T T) -7 NIL NIL) (-943 2307294 2310226 2310254 "RCFIELD" 2311531 T RCFIELD (NIL) -9 NIL 2312261) (-942 2305363 2305867 2306560 "RCFIELD-" 2306633 NIL RCFIELD- (NIL T) -8 NIL NIL) (-941 2301695 2303480 2303521 "RCAGG" 2304592 NIL RCAGG (NIL T) -9 NIL 2305057) (-940 2301326 2301420 2301580 "RCAGG-" 2301585 NIL RCAGG- (NIL T T) -8 NIL NIL) (-939 2300648 2300760 2300922 "RATRET" 2301210 NIL RATRET (NIL T) -7 NIL NIL) (-938 2300205 2300272 2300391 "RATFACT" 2300576 NIL RATFACT (NIL T) -7 NIL NIL) (-937 2299520 2299640 2299790 "RANDSRC" 2300075 T RANDSRC (NIL) -7 NIL NIL) (-936 2299257 2299301 2299372 "RADUTIL" 2299469 T RADUTIL (NIL) -7 NIL NIL) (-935 2292264 2298000 2298317 "RADIX" 2298972 NIL RADIX (NIL NIL) -8 NIL NIL) (-934 2283834 2292108 2292236 "RADFF" 2292241 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-933 2283486 2283561 2283589 "RADCAT" 2283746 T RADCAT (NIL) -9 NIL NIL) (-932 2283271 2283319 2283416 "RADCAT-" 2283421 NIL RADCAT- (NIL T) -8 NIL NIL) (-931 2281422 2283046 2283135 "QUEUE" 2283215 NIL QUEUE (NIL T) -8 NIL NIL) (-930 2277919 2281359 2281404 "QUAT" 2281409 NIL QUAT (NIL T) -8 NIL NIL) (-929 2277557 2277600 2277727 "QUATCT2" 2277870 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-928 2271351 2274731 2274771 "QUATCAT" 2275550 NIL QUATCAT (NIL T) -9 NIL 2276315) (-927 2267495 2268532 2269919 "QUATCAT-" 2270013 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-926 2265016 2266580 2266621 "QUAGG" 2266996 NIL QUAGG (NIL T) -9 NIL 2267171) (-925 2263941 2264414 2264586 "QFORM" 2264888 NIL QFORM (NIL NIL T) -8 NIL NIL) (-924 2255238 2260496 2260536 "QFCAT" 2261194 NIL QFCAT (NIL T) -9 NIL 2262187) (-923 2250810 2252011 2253602 "QFCAT-" 2253696 NIL QFCAT- (NIL T T) -8 NIL NIL) (-922 2250448 2250491 2250618 "QFCAT2" 2250761 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-921 2249908 2250018 2250148 "QEQUAT" 2250338 T QEQUAT (NIL) -8 NIL NIL) (-920 2243094 2244165 2245347 "QCMPACK" 2248841 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-919 2240670 2241091 2241519 "QALGSET" 2242749 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-918 2239915 2240089 2240321 "QALGSET2" 2240490 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-917 2238606 2238829 2239146 "PWFFINTB" 2239688 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-916 2236794 2236962 2237315 "PUSHVAR" 2238420 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-915 2232712 2233766 2233807 "PTRANFN" 2235691 NIL PTRANFN (NIL T) -9 NIL NIL) (-914 2231124 2231415 2231736 "PTPACK" 2232423 NIL PTPACK (NIL T) -7 NIL NIL) (-913 2230760 2230817 2230924 "PTFUNC2" 2231061 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-912 2225237 2229578 2229618 "PTCAT" 2229986 NIL PTCAT (NIL T) -9 NIL 2230148) (-911 2224895 2224930 2225054 "PSQFR" 2225196 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-910 2223490 2223788 2224122 "PSEUDLIN" 2224593 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-909 2210297 2212662 2214985 "PSETPK" 2221250 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-908 2203384 2206098 2206192 "PSETCAT" 2209173 NIL PSETCAT (NIL T T T T) -9 NIL 2209987) (-907 2201222 2201856 2202675 "PSETCAT-" 2202680 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-906 2200571 2200736 2200764 "PSCURVE" 2201032 T PSCURVE (NIL) -9 NIL 2201199) (-905 2197023 2198549 2198613 "PSCAT" 2199449 NIL PSCAT (NIL T T T) -9 NIL 2199689) (-904 2196087 2196303 2196702 "PSCAT-" 2196707 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-903 2194739 2195372 2195586 "PRTITION" 2195893 T PRTITION (NIL) -8 NIL NIL) (-902 2183837 2186043 2188231 "PRS" 2192601 NIL PRS (NIL T T) -7 NIL NIL) (-901 2181696 2183188 2183228 "PRQAGG" 2183411 NIL PRQAGG (NIL T) -9 NIL 2183513) (-900 2181267 2181369 2181397 "PROPLOG" 2181582 T PROPLOG (NIL) -9 NIL NIL) (-899 2178390 2178955 2179482 "PROPFRML" 2180772 NIL PROPFRML (NIL T) -8 NIL NIL) (-898 2177850 2177960 2178090 "PROPERTY" 2178280 T PROPERTY (NIL) -8 NIL NIL) (-897 2171624 2176016 2176836 "PRODUCT" 2177076 NIL PRODUCT (NIL T T) -8 NIL NIL) (-896 2168900 2171084 2171317 "PR" 2171435 NIL PR (NIL T T) -8 NIL NIL) (-895 2168696 2168728 2168787 "PRINT" 2168861 T PRINT (NIL) -7 NIL NIL) (-894 2168036 2168153 2168305 "PRIMES" 2168576 NIL PRIMES (NIL T) -7 NIL NIL) (-893 2166101 2166502 2166968 "PRIMELT" 2167615 NIL PRIMELT (NIL T) -7 NIL NIL) (-892 2165830 2165879 2165907 "PRIMCAT" 2166031 T PRIMCAT (NIL) -9 NIL NIL) (-891 2161991 2165768 2165813 "PRIMARR" 2165818 NIL PRIMARR (NIL T) -8 NIL NIL) (-890 2160998 2161176 2161404 "PRIMARR2" 2161809 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-889 2160641 2160697 2160808 "PREASSOC" 2160936 NIL PREASSOC (NIL T T) -7 NIL NIL) (-888 2160116 2160249 2160277 "PPCURVE" 2160482 T PPCURVE (NIL) -9 NIL 2160618) (-887 2157475 2157874 2158466 "POLYROOT" 2159697 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-886 2151381 2157081 2157240 "POLY" 2157348 NIL POLY (NIL T) -8 NIL NIL) (-885 2150766 2150824 2151057 "POLYLIFT" 2151317 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-884 2147051 2147500 2148128 "POLYCATQ" 2150311 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-883 2134092 2139489 2139553 "POLYCAT" 2143038 NIL POLYCAT (NIL T T T) -9 NIL 2144965) (-882 2127543 2129404 2131787 "POLYCAT-" 2131792 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-881 2127132 2127200 2127319 "POLY2UP" 2127469 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-880 2126768 2126825 2126932 "POLY2" 2127069 NIL POLY2 (NIL T T) -7 NIL NIL) (-879 2125453 2125692 2125968 "POLUTIL" 2126542 NIL POLUTIL (NIL T T) -7 NIL NIL) (-878 2123815 2124092 2124422 "POLTOPOL" 2125175 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-877 2119338 2123752 2123797 "POINT" 2123802 NIL POINT (NIL T) -8 NIL NIL) (-876 2117525 2117882 2118257 "PNTHEORY" 2118983 T PNTHEORY (NIL) -7 NIL NIL) (-875 2115953 2116250 2116659 "PMTOOLS" 2117223 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-874 2115546 2115624 2115741 "PMSYM" 2115869 NIL PMSYM (NIL T) -7 NIL NIL) (-873 2115049 2115118 2115292 "PMQFCAT" 2115471 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-872 2114404 2114514 2114670 "PMPRED" 2114926 NIL PMPRED (NIL T) -7 NIL NIL) (-871 2113800 2113886 2114047 "PMPREDFS" 2114305 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-870 2112432 2112640 2113024 "PMPLCAT" 2113562 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-869 2111964 2112043 2112195 "PMLSAGG" 2112347 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-868 2111434 2111510 2111690 "PMKERNEL" 2111882 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-867 2111051 2111126 2111239 "PMINS" 2111353 NIL PMINS (NIL T) -7 NIL NIL) (-866 2110474 2110543 2110758 "PMFS" 2110976 NIL PMFS (NIL T T T) -7 NIL NIL) (-865 2109705 2109823 2110027 "PMDOWN" 2110351 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-864 2108868 2109027 2109209 "PMASS" 2109543 T PMASS (NIL) -7 NIL NIL) (-863 2108142 2108253 2108416 "PMASSFS" 2108754 NIL PMASSFS (NIL T T) -7 NIL NIL) (-862 2107797 2107865 2107959 "PLOTTOOL" 2108068 T PLOTTOOL (NIL) -7 NIL NIL) (-861 2102419 2103608 2104756 "PLOT" 2106669 T PLOT (NIL) -8 NIL NIL) (-860 2098233 2099267 2100188 "PLOT3D" 2101518 T PLOT3D (NIL) -8 NIL NIL) (-859 2097145 2097322 2097557 "PLOT1" 2098037 NIL PLOT1 (NIL T) -7 NIL NIL) (-858 2072539 2077211 2082062 "PLEQN" 2092411 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-857 2071857 2071979 2072159 "PINTERP" 2072404 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-856 2071550 2071597 2071700 "PINTERPA" 2071804 NIL PINTERPA (NIL T T) -7 NIL NIL) (-855 2070789 2071356 2071443 "PI" 2071483 T PI (NIL) -8 NIL NIL) (-854 2069181 2070166 2070194 "PID" 2070376 T PID (NIL) -9 NIL 2070510) (-853 2068906 2068943 2069031 "PICOERCE" 2069138 NIL PICOERCE (NIL T) -7 NIL NIL) (-852 2068226 2068365 2068541 "PGROEB" 2068762 NIL PGROEB (NIL T) -7 NIL NIL) (-851 2063813 2064627 2065532 "PGE" 2067341 T PGE (NIL) -7 NIL NIL) (-850 2061937 2062183 2062549 "PGCD" 2063530 NIL PGCD (NIL T T T T) -7 NIL NIL) (-849 2061275 2061378 2061539 "PFRPAC" 2061821 NIL PFRPAC (NIL T) -7 NIL NIL) (-848 2057890 2059823 2060176 "PFR" 2060954 NIL PFR (NIL T) -8 NIL NIL) (-847 2056263 2056507 2056832 "PFOTOOLS" 2057637 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-846 2054796 2055035 2055386 "PFOQ" 2056020 NIL PFOQ (NIL T T T) -7 NIL NIL) (-845 2053273 2053485 2053847 "PFO" 2054580 NIL PFO (NIL T T T T T) -7 NIL NIL) (-844 2049796 2053162 2053231 "PF" 2053236 NIL PF (NIL NIL) -8 NIL NIL) (-843 2047225 2048506 2048534 "PFECAT" 2049119 T PFECAT (NIL) -9 NIL 2049503) (-842 2046670 2046824 2047038 "PFECAT-" 2047043 NIL PFECAT- (NIL T) -8 NIL NIL) (-841 2045274 2045525 2045826 "PFBRU" 2046419 NIL PFBRU (NIL T T) -7 NIL NIL) (-840 2043141 2043492 2043924 "PFBR" 2044925 NIL PFBR (NIL T T T T) -7 NIL NIL) (-839 2038992 2040517 2041193 "PERM" 2042498 NIL PERM (NIL T) -8 NIL NIL) (-838 2034257 2035199 2036069 "PERMGRP" 2038155 NIL PERMGRP (NIL T) -8 NIL NIL) (-837 2032328 2033321 2033362 "PERMCAT" 2033808 NIL PERMCAT (NIL T) -9 NIL 2034113) (-836 2031983 2032024 2032147 "PERMAN" 2032281 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-835 2029423 2031552 2031683 "PENDTREE" 2031885 NIL PENDTREE (NIL T) -8 NIL NIL) (-834 2027496 2028274 2028315 "PDRING" 2028972 NIL PDRING (NIL T) -9 NIL 2029257) (-833 2026599 2026817 2027179 "PDRING-" 2027184 NIL PDRING- (NIL T T) -8 NIL NIL) (-832 2023740 2024491 2025182 "PDEPROB" 2025928 T PDEPROB (NIL) -8 NIL NIL) (-831 2021303 2021799 2022348 "PDEPACK" 2023211 T PDEPACK (NIL) -7 NIL NIL) (-830 2020215 2020405 2020656 "PDECOMP" 2021102 NIL PDECOMP (NIL T T) -7 NIL NIL) (-829 2017827 2018642 2018670 "PDECAT" 2019455 T PDECAT (NIL) -9 NIL 2020166) (-828 2017580 2017613 2017702 "PCOMP" 2017788 NIL PCOMP (NIL T T) -7 NIL NIL) (-827 2015787 2016383 2016679 "PBWLB" 2017310 NIL PBWLB (NIL T) -8 NIL NIL) (-826 2008295 2009864 2011200 "PATTERN" 2014472 NIL PATTERN (NIL T) -8 NIL NIL) (-825 2007927 2007984 2008093 "PATTERN2" 2008232 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-824 2005684 2006072 2006529 "PATTERN1" 2007516 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-823 2003079 2003633 2004114 "PATRES" 2005249 NIL PATRES (NIL T T) -8 NIL NIL) (-822 2002643 2002710 2002842 "PATRES2" 2003006 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-821 2000540 2000940 2001345 "PATMATCH" 2002312 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-820 2000077 2000260 2000301 "PATMAB" 2000408 NIL PATMAB (NIL T) -9 NIL 2000491) (-819 1998622 1998931 1999189 "PATLRES" 1999882 NIL PATLRES (NIL T T T) -8 NIL NIL) (-818 1998168 1998291 1998332 "PATAB" 1998337 NIL PATAB (NIL T) -9 NIL 1998509) (-817 1995649 1996181 1996754 "PARTPERM" 1997615 T PARTPERM (NIL) -7 NIL NIL) (-816 1995270 1995333 1995435 "PARSURF" 1995580 NIL PARSURF (NIL T) -8 NIL NIL) (-815 1994902 1994959 1995068 "PARSU2" 1995207 NIL PARSU2 (NIL T T) -7 NIL NIL) (-814 1994666 1994706 1994773 "PARSER" 1994855 T PARSER (NIL) -7 NIL NIL) (-813 1994287 1994350 1994452 "PARSCURV" 1994597 NIL PARSCURV (NIL T) -8 NIL NIL) (-812 1993919 1993976 1994085 "PARSC2" 1994224 NIL PARSC2 (NIL T T) -7 NIL NIL) (-811 1993558 1993616 1993713 "PARPCURV" 1993855 NIL PARPCURV (NIL T) -8 NIL NIL) (-810 1993190 1993247 1993356 "PARPC2" 1993495 NIL PARPC2 (NIL T T) -7 NIL NIL) (-809 1992710 1992796 1992915 "PAN2EXPR" 1993091 T PAN2EXPR (NIL) -7 NIL NIL) (-808 1991516 1991831 1992059 "PALETTE" 1992502 T PALETTE (NIL) -8 NIL NIL) (-807 1989984 1990521 1990881 "PAIR" 1991202 NIL PAIR (NIL T T) -8 NIL NIL) (-806 1983826 1989235 1989429 "PADICRC" 1989839 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-805 1977026 1983164 1983348 "PADICRAT" 1983674 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-804 1975330 1976963 1977008 "PADIC" 1977013 NIL PADIC (NIL NIL) -8 NIL NIL) (-803 1972535 1974109 1974149 "PADICCT" 1974730 NIL PADICCT (NIL NIL) -9 NIL 1975012) (-802 1971492 1971692 1971960 "PADEPAC" 1972322 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-801 1970704 1970837 1971043 "PADE" 1971354 NIL PADE (NIL T T T) -7 NIL NIL) (-800 1968707 1969539 1969854 "OWP" 1970472 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-799 1967811 1968307 1968479 "OVAR" 1968575 NIL OVAR (NIL NIL) -8 NIL NIL) (-798 1967075 1967196 1967357 "OUT" 1967670 T OUT (NIL) -7 NIL NIL) (-797 1956129 1958300 1960470 "OUTFORM" 1964925 T OUTFORM (NIL) -8 NIL NIL) (-796 1955537 1955858 1955947 "OSI" 1956060 T OSI (NIL) -8 NIL NIL) (-795 1954282 1954509 1954794 "ORTHPOL" 1955284 NIL ORTHPOL (NIL T) -7 NIL NIL) (-794 1951653 1953943 1954081 "OREUP" 1954225 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-793 1949049 1951346 1951472 "ORESUP" 1951595 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-792 1946584 1947084 1947644 "OREPCTO" 1948538 NIL OREPCTO (NIL T T) -7 NIL NIL) (-791 1940494 1942700 1942740 "OREPCAT" 1945061 NIL OREPCAT (NIL T) -9 NIL 1946164) (-790 1937642 1938424 1939481 "OREPCAT-" 1939486 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-789 1936820 1937092 1937120 "ORDSET" 1937429 T ORDSET (NIL) -9 NIL 1937593) (-788 1936339 1936461 1936654 "ORDSET-" 1936659 NIL ORDSET- (NIL T) -8 NIL NIL) (-787 1934953 1935754 1935782 "ORDRING" 1935984 T ORDRING (NIL) -9 NIL 1936108) (-786 1934598 1934692 1934836 "ORDRING-" 1934841 NIL ORDRING- (NIL T) -8 NIL NIL) (-785 1933974 1934455 1934483 "ORDMON" 1934488 T ORDMON (NIL) -9 NIL 1934509) (-784 1933136 1933283 1933478 "ORDFUNS" 1933823 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-783 1932648 1933007 1933035 "ORDFIN" 1933040 T ORDFIN (NIL) -9 NIL 1933061) (-782 1929160 1931234 1931643 "ORDCOMP" 1932272 NIL ORDCOMP (NIL T) -8 NIL NIL) (-781 1928426 1928553 1928739 "ORDCOMP2" 1929020 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-780 1924933 1925816 1926653 "OPTPROB" 1927609 T OPTPROB (NIL) -8 NIL NIL) (-779 1921775 1922404 1923098 "OPTPACK" 1924259 T OPTPACK (NIL) -7 NIL NIL) (-778 1919501 1920237 1920265 "OPTCAT" 1921080 T OPTCAT (NIL) -9 NIL 1921726) (-777 1919269 1919308 1919374 "OPQUERY" 1919455 T OPQUERY (NIL) -7 NIL NIL) (-776 1916405 1917596 1918096 "OP" 1918801 NIL OP (NIL T) -8 NIL NIL) (-775 1913170 1915202 1915571 "ONECOMP" 1916069 NIL ONECOMP (NIL T) -8 NIL NIL) (-774 1912475 1912590 1912764 "ONECOMP2" 1913042 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-773 1911894 1912000 1912130 "OMSERVER" 1912365 T OMSERVER (NIL) -7 NIL NIL) (-772 1908783 1911335 1911375 "OMSAGG" 1911436 NIL OMSAGG (NIL T) -9 NIL 1911500) (-771 1907406 1907669 1907951 "OMPKG" 1908521 T OMPKG (NIL) -7 NIL NIL) (-770 1906836 1906939 1906967 "OM" 1907266 T OM (NIL) -9 NIL NIL) (-769 1905375 1906388 1906556 "OMLO" 1906717 NIL OMLO (NIL T T) -8 NIL NIL) (-768 1904305 1904452 1904678 "OMEXPR" 1905201 NIL OMEXPR (NIL T) -7 NIL NIL) (-767 1903623 1903851 1903987 "OMERR" 1904189 T OMERR (NIL) -8 NIL NIL) (-766 1902801 1903044 1903204 "OMERRK" 1903483 T OMERRK (NIL) -8 NIL NIL) (-765 1902279 1902478 1902586 "OMENC" 1902713 T OMENC (NIL) -8 NIL NIL) (-764 1896174 1897359 1898530 "OMDEV" 1901128 T OMDEV (NIL) -8 NIL NIL) (-763 1895243 1895414 1895608 "OMCONN" 1896000 T OMCONN (NIL) -8 NIL NIL) (-762 1893859 1894845 1894873 "OINTDOM" 1894878 T OINTDOM (NIL) -9 NIL 1894899) (-761 1889621 1890851 1891566 "OFMONOID" 1893176 NIL OFMONOID (NIL T) -8 NIL NIL) (-760 1889059 1889558 1889603 "ODVAR" 1889608 NIL ODVAR (NIL T) -8 NIL NIL) (-759 1886184 1888556 1888741 "ODR" 1888934 NIL ODR (NIL T T NIL) -8 NIL NIL) (-758 1878490 1885963 1886087 "ODPOL" 1886092 NIL ODPOL (NIL T) -8 NIL NIL) (-757 1872313 1878362 1878467 "ODP" 1878472 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-756 1871079 1871294 1871569 "ODETOOLS" 1872087 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-755 1868048 1868704 1869420 "ODESYS" 1870412 NIL ODESYS (NIL T T) -7 NIL NIL) (-754 1862952 1863860 1864883 "ODERTRIC" 1867123 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-753 1862378 1862460 1862654 "ODERED" 1862864 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-752 1859280 1859828 1860503 "ODERAT" 1861801 NIL ODERAT (NIL T T) -7 NIL NIL) (-751 1856241 1856705 1857301 "ODEPRRIC" 1858809 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-750 1854110 1854679 1855188 "ODEPROB" 1855752 T ODEPROB (NIL) -8 NIL NIL) (-749 1850635 1851118 1851764 "ODEPRIM" 1853589 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-748 1849888 1849990 1850248 "ODEPAL" 1850527 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-747 1846066 1846847 1847701 "ODEPACK" 1849054 T ODEPACK (NIL) -7 NIL NIL) (-746 1845103 1845210 1845438 "ODEINT" 1845955 NIL ODEINT (NIL T T) -7 NIL NIL) (-745 1839204 1840629 1842076 "ODEIFTBL" 1843676 T ODEIFTBL (NIL) -8 NIL NIL) (-744 1834548 1835334 1836292 "ODEEF" 1838363 NIL ODEEF (NIL T T) -7 NIL NIL) (-743 1833885 1833974 1834203 "ODECONST" 1834453 NIL ODECONST (NIL T T T) -7 NIL NIL) (-742 1832043 1832676 1832704 "ODECAT" 1833307 T ODECAT (NIL) -9 NIL 1833836) (-741 1828915 1831755 1831874 "OCT" 1831956 NIL OCT (NIL T) -8 NIL NIL) (-740 1828553 1828596 1828723 "OCTCT2" 1828866 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-739 1823387 1825825 1825865 "OC" 1826961 NIL OC (NIL T) -9 NIL 1827818) (-738 1820614 1821362 1822352 "OC-" 1822446 NIL OC- (NIL T T) -8 NIL NIL) (-737 1819993 1820435 1820463 "OCAMON" 1820468 T OCAMON (NIL) -9 NIL 1820489) (-736 1819551 1819866 1819894 "OASGP" 1819899 T OASGP (NIL) -9 NIL 1819919) (-735 1818839 1819302 1819330 "OAMONS" 1819370 T OAMONS (NIL) -9 NIL 1819413) (-734 1818280 1818687 1818715 "OAMON" 1818720 T OAMON (NIL) -9 NIL 1818740) (-733 1817585 1818077 1818105 "OAGROUP" 1818110 T OAGROUP (NIL) -9 NIL 1818130) (-732 1817275 1817325 1817413 "NUMTUBE" 1817529 NIL NUMTUBE (NIL T) -7 NIL NIL) (-731 1810848 1812366 1813902 "NUMQUAD" 1815759 T NUMQUAD (NIL) -7 NIL NIL) (-730 1806556 1807544 1808569 "NUMODE" 1809843 T NUMODE (NIL) -7 NIL NIL) (-729 1803960 1804806 1804834 "NUMINT" 1805751 T NUMINT (NIL) -9 NIL 1806507) (-728 1802908 1803105 1803323 "NUMFMT" 1803762 T NUMFMT (NIL) -7 NIL NIL) (-727 1789231 1792168 1794698 "NUMERIC" 1800417 NIL NUMERIC (NIL T) -7 NIL NIL) (-726 1783632 1788684 1788778 "NTSCAT" 1788783 NIL NTSCAT (NIL T T T T) -9 NIL 1788821) (-725 1782826 1782991 1783184 "NTPOLFN" 1783471 NIL NTPOLFN (NIL T) -7 NIL NIL) (-724 1770642 1779668 1780478 "NSUP" 1782048 NIL NSUP (NIL T) -8 NIL NIL) (-723 1770278 1770335 1770442 "NSUP2" 1770579 NIL NSUP2 (NIL T T) -7 NIL NIL) (-722 1760240 1770057 1770187 "NSMP" 1770192 NIL NSMP (NIL T T) -8 NIL NIL) (-721 1758672 1758973 1759330 "NREP" 1759928 NIL NREP (NIL T) -7 NIL NIL) (-720 1757263 1757515 1757873 "NPCOEF" 1758415 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-719 1756329 1756444 1756660 "NORMRETR" 1757144 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-718 1754382 1754672 1755079 "NORMPK" 1756037 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-717 1754067 1754095 1754219 "NORMMA" 1754348 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-716 1753894 1754024 1754053 "NONE" 1754058 T NONE (NIL) -8 NIL NIL) (-715 1753683 1753712 1753781 "NONE1" 1753858 NIL NONE1 (NIL T) -7 NIL NIL) (-714 1753168 1753230 1753415 "NODE1" 1753615 NIL NODE1 (NIL T T) -7 NIL NIL) (-713 1751461 1752331 1752586 "NNI" 1752933 T NNI (NIL) -8 NIL NIL) (-712 1749881 1750194 1750558 "NLINSOL" 1751129 NIL NLINSOL (NIL T) -7 NIL NIL) (-711 1746048 1747016 1747938 "NIPROB" 1748979 T NIPROB (NIL) -8 NIL NIL) (-710 1744777 1745011 1745313 "NFINTBAS" 1745810 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-709 1743485 1743716 1743997 "NCODIV" 1744545 NIL NCODIV (NIL T T) -7 NIL NIL) (-708 1743247 1743284 1743359 "NCNTFRAC" 1743442 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-707 1741427 1741791 1742211 "NCEP" 1742872 NIL NCEP (NIL T) -7 NIL NIL) (-706 1740339 1741078 1741106 "NASRING" 1741216 T NASRING (NIL) -9 NIL 1741290) (-705 1740134 1740178 1740272 "NASRING-" 1740277 NIL NASRING- (NIL T) -8 NIL NIL) (-704 1739288 1739787 1739815 "NARNG" 1739932 T NARNG (NIL) -9 NIL 1740023) (-703 1738980 1739047 1739181 "NARNG-" 1739186 NIL NARNG- (NIL T) -8 NIL NIL) (-702 1737859 1738066 1738301 "NAGSP" 1738765 T NAGSP (NIL) -7 NIL NIL) (-701 1729283 1730929 1732564 "NAGS" 1736244 T NAGS (NIL) -7 NIL NIL) (-700 1727847 1728151 1728478 "NAGF07" 1728976 T NAGF07 (NIL) -7 NIL NIL) (-699 1722429 1723709 1725005 "NAGF04" 1726571 T NAGF04 (NIL) -7 NIL NIL) (-698 1715461 1717059 1718676 "NAGF02" 1720832 T NAGF02 (NIL) -7 NIL NIL) (-697 1710725 1711815 1712922 "NAGF01" 1714374 T NAGF01 (NIL) -7 NIL NIL) (-696 1704385 1705943 1707520 "NAGE04" 1709168 T NAGE04 (NIL) -7 NIL NIL) (-695 1695626 1697729 1699841 "NAGE02" 1702293 T NAGE02 (NIL) -7 NIL NIL) (-694 1691619 1692556 1693510 "NAGE01" 1694692 T NAGE01 (NIL) -7 NIL NIL) (-693 1689426 1689957 1690512 "NAGD03" 1691084 T NAGD03 (NIL) -7 NIL NIL) (-692 1681212 1683131 1685076 "NAGD02" 1687501 T NAGD02 (NIL) -7 NIL NIL) (-691 1675071 1676484 1677912 "NAGD01" 1679804 T NAGD01 (NIL) -7 NIL NIL) (-690 1671328 1672138 1672963 "NAGC06" 1674266 T NAGC06 (NIL) -7 NIL NIL) (-689 1669805 1670134 1670487 "NAGC05" 1670995 T NAGC05 (NIL) -7 NIL NIL) (-688 1669189 1669306 1669448 "NAGC02" 1669683 T NAGC02 (NIL) -7 NIL NIL) (-687 1668251 1668808 1668848 "NAALG" 1668927 NIL NAALG (NIL T) -9 NIL 1668988) (-686 1668086 1668115 1668205 "NAALG-" 1668210 NIL NAALG- (NIL T T) -8 NIL NIL) (-685 1662036 1663144 1664331 "MULTSQFR" 1666982 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-684 1661355 1661430 1661614 "MULTFACT" 1661948 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-683 1654549 1658460 1658512 "MTSCAT" 1659572 NIL MTSCAT (NIL T T) -9 NIL 1660086) (-682 1654261 1654315 1654407 "MTHING" 1654489 NIL MTHING (NIL T) -7 NIL NIL) (-681 1654053 1654086 1654146 "MSYSCMD" 1654221 T MSYSCMD (NIL) -7 NIL NIL) (-680 1650165 1652808 1653128 "MSET" 1653766 NIL MSET (NIL T) -8 NIL NIL) (-679 1647261 1649727 1649768 "MSETAGG" 1649773 NIL MSETAGG (NIL T) -9 NIL 1649807) (-678 1643117 1644659 1645400 "MRING" 1646564 NIL MRING (NIL T T) -8 NIL NIL) (-677 1642687 1642754 1642883 "MRF2" 1643044 NIL MRF2 (NIL T T T) -7 NIL NIL) (-676 1642305 1642340 1642484 "MRATFAC" 1642646 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-675 1639903 1640198 1640629 "MPRFF" 1642010 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-674 1633923 1639758 1639854 "MPOLY" 1639859 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-673 1633413 1633448 1633656 "MPCPF" 1633882 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-672 1632929 1632972 1633155 "MPC3" 1633364 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-671 1632130 1632211 1632430 "MPC2" 1632844 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-670 1630431 1630768 1631158 "MONOTOOL" 1631790 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-669 1629556 1629891 1629919 "MONOID" 1630196 T MONOID (NIL) -9 NIL 1630368) (-668 1628934 1629097 1629340 "MONOID-" 1629345 NIL MONOID- (NIL T) -8 NIL NIL) (-667 1619915 1625901 1625960 "MONOGEN" 1626634 NIL MONOGEN (NIL T T) -9 NIL 1627090) (-666 1617133 1617868 1618868 "MONOGEN-" 1618987 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-665 1615993 1616413 1616441 "MONADWU" 1616833 T MONADWU (NIL) -9 NIL 1617071) (-664 1615365 1615524 1615772 "MONADWU-" 1615777 NIL MONADWU- (NIL T) -8 NIL NIL) (-663 1614751 1614969 1614997 "MONAD" 1615204 T MONAD (NIL) -9 NIL 1615316) (-662 1614436 1614514 1614646 "MONAD-" 1614651 NIL MONAD- (NIL T) -8 NIL NIL) (-661 1612687 1613349 1613628 "MOEBIUS" 1614189 NIL MOEBIUS (NIL T) -8 NIL NIL) (-660 1612081 1612459 1612499 "MODULE" 1612504 NIL MODULE (NIL T) -9 NIL 1612530) (-659 1611649 1611745 1611935 "MODULE-" 1611940 NIL MODULE- (NIL T T) -8 NIL NIL) (-658 1609320 1610015 1610341 "MODRING" 1611474 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-657 1606276 1607441 1607958 "MODOP" 1608852 NIL MODOP (NIL T T) -8 NIL NIL) (-656 1604335 1604787 1605128 "MODMONOM" 1606075 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-655 1594014 1602539 1602961 "MODMON" 1603963 NIL MODMON (NIL T T) -8 NIL NIL) (-654 1591140 1592858 1593134 "MODFIELD" 1593889 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-653 1590144 1590421 1590611 "MMLFORM" 1590970 T MMLFORM (NIL) -8 NIL NIL) (-652 1589670 1589713 1589892 "MMAP" 1590095 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-651 1587907 1588684 1588724 "MLO" 1589141 NIL MLO (NIL T) -9 NIL 1589382) (-650 1585274 1585789 1586391 "MLIFT" 1587388 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-649 1584665 1584749 1584903 "MKUCFUNC" 1585185 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-648 1584264 1584334 1584457 "MKRECORD" 1584588 NIL MKRECORD (NIL T T) -7 NIL NIL) (-647 1583312 1583473 1583701 "MKFUNC" 1584075 NIL MKFUNC (NIL T) -7 NIL NIL) (-646 1582700 1582804 1582960 "MKFLCFN" 1583195 NIL MKFLCFN (NIL T) -7 NIL NIL) (-645 1582126 1582493 1582582 "MKCHSET" 1582644 NIL MKCHSET (NIL T) -8 NIL NIL) (-644 1581403 1581505 1581690 "MKBCFUNC" 1582019 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-643 1578087 1580957 1581093 "MINT" 1581287 T MINT (NIL) -8 NIL NIL) (-642 1576899 1577142 1577419 "MHROWRED" 1577842 NIL MHROWRED (NIL T) -7 NIL NIL) (-641 1572170 1575344 1575768 "MFLOAT" 1576495 T MFLOAT (NIL) -8 NIL NIL) (-640 1571527 1571603 1571774 "MFINFACT" 1572082 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-639 1567842 1568690 1569574 "MESH" 1570663 T MESH (NIL) -7 NIL NIL) (-638 1566204 1566516 1566869 "MDDFACT" 1567529 NIL MDDFACT (NIL T) -7 NIL NIL) (-637 1563047 1565364 1565405 "MDAGG" 1565660 NIL MDAGG (NIL T) -9 NIL 1565803) (-636 1552745 1562340 1562547 "MCMPLX" 1562860 T MCMPLX (NIL) -8 NIL NIL) (-635 1551886 1552032 1552232 "MCDEN" 1552594 NIL MCDEN (NIL T T) -7 NIL NIL) (-634 1549776 1550046 1550426 "MCALCFN" 1551616 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-633 1547398 1547921 1548482 "MATSTOR" 1549247 NIL MATSTOR (NIL T) -7 NIL NIL) (-632 1543407 1546773 1547020 "MATRIX" 1547183 NIL MATRIX (NIL T) -8 NIL NIL) (-631 1539176 1539880 1540616 "MATLIN" 1542764 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-630 1529374 1532512 1532588 "MATCAT" 1537426 NIL MATCAT (NIL T T T) -9 NIL 1538843) (-629 1525739 1526752 1528107 "MATCAT-" 1528112 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-628 1524341 1524494 1524825 "MATCAT2" 1525574 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-627 1522453 1522777 1523161 "MAPPKG3" 1524016 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-626 1521434 1521607 1521829 "MAPPKG2" 1522277 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-625 1519933 1520217 1520544 "MAPPKG1" 1521140 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-624 1519544 1519602 1519725 "MAPHACK3" 1519869 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-623 1519136 1519197 1519311 "MAPHACK2" 1519476 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-622 1518574 1518677 1518819 "MAPHACK1" 1519027 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-621 1516682 1517276 1517579 "MAGMA" 1518303 NIL MAGMA (NIL T) -8 NIL NIL) (-620 1513156 1514926 1515386 "M3D" 1516255 NIL M3D (NIL T) -8 NIL NIL) (-619 1507312 1511527 1511568 "LZSTAGG" 1512350 NIL LZSTAGG (NIL T) -9 NIL 1512645) (-618 1503285 1504443 1505900 "LZSTAGG-" 1505905 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-617 1500401 1501178 1501664 "LWORD" 1502831 NIL LWORD (NIL T) -8 NIL NIL) (-616 1493561 1500172 1500306 "LSQM" 1500311 NIL LSQM (NIL NIL T) -8 NIL NIL) (-615 1492785 1492924 1493152 "LSPP" 1493416 NIL LSPP (NIL T T T T) -7 NIL NIL) (-614 1490597 1490898 1491354 "LSMP" 1492474 NIL LSMP (NIL T T T T) -7 NIL NIL) (-613 1487376 1488050 1488780 "LSMP1" 1489899 NIL LSMP1 (NIL T) -7 NIL NIL) (-612 1481303 1486545 1486586 "LSAGG" 1486648 NIL LSAGG (NIL T) -9 NIL 1486726) (-611 1477998 1478922 1480135 "LSAGG-" 1480140 NIL LSAGG- (NIL T T) -8 NIL NIL) (-610 1475624 1477142 1477391 "LPOLY" 1477793 NIL LPOLY (NIL T T) -8 NIL NIL) (-609 1475206 1475291 1475414 "LPEFRAC" 1475533 NIL LPEFRAC (NIL T) -7 NIL NIL) (-608 1473553 1474300 1474553 "LO" 1475038 NIL LO (NIL T T T) -8 NIL NIL) (-607 1473207 1473319 1473347 "LOGIC" 1473458 T LOGIC (NIL) -9 NIL 1473538) (-606 1473069 1473092 1473163 "LOGIC-" 1473168 NIL LOGIC- (NIL T) -8 NIL NIL) (-605 1472262 1472402 1472595 "LODOOPS" 1472925 NIL LODOOPS (NIL T T) -7 NIL NIL) (-604 1469680 1472179 1472244 "LODO" 1472249 NIL LODO (NIL T NIL) -8 NIL NIL) (-603 1468226 1468461 1468812 "LODOF" 1469427 NIL LODOF (NIL T T) -7 NIL NIL) (-602 1464646 1467082 1467122 "LODOCAT" 1467554 NIL LODOCAT (NIL T) -9 NIL 1467765) (-601 1464380 1464438 1464564 "LODOCAT-" 1464569 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-600 1461694 1464221 1464339 "LODO2" 1464344 NIL LODO2 (NIL T T) -8 NIL NIL) (-599 1459123 1461631 1461676 "LODO1" 1461681 NIL LODO1 (NIL T) -8 NIL NIL) (-598 1457986 1458151 1458462 "LODEEF" 1458946 NIL LODEEF (NIL T T T) -7 NIL NIL) (-597 1453273 1456117 1456158 "LNAGG" 1457105 NIL LNAGG (NIL T) -9 NIL 1457549) (-596 1452420 1452634 1452976 "LNAGG-" 1452981 NIL LNAGG- (NIL T T) -8 NIL NIL) (-595 1448585 1449347 1449985 "LMOPS" 1451836 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-594 1447983 1448345 1448385 "LMODULE" 1448445 NIL LMODULE (NIL T) -9 NIL 1448487) (-593 1445229 1447628 1447751 "LMDICT" 1447893 NIL LMDICT (NIL T) -8 NIL NIL) (-592 1438456 1444175 1444473 "LIST" 1444964 NIL LIST (NIL T) -8 NIL NIL) (-591 1437981 1438055 1438194 "LIST3" 1438376 NIL LIST3 (NIL T T T) -7 NIL NIL) (-590 1436988 1437166 1437394 "LIST2" 1437799 NIL LIST2 (NIL T T) -7 NIL NIL) (-589 1435122 1435434 1435833 "LIST2MAP" 1436635 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-588 1433835 1434515 1434555 "LINEXP" 1434808 NIL LINEXP (NIL T) -9 NIL 1434956) (-587 1432482 1432742 1433039 "LINDEP" 1433587 NIL LINDEP (NIL T T) -7 NIL NIL) (-586 1429179 1429898 1430675 "LIMITRF" 1431737 NIL LIMITRF (NIL T) -7 NIL NIL) (-585 1427459 1427754 1428169 "LIMITPS" 1428874 NIL LIMITPS (NIL T T) -7 NIL NIL) (-584 1421914 1426970 1427198 "LIE" 1427280 NIL LIE (NIL T T) -8 NIL NIL) (-583 1420965 1421408 1421448 "LIECAT" 1421588 NIL LIECAT (NIL T) -9 NIL 1421739) (-582 1420806 1420833 1420921 "LIECAT-" 1420926 NIL LIECAT- (NIL T T) -8 NIL NIL) (-581 1413418 1420255 1420420 "LIB" 1420661 T LIB (NIL) -8 NIL NIL) (-580 1409055 1409936 1410871 "LGROBP" 1412535 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-579 1406921 1407195 1407557 "LF" 1408776 NIL LF (NIL T T) -7 NIL NIL) (-578 1405761 1406453 1406481 "LFCAT" 1406688 T LFCAT (NIL) -9 NIL 1406827) (-577 1402673 1403299 1403985 "LEXTRIPK" 1405127 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-576 1399379 1400243 1400746 "LEXP" 1402253 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-575 1397777 1398090 1398491 "LEADCDET" 1399061 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-574 1396973 1397047 1397274 "LAZM3PK" 1397698 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-573 1391890 1395052 1395589 "LAUPOL" 1396486 NIL LAUPOL (NIL T T) -8 NIL NIL) (-572 1391457 1391501 1391668 "LAPLACE" 1391840 NIL LAPLACE (NIL T T) -7 NIL NIL) (-571 1389385 1390558 1390809 "LA" 1391290 NIL LA (NIL T T T) -8 NIL NIL) (-570 1388448 1389042 1389082 "LALG" 1389143 NIL LALG (NIL T) -9 NIL 1389201) (-569 1388163 1388222 1388357 "LALG-" 1388362 NIL LALG- (NIL T T) -8 NIL NIL) (-568 1387073 1387260 1387557 "KOVACIC" 1387963 NIL KOVACIC (NIL T T) -7 NIL NIL) (-567 1386908 1386932 1386973 "KONVERT" 1387035 NIL KONVERT (NIL T) -9 NIL NIL) (-566 1386743 1386767 1386808 "KOERCE" 1386870 NIL KOERCE (NIL T) -9 NIL NIL) (-565 1384477 1385237 1385630 "KERNEL" 1386382 NIL KERNEL (NIL T) -8 NIL NIL) (-564 1383979 1384060 1384190 "KERNEL2" 1384391 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-563 1377831 1382519 1382573 "KDAGG" 1382950 NIL KDAGG (NIL T T) -9 NIL 1383156) (-562 1377360 1377484 1377689 "KDAGG-" 1377694 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-561 1370535 1377021 1377176 "KAFILE" 1377238 NIL KAFILE (NIL T) -8 NIL NIL) (-560 1364990 1370046 1370274 "JORDAN" 1370356 NIL JORDAN (NIL T T) -8 NIL NIL) (-559 1364719 1364778 1364865 "JAVACODE" 1364923 T JAVACODE (NIL) -8 NIL NIL) (-558 1361019 1362925 1362979 "IXAGG" 1363908 NIL IXAGG (NIL T T) -9 NIL 1364367) (-557 1359938 1360244 1360663 "IXAGG-" 1360668 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-556 1355523 1359860 1359919 "IVECTOR" 1359924 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-555 1354289 1354526 1354792 "ITUPLE" 1355290 NIL ITUPLE (NIL T) -8 NIL NIL) (-554 1352725 1352902 1353208 "ITRIGMNP" 1354111 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-553 1351470 1351674 1351957 "ITFUN3" 1352501 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-552 1351102 1351159 1351268 "ITFUN2" 1351407 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-551 1348904 1349975 1350272 "ITAYLOR" 1350837 NIL ITAYLOR (NIL T) -8 NIL NIL) (-550 1337881 1343079 1344238 "ISUPS" 1347777 NIL ISUPS (NIL T) -8 NIL NIL) (-549 1336985 1337125 1337361 "ISUMP" 1337728 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-548 1332245 1336782 1336861 "ISTRING" 1336938 NIL ISTRING (NIL NIL) -8 NIL NIL) (-547 1331458 1331539 1331754 "IRURPK" 1332159 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-546 1330394 1330595 1330835 "IRSN" 1331238 T IRSN (NIL) -7 NIL NIL) (-545 1328429 1328784 1329219 "IRRF2F" 1330032 NIL IRRF2F (NIL T) -7 NIL NIL) (-544 1328176 1328214 1328290 "IRREDFFX" 1328385 NIL IRREDFFX (NIL T) -7 NIL NIL) (-543 1326791 1327050 1327349 "IROOT" 1327909 NIL IROOT (NIL T) -7 NIL NIL) (-542 1323419 1324470 1325160 "IR" 1326133 NIL IR (NIL T) -8 NIL NIL) (-541 1321032 1321527 1322093 "IR2" 1322897 NIL IR2 (NIL T T) -7 NIL NIL) (-540 1320108 1320221 1320441 "IR2F" 1320915 NIL IR2F (NIL T T) -7 NIL NIL) (-539 1319899 1319933 1319993 "IPRNTPK" 1320068 T IPRNTPK (NIL) -7 NIL NIL) (-538 1316453 1319788 1319857 "IPF" 1319862 NIL IPF (NIL NIL) -8 NIL NIL) (-537 1314770 1316378 1316435 "IPADIC" 1316440 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-536 1314269 1314327 1314516 "INVLAPLA" 1314706 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-535 1303855 1306208 1308594 "INTTR" 1311933 NIL INTTR (NIL T T) -7 NIL NIL) (-534 1300198 1300939 1301802 "INTTOOLS" 1303041 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-533 1299784 1299875 1299992 "INTSLPE" 1300101 T INTSLPE (NIL) -7 NIL NIL) (-532 1297734 1299707 1299766 "INTRVL" 1299771 NIL INTRVL (NIL T) -8 NIL NIL) (-531 1295299 1295811 1296385 "INTRF" 1297219 NIL INTRF (NIL T) -7 NIL NIL) (-530 1294706 1294803 1294944 "INTRET" 1295197 NIL INTRET (NIL T) -7 NIL NIL) (-529 1292687 1293076 1293545 "INTRAT" 1294314 NIL INTRAT (NIL T T) -7 NIL NIL) (-528 1289920 1290503 1291128 "INTPM" 1292172 NIL INTPM (NIL T T) -7 NIL NIL) (-527 1286629 1287228 1287972 "INTPAF" 1289306 NIL INTPAF (NIL T T T) -7 NIL NIL) (-526 1281872 1282818 1283853 "INTPACK" 1285614 T INTPACK (NIL) -7 NIL NIL) (-525 1278726 1281601 1281728 "INT" 1281765 T INT (NIL) -8 NIL NIL) (-524 1277978 1278130 1278338 "INTHERTR" 1278568 NIL INTHERTR (NIL T T) -7 NIL NIL) (-523 1277417 1277497 1277685 "INTHERAL" 1277892 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-522 1275263 1275706 1276163 "INTHEORY" 1276980 T INTHEORY (NIL) -7 NIL NIL) (-521 1266585 1268206 1269984 "INTG0" 1273615 NIL INTG0 (NIL T T T) -7 NIL NIL) (-520 1247158 1251948 1256758 "INTFTBL" 1261795 T INTFTBL (NIL) -8 NIL NIL) (-519 1246407 1246545 1246718 "INTFACT" 1247017 NIL INTFACT (NIL T) -7 NIL NIL) (-518 1243798 1244244 1244807 "INTEF" 1245961 NIL INTEF (NIL T T) -7 NIL NIL) (-517 1242260 1243009 1243037 "INTDOM" 1243338 T INTDOM (NIL) -9 NIL 1243545) (-516 1241629 1241803 1242045 "INTDOM-" 1242050 NIL INTDOM- (NIL T) -8 NIL NIL) (-515 1238122 1240054 1240108 "INTCAT" 1240907 NIL INTCAT (NIL T) -9 NIL 1241226) (-514 1237595 1237697 1237825 "INTBIT" 1238014 T INTBIT (NIL) -7 NIL NIL) (-513 1236270 1236424 1236737 "INTALG" 1237440 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-512 1235727 1235817 1235987 "INTAF" 1236174 NIL INTAF (NIL T T) -7 NIL NIL) (-511 1229181 1235537 1235677 "INTABL" 1235682 NIL INTABL (NIL T T T) -8 NIL NIL) (-510 1224132 1226861 1226889 "INS" 1227857 T INS (NIL) -9 NIL 1228538) (-509 1221372 1222143 1223117 "INS-" 1223190 NIL INS- (NIL T) -8 NIL NIL) (-508 1220151 1220378 1220675 "INPSIGN" 1221125 NIL INPSIGN (NIL T T) -7 NIL NIL) (-507 1219265 1219382 1219579 "INPRODPF" 1220031 NIL INPRODPF (NIL T T) -7 NIL NIL) (-506 1218155 1218272 1218509 "INPRODFF" 1219145 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-505 1217155 1217307 1217567 "INNMFACT" 1217991 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-504 1216352 1216449 1216637 "INMODGCD" 1217054 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-503 1214861 1215105 1215429 "INFSP" 1216097 NIL INFSP (NIL T T T) -7 NIL NIL) (-502 1214045 1214162 1214345 "INFPROD0" 1214741 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-501 1211056 1212214 1212705 "INFORM" 1213562 T INFORM (NIL) -8 NIL NIL) (-500 1210666 1210726 1210824 "INFORM1" 1210991 NIL INFORM1 (NIL T) -7 NIL NIL) (-499 1210189 1210278 1210392 "INFINITY" 1210572 T INFINITY (NIL) -7 NIL NIL) (-498 1208806 1209055 1209376 "INEP" 1209937 NIL INEP (NIL T T T) -7 NIL NIL) (-497 1208082 1208703 1208768 "INDE" 1208773 NIL INDE (NIL T) -8 NIL NIL) (-496 1207646 1207714 1207831 "INCRMAPS" 1208009 NIL INCRMAPS (NIL T) -7 NIL NIL) (-495 1202957 1203882 1204826 "INBFF" 1206734 NIL INBFF (NIL T) -7 NIL NIL) (-494 1199452 1202802 1202905 "IMATRIX" 1202910 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-493 1198164 1198287 1198602 "IMATQF" 1199308 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-492 1196384 1196611 1196948 "IMATLIN" 1197920 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-491 1191010 1196308 1196366 "ILIST" 1196371 NIL ILIST (NIL T NIL) -8 NIL NIL) (-490 1188963 1190870 1190983 "IIARRAY2" 1190988 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-489 1184331 1188874 1188938 "IFF" 1188943 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-488 1179370 1183619 1183807 "IFARRAY" 1184188 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-487 1178577 1179274 1179347 "IFAMON" 1179352 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-486 1178161 1178226 1178280 "IEVALAB" 1178487 NIL IEVALAB (NIL T T) -9 NIL NIL) (-485 1177836 1177904 1178064 "IEVALAB-" 1178069 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-484 1177494 1177750 1177813 "IDPO" 1177818 NIL IDPO (NIL T T) -8 NIL NIL) (-483 1176771 1177383 1177458 "IDPOAMS" 1177463 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-482 1176105 1176660 1176735 "IDPOAM" 1176740 NIL IDPOAM (NIL T T) -8 NIL NIL) (-481 1175191 1175441 1175494 "IDPC" 1175907 NIL IDPC (NIL T T) -9 NIL 1176056) (-480 1174687 1175083 1175156 "IDPAM" 1175161 NIL IDPAM (NIL T T) -8 NIL NIL) (-479 1174090 1174579 1174652 "IDPAG" 1174657 NIL IDPAG (NIL T T) -8 NIL NIL) (-478 1170345 1171193 1172088 "IDECOMP" 1173247 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-477 1163218 1164268 1165315 "IDEAL" 1169381 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-476 1162382 1162494 1162693 "ICDEN" 1163102 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-475 1161481 1161862 1162009 "ICARD" 1162255 T ICARD (NIL) -8 NIL NIL) (-474 1159553 1159866 1160269 "IBPTOOLS" 1161158 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-473 1155167 1159173 1159286 "IBITS" 1159472 NIL IBITS (NIL NIL) -8 NIL NIL) (-472 1151890 1152466 1153161 "IBATOOL" 1154584 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-471 1149670 1150131 1150664 "IBACHIN" 1151425 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-470 1147547 1149516 1149619 "IARRAY2" 1149624 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-469 1143700 1147473 1147530 "IARRAY1" 1147535 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-468 1137638 1142118 1142596 "IAN" 1143242 T IAN (NIL) -8 NIL NIL) (-467 1137149 1137206 1137379 "IALGFACT" 1137575 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-466 1136677 1136790 1136818 "HYPCAT" 1137025 T HYPCAT (NIL) -9 NIL NIL) (-465 1136215 1136332 1136518 "HYPCAT-" 1136523 NIL HYPCAT- (NIL T) -8 NIL NIL) (-464 1132895 1134226 1134267 "HOAGG" 1135248 NIL HOAGG (NIL T) -9 NIL 1135927) (-463 1131489 1131888 1132414 "HOAGG-" 1132419 NIL HOAGG- (NIL T T) -8 NIL NIL) (-462 1125319 1130930 1131096 "HEXADEC" 1131343 T HEXADEC (NIL) -8 NIL NIL) (-461 1124063 1124285 1124548 "HEUGCD" 1125096 NIL HEUGCD (NIL T) -7 NIL NIL) (-460 1123166 1123900 1124030 "HELLFDIV" 1124035 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-459 1121394 1122943 1123031 "HEAP" 1123110 NIL HEAP (NIL T) -8 NIL NIL) (-458 1115261 1121309 1121371 "HDP" 1121376 NIL HDP (NIL NIL T) -8 NIL NIL) (-457 1108973 1114898 1115049 "HDMP" 1115162 NIL HDMP (NIL NIL T) -8 NIL NIL) (-456 1108298 1108437 1108601 "HB" 1108829 T HB (NIL) -7 NIL NIL) (-455 1101795 1108144 1108248 "HASHTBL" 1108253 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-454 1099548 1101423 1101602 "HACKPI" 1101636 T HACKPI (NIL) -8 NIL NIL) (-453 1095244 1099402 1099514 "GTSET" 1099519 NIL GTSET (NIL T T T T) -8 NIL NIL) (-452 1088770 1095122 1095220 "GSTBL" 1095225 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-451 1081003 1087806 1088070 "GSERIES" 1088561 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-450 1080026 1080479 1080507 "GROUP" 1080768 T GROUP (NIL) -9 NIL 1080927) (-449 1079142 1079365 1079709 "GROUP-" 1079714 NIL GROUP- (NIL T) -8 NIL NIL) (-448 1077511 1077830 1078217 "GROEBSOL" 1078819 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-447 1076452 1076714 1076765 "GRMOD" 1077294 NIL GRMOD (NIL T T) -9 NIL 1077462) (-446 1076220 1076256 1076384 "GRMOD-" 1076389 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-445 1071546 1072574 1073574 "GRIMAGE" 1075240 T GRIMAGE (NIL) -8 NIL NIL) (-444 1070013 1070273 1070597 "GRDEF" 1071242 T GRDEF (NIL) -7 NIL NIL) (-443 1069457 1069573 1069714 "GRAY" 1069892 T GRAY (NIL) -7 NIL NIL) (-442 1068691 1069071 1069122 "GRALG" 1069275 NIL GRALG (NIL T T) -9 NIL 1069367) (-441 1068352 1068425 1068588 "GRALG-" 1068593 NIL GRALG- (NIL T T T) -8 NIL NIL) (-440 1065160 1067941 1068117 "GPOLSET" 1068259 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-439 1064516 1064573 1064830 "GOSPER" 1065097 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-438 1060275 1060954 1061480 "GMODPOL" 1064215 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-437 1059280 1059464 1059702 "GHENSEL" 1060087 NIL GHENSEL (NIL T T) -7 NIL NIL) (-436 1053346 1054189 1055215 "GENUPS" 1058364 NIL GENUPS (NIL T T) -7 NIL NIL) (-435 1053043 1053094 1053183 "GENUFACT" 1053289 NIL GENUFACT (NIL T) -7 NIL NIL) (-434 1052455 1052532 1052697 "GENPGCD" 1052961 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-433 1051929 1051964 1052177 "GENMFACT" 1052414 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-432 1050497 1050752 1051059 "GENEEZ" 1051672 NIL GENEEZ (NIL T T) -7 NIL NIL) (-431 1044371 1050110 1050271 "GDMP" 1050420 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-430 1033738 1038132 1039238 "GCNAALG" 1043354 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-429 1032160 1033032 1033060 "GCDDOM" 1033315 T GCDDOM (NIL) -9 NIL 1033472) (-428 1031630 1031757 1031972 "GCDDOM-" 1031977 NIL GCDDOM- (NIL T) -8 NIL NIL) (-427 1030302 1030487 1030791 "GB" 1031409 NIL GB (NIL T T T T) -7 NIL NIL) (-426 1018922 1021248 1023640 "GBINTERN" 1027993 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-425 1016759 1017051 1017472 "GBF" 1018597 NIL GBF (NIL T T T T) -7 NIL NIL) (-424 1015540 1015705 1015972 "GBEUCLID" 1016575 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-423 1014889 1015014 1015163 "GAUSSFAC" 1015411 T GAUSSFAC (NIL) -7 NIL NIL) (-422 1013266 1013568 1013881 "GALUTIL" 1014608 NIL GALUTIL (NIL T) -7 NIL NIL) (-421 1011583 1011857 1012180 "GALPOLYU" 1012993 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-420 1008972 1009262 1009667 "GALFACTU" 1011280 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-419 1000778 1002277 1003885 "GALFACT" 1007404 NIL GALFACT (NIL T) -7 NIL NIL) (-418 998166 998824 998852 "FVFUN" 1000008 T FVFUN (NIL) -9 NIL 1000728) (-417 997432 997614 997642 "FVC" 997933 T FVC (NIL) -9 NIL 998116) (-416 997069 997224 997305 "FUNCTION" 997384 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-415 994739 995290 995779 "FT" 996600 T FT (NIL) -8 NIL NIL) (-414 993557 994040 994243 "FTEM" 994556 T FTEM (NIL) -8 NIL NIL) (-413 991822 992110 992512 "FSUPFACT" 993249 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-412 990219 990508 990840 "FST" 991510 T FST (NIL) -8 NIL NIL) (-411 989394 989500 989694 "FSRED" 990101 NIL FSRED (NIL T T) -7 NIL NIL) (-410 988073 988328 988682 "FSPRMELT" 989109 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-409 985158 985596 986095 "FSPECF" 987636 NIL FSPECF (NIL T T) -7 NIL NIL) (-408 967532 976089 976129 "FS" 979967 NIL FS (NIL T) -9 NIL 982249) (-407 956182 959172 963228 "FS-" 963525 NIL FS- (NIL T T) -8 NIL NIL) (-406 955698 955752 955928 "FSINT" 956123 NIL FSINT (NIL T T) -7 NIL NIL) (-405 953979 954691 954994 "FSERIES" 955477 NIL FSERIES (NIL T T) -8 NIL NIL) (-404 952997 953113 953343 "FSCINT" 953859 NIL FSCINT (NIL T T) -7 NIL NIL) (-403 949232 951942 951983 "FSAGG" 952353 NIL FSAGG (NIL T) -9 NIL 952612) (-402 946994 947595 948391 "FSAGG-" 948486 NIL FSAGG- (NIL T T) -8 NIL NIL) (-401 946036 946179 946406 "FSAGG2" 946847 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-400 943695 943974 944527 "FS2UPS" 945754 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-399 943281 943324 943477 "FS2" 943646 NIL FS2 (NIL T T T T) -7 NIL NIL) (-398 942141 942312 942620 "FS2EXPXP" 943106 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-397 941567 941682 941834 "FRUTIL" 942021 NIL FRUTIL (NIL T) -7 NIL NIL) (-396 932987 937066 938422 "FR" 940243 NIL FR (NIL T) -8 NIL NIL) (-395 928064 930707 930747 "FRNAALG" 932143 NIL FRNAALG (NIL T) -9 NIL 932750) (-394 923742 924813 926088 "FRNAALG-" 926838 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-393 923380 923423 923550 "FRNAAF2" 923693 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-392 921729 922221 922515 "FRMOD" 923193 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-391 919451 920120 920436 "FRIDEAL" 921520 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-390 918650 918737 919024 "FRIDEAL2" 919358 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-389 917908 918316 918357 "FRETRCT" 918362 NIL FRETRCT (NIL T) -9 NIL 918533) (-388 917020 917251 917602 "FRETRCT-" 917607 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-387 914230 915450 915509 "FRAMALG" 916391 NIL FRAMALG (NIL T T) -9 NIL 916683) (-386 912363 912819 913449 "FRAMALG-" 913672 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-385 906265 911838 912114 "FRAC" 912119 NIL FRAC (NIL T) -8 NIL NIL) (-384 905901 905958 906065 "FRAC2" 906202 NIL FRAC2 (NIL T T) -7 NIL NIL) (-383 905537 905594 905701 "FR2" 905838 NIL FR2 (NIL T T) -7 NIL NIL) (-382 900211 903124 903152 "FPS" 904271 T FPS (NIL) -9 NIL 904827) (-381 899660 899769 899933 "FPS-" 900079 NIL FPS- (NIL T) -8 NIL NIL) (-380 897109 898806 898834 "FPC" 899059 T FPC (NIL) -9 NIL 899201) (-379 896902 896942 897039 "FPC-" 897044 NIL FPC- (NIL T) -8 NIL NIL) (-378 895781 896391 896432 "FPATMAB" 896437 NIL FPATMAB (NIL T) -9 NIL 896589) (-377 893481 893957 894383 "FPARFRAC" 895418 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-376 888874 889373 890055 "FORTRAN" 892913 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-375 886546 887046 887585 "FORT" 888355 T FORT (NIL) -7 NIL NIL) (-374 884222 884784 884812 "FORTFN" 885872 T FORTFN (NIL) -9 NIL 886496) (-373 883986 884036 884064 "FORTCAT" 884123 T FORTCAT (NIL) -9 NIL 884185) (-372 882046 882529 882928 "FORMULA" 883607 T FORMULA (NIL) -8 NIL NIL) (-371 881834 881864 881933 "FORMULA1" 882010 NIL FORMULA1 (NIL T) -7 NIL NIL) (-370 881357 881409 881582 "FORDER" 881776 NIL FORDER (NIL T T T T) -7 NIL NIL) (-369 880453 880617 880810 "FOP" 881184 T FOP (NIL) -7 NIL NIL) (-368 879045 879717 879891 "FNLA" 880335 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-367 877714 878103 878131 "FNCAT" 878703 T FNCAT (NIL) -9 NIL 878996) (-366 877280 877673 877701 "FNAME" 877706 T FNAME (NIL) -8 NIL NIL) (-365 875940 876913 876941 "FMTC" 876946 T FMTC (NIL) -9 NIL 876981) (-364 872258 873465 874093 "FMONOID" 875345 NIL FMONOID (NIL T) -8 NIL NIL) (-363 871478 872001 872149 "FM" 872154 NIL FM (NIL T T) -8 NIL NIL) (-362 868902 869548 869576 "FMFUN" 870720 T FMFUN (NIL) -9 NIL 871428) (-361 868171 868352 868380 "FMC" 868670 T FMC (NIL) -9 NIL 868852) (-360 865401 866235 866288 "FMCAT" 867470 NIL FMCAT (NIL T T) -9 NIL 867964) (-359 864296 865169 865268 "FM1" 865346 NIL FM1 (NIL T T) -8 NIL NIL) (-358 862070 862486 862980 "FLOATRP" 863847 NIL FLOATRP (NIL T) -7 NIL NIL) (-357 855556 859726 860356 "FLOAT" 861460 T FLOAT (NIL) -8 NIL NIL) (-356 852994 853494 854072 "FLOATCP" 855023 NIL FLOATCP (NIL T) -7 NIL NIL) (-355 851783 852631 852671 "FLINEXP" 852676 NIL FLINEXP (NIL T) -9 NIL 852769) (-354 850938 851173 851500 "FLINEXP-" 851505 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-353 850014 850158 850382 "FLASORT" 850790 NIL FLASORT (NIL T T) -7 NIL NIL) (-352 847233 848075 848127 "FLALG" 849354 NIL FLALG (NIL T T) -9 NIL 849821) (-351 841018 844720 844761 "FLAGG" 846023 NIL FLAGG (NIL T) -9 NIL 846675) (-350 839744 840083 840573 "FLAGG-" 840578 NIL FLAGG- (NIL T T) -8 NIL NIL) (-349 838786 838929 839156 "FLAGG2" 839597 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-348 835759 836777 836836 "FINRALG" 837964 NIL FINRALG (NIL T T) -9 NIL 838472) (-347 834919 835148 835487 "FINRALG-" 835492 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-346 834326 834539 834567 "FINITE" 834763 T FINITE (NIL) -9 NIL 834870) (-345 826786 828947 828987 "FINAALG" 832654 NIL FINAALG (NIL T) -9 NIL 834107) (-344 822127 823168 824312 "FINAALG-" 825691 NIL FINAALG- (NIL T T) -8 NIL NIL) (-343 821522 821882 821985 "FILE" 822057 NIL FILE (NIL T) -8 NIL NIL) (-342 820207 820519 820573 "FILECAT" 821257 NIL FILECAT (NIL T T) -9 NIL 821473) (-341 818070 819626 819654 "FIELD" 819694 T FIELD (NIL) -9 NIL 819774) (-340 816690 817075 817586 "FIELD-" 817591 NIL FIELD- (NIL T) -8 NIL NIL) (-339 814505 815327 815673 "FGROUP" 816377 NIL FGROUP (NIL T) -8 NIL NIL) (-338 813595 813759 813979 "FGLMICPK" 814337 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-337 809397 813520 813577 "FFX" 813582 NIL FFX (NIL T NIL) -8 NIL NIL) (-336 808998 809059 809194 "FFSLPE" 809330 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-335 804991 805770 806566 "FFPOLY" 808234 NIL FFPOLY (NIL T) -7 NIL NIL) (-334 804495 804531 804740 "FFPOLY2" 804949 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-333 800316 804414 804477 "FFP" 804482 NIL FFP (NIL T NIL) -8 NIL NIL) (-332 795684 800227 800291 "FF" 800296 NIL FF (NIL NIL NIL) -8 NIL NIL) (-331 790780 795027 795217 "FFNBX" 795538 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-330 785637 789863 790121 "FFNBP" 790634 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-329 780240 784921 785132 "FFNB" 785470 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-328 779072 779270 779585 "FFINTBAS" 780037 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-327 775296 777536 777564 "FFIELDC" 778184 T FFIELDC (NIL) -9 NIL 778560) (-326 773959 774329 774826 "FFIELDC-" 774831 NIL FFIELDC- (NIL T) -8 NIL NIL) (-325 773529 773574 773698 "FFHOM" 773901 NIL FFHOM (NIL T T T) -7 NIL NIL) (-324 771227 771711 772228 "FFF" 773044 NIL FFF (NIL T) -7 NIL NIL) (-323 766815 770969 771070 "FFCGX" 771170 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-322 762417 766547 766654 "FFCGP" 766758 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-321 757570 762144 762252 "FFCG" 762353 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-320 739516 748639 748725 "FFCAT" 753890 NIL FFCAT (NIL T T T) -9 NIL 755377) (-319 734714 735761 737075 "FFCAT-" 738305 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-318 734125 734168 734403 "FFCAT2" 734665 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-317 723281 727071 728288 "FEXPR" 732980 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-316 722281 722716 722757 "FEVALAB" 722841 NIL FEVALAB (NIL T) -9 NIL 723102) (-315 721440 721650 721988 "FEVALAB-" 721993 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-314 720033 720823 721026 "FDIV" 721339 NIL FDIV (NIL T T T T) -8 NIL NIL) (-313 717100 717815 717930 "FDIVCAT" 719498 NIL FDIVCAT (NIL T T T T) -9 NIL 719935) (-312 716862 716889 717059 "FDIVCAT-" 717064 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-311 716082 716169 716446 "FDIV2" 716769 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-310 714768 715027 715316 "FCPAK1" 715813 T FCPAK1 (NIL) -7 NIL NIL) (-309 713896 714268 714409 "FCOMP" 714659 NIL FCOMP (NIL T) -8 NIL NIL) (-308 697531 700945 704506 "FC" 710355 T FC (NIL) -8 NIL NIL) (-307 690127 694173 694213 "FAXF" 696015 NIL FAXF (NIL T) -9 NIL 696706) (-306 687406 688061 688886 "FAXF-" 689351 NIL FAXF- (NIL T T) -8 NIL NIL) (-305 682506 686782 686958 "FARRAY" 687263 NIL FARRAY (NIL T) -8 NIL NIL) (-304 677897 679968 680020 "FAMR" 681032 NIL FAMR (NIL T T) -9 NIL 681492) (-303 676788 677090 677524 "FAMR-" 677529 NIL FAMR- (NIL T T T) -8 NIL NIL) (-302 675984 676710 676763 "FAMONOID" 676768 NIL FAMONOID (NIL T) -8 NIL NIL) (-301 673817 674501 674554 "FAMONC" 675495 NIL FAMONC (NIL T T) -9 NIL 675880) (-300 672509 673571 673708 "FAGROUP" 673713 NIL FAGROUP (NIL T) -8 NIL NIL) (-299 670312 670631 671033 "FACUTIL" 672190 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-298 669411 669596 669818 "FACTFUNC" 670122 NIL FACTFUNC (NIL T) -7 NIL NIL) (-297 661731 668662 668874 "EXPUPXS" 669267 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-296 659214 659754 660340 "EXPRTUBE" 661165 T EXPRTUBE (NIL) -7 NIL NIL) (-295 655408 656000 656737 "EXPRODE" 658553 NIL EXPRODE (NIL T T) -7 NIL NIL) (-294 640539 654039 654465 "EXPR" 655014 NIL EXPR (NIL T) -8 NIL NIL) (-293 634951 635538 636350 "EXPR2UPS" 639837 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-292 634587 634644 634751 "EXPR2" 634888 NIL EXPR2 (NIL T T) -7 NIL NIL) (-291 625941 633724 634019 "EXPEXPAN" 634425 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-290 625768 625898 625927 "EXIT" 625932 T EXIT (NIL) -8 NIL NIL) (-289 625395 625457 625570 "EVALCYC" 625700 NIL EVALCYC (NIL T) -7 NIL NIL) (-288 624936 625054 625095 "EVALAB" 625265 NIL EVALAB (NIL T) -9 NIL 625369) (-287 624417 624539 624760 "EVALAB-" 624765 NIL EVALAB- (NIL T T) -8 NIL NIL) (-286 621880 623192 623220 "EUCDOM" 623775 T EUCDOM (NIL) -9 NIL 624125) (-285 620285 620727 621317 "EUCDOM-" 621322 NIL EUCDOM- (NIL T) -8 NIL NIL) (-284 607863 610611 613351 "ESTOOLS" 617565 T ESTOOLS (NIL) -7 NIL NIL) (-283 607499 607556 607663 "ESTOOLS2" 607800 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-282 607250 607292 607372 "ESTOOLS1" 607451 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-281 601188 602912 602940 "ES" 605704 T ES (NIL) -9 NIL 607110) (-280 596135 597422 599239 "ES-" 599403 NIL ES- (NIL T) -8 NIL NIL) (-279 592510 593270 594050 "ESCONT" 595375 T ESCONT (NIL) -7 NIL NIL) (-278 592247 592279 592361 "ESCONT1" 592472 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-277 591922 591972 592072 "ES2" 592191 NIL ES2 (NIL T T) -7 NIL NIL) (-276 591552 591610 591719 "ES1" 591858 NIL ES1 (NIL T T) -7 NIL NIL) (-275 590768 590897 591073 "ERROR" 591396 T ERROR (NIL) -7 NIL NIL) (-274 584271 590627 590718 "EQTBL" 590723 NIL EQTBL (NIL T T) -8 NIL NIL) (-273 576708 579589 581036 "EQ" 582857 NIL -2675 (NIL T) -8 NIL NIL) (-272 576340 576397 576506 "EQ2" 576645 NIL EQ2 (NIL T T) -7 NIL NIL) (-271 571632 572678 573771 "EP" 575279 NIL EP (NIL T) -7 NIL NIL) (-270 570215 570515 570832 "ENV" 571335 T ENV (NIL) -8 NIL NIL) (-269 569375 569939 569967 "ENTIRER" 569972 T ENTIRER (NIL) -9 NIL 570017) (-268 565831 567330 567700 "EMR" 569174 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-267 564975 565160 565214 "ELTAGG" 565594 NIL ELTAGG (NIL T T) -9 NIL 565805) (-266 564694 564756 564897 "ELTAGG-" 564902 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-265 564483 564512 564566 "ELTAB" 564650 NIL ELTAB (NIL T T) -9 NIL NIL) (-264 563609 563755 563954 "ELFUTS" 564334 NIL ELFUTS (NIL T T) -7 NIL NIL) (-263 563351 563407 563435 "ELEMFUN" 563540 T ELEMFUN (NIL) -9 NIL NIL) (-262 563221 563242 563310 "ELEMFUN-" 563315 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-261 558113 561322 561363 "ELAGG" 562303 NIL ELAGG (NIL T) -9 NIL 562766) (-260 556398 556832 557495 "ELAGG-" 557500 NIL ELAGG- (NIL T T) -8 NIL NIL) (-259 555055 555335 555630 "ELABEXPR" 556123 T ELABEXPR (NIL) -8 NIL NIL) (-258 547912 549711 550538 "EFUPXS" 554331 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-257 541351 543152 543962 "EFULS" 547188 NIL EFULS (NIL T T T) -8 NIL NIL) (-256 538782 539140 539618 "EFSTRUC" 540983 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-255 527854 529419 530979 "EF" 537297 NIL EF (NIL T T) -7 NIL NIL) (-254 526955 527339 527488 "EAB" 527725 T EAB (NIL) -8 NIL NIL) (-253 526168 526914 526942 "E04UCFA" 526947 T E04UCFA (NIL) -8 NIL NIL) (-252 525381 526127 526155 "E04NAFA" 526160 T E04NAFA (NIL) -8 NIL NIL) (-251 524594 525340 525368 "E04MBFA" 525373 T E04MBFA (NIL) -8 NIL NIL) (-250 523807 524553 524581 "E04JAFA" 524586 T E04JAFA (NIL) -8 NIL NIL) (-249 523022 523766 523794 "E04GCFA" 523799 T E04GCFA (NIL) -8 NIL NIL) (-248 522237 522981 523009 "E04FDFA" 523014 T E04FDFA (NIL) -8 NIL NIL) (-247 521450 522196 522224 "E04DGFA" 522229 T E04DGFA (NIL) -8 NIL NIL) (-246 515635 516980 518342 "E04AGNT" 520108 T E04AGNT (NIL) -7 NIL NIL) (-245 514362 514842 514882 "DVARCAT" 515357 NIL DVARCAT (NIL T) -9 NIL 515555) (-244 513566 513778 514092 "DVARCAT-" 514097 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-243 506428 513368 513495 "DSMP" 513500 NIL DSMP (NIL T T T) -8 NIL NIL) (-242 501238 502373 503441 "DROPT" 505380 T DROPT (NIL) -8 NIL NIL) (-241 500903 500962 501060 "DROPT1" 501173 NIL DROPT1 (NIL T) -7 NIL NIL) (-240 496018 497144 498281 "DROPT0" 499786 T DROPT0 (NIL) -7 NIL NIL) (-239 494363 494688 495074 "DRAWPT" 495652 T DRAWPT (NIL) -7 NIL NIL) (-238 488950 489873 490952 "DRAW" 493337 NIL DRAW (NIL T) -7 NIL NIL) (-237 488583 488636 488754 "DRAWHACK" 488891 NIL DRAWHACK (NIL T) -7 NIL NIL) (-236 487314 487583 487874 "DRAWCX" 488312 T DRAWCX (NIL) -7 NIL NIL) (-235 486832 486900 487050 "DRAWCURV" 487240 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-234 477303 479262 481377 "DRAWCFUN" 484737 T DRAWCFUN (NIL) -7 NIL NIL) (-233 474117 475999 476040 "DQAGG" 476669 NIL DQAGG (NIL T) -9 NIL 476942) (-232 462624 469362 469444 "DPOLCAT" 471282 NIL DPOLCAT (NIL T T T T) -9 NIL 471826) (-231 457464 458810 460767 "DPOLCAT-" 460772 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-230 451548 457326 457423 "DPMO" 457428 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-229 445535 451329 451495 "DPMM" 451500 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-228 445048 445146 445266 "DOMAIN" 445435 T DOMAIN (NIL) -8 NIL NIL) (-227 438760 444685 444836 "DMP" 444949 NIL DMP (NIL NIL T) -8 NIL NIL) (-226 438360 438416 438560 "DLP" 438698 NIL DLP (NIL T) -7 NIL NIL) (-225 432004 437461 437688 "DLIST" 438165 NIL DLIST (NIL T) -8 NIL NIL) (-224 428851 430860 430901 "DLAGG" 431451 NIL DLAGG (NIL T) -9 NIL 431680) (-223 427561 428253 428281 "DIVRING" 428431 T DIVRING (NIL) -9 NIL 428539) (-222 426549 426802 427195 "DIVRING-" 427200 NIL DIVRING- (NIL T) -8 NIL NIL) (-221 424651 425008 425414 "DISPLAY" 426163 T DISPLAY (NIL) -7 NIL NIL) (-220 418540 424565 424628 "DIRPROD" 424633 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-219 417388 417591 417856 "DIRPROD2" 418333 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-218 407019 413024 413077 "DIRPCAT" 413485 NIL DIRPCAT (NIL NIL T) -9 NIL 414312) (-217 404337 404979 405860 "DIRPCAT-" 406205 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-216 403624 403784 403970 "DIOSP" 404171 T DIOSP (NIL) -7 NIL NIL) (-215 400327 402537 402578 "DIOPS" 403012 NIL DIOPS (NIL T) -9 NIL 403241) (-214 399876 399990 400181 "DIOPS-" 400186 NIL DIOPS- (NIL T T) -8 NIL NIL) (-213 398748 399386 399414 "DIFRING" 399601 T DIFRING (NIL) -9 NIL 399710) (-212 398394 398471 398623 "DIFRING-" 398628 NIL DIFRING- (NIL T) -8 NIL NIL) (-211 396184 397466 397506 "DIFEXT" 397865 NIL DIFEXT (NIL T) -9 NIL 398158) (-210 394470 394898 395563 "DIFEXT-" 395568 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-209 391793 394003 394044 "DIAGG" 394049 NIL DIAGG (NIL T) -9 NIL 394069) (-208 391177 391334 391586 "DIAGG-" 391591 NIL DIAGG- (NIL T T) -8 NIL NIL) (-207 386642 390136 390413 "DHMATRIX" 390946 NIL DHMATRIX (NIL T) -8 NIL NIL) (-206 382254 383163 384173 "DFSFUN" 385652 T DFSFUN (NIL) -7 NIL NIL) (-205 377040 380968 381333 "DFLOAT" 381909 T DFLOAT (NIL) -8 NIL NIL) (-204 375273 375554 375949 "DFINTTLS" 376748 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-203 372306 373308 373706 "DERHAM" 374940 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-202 370155 372081 372170 "DEQUEUE" 372250 NIL DEQUEUE (NIL T) -8 NIL NIL) (-201 369373 369506 369701 "DEGRED" 370017 NIL DEGRED (NIL T T) -7 NIL NIL) (-200 365773 366518 367370 "DEFINTRF" 368601 NIL DEFINTRF (NIL T) -7 NIL NIL) (-199 363304 363773 364371 "DEFINTEF" 365292 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-198 357134 362745 362911 "DECIMAL" 363158 T DECIMAL (NIL) -8 NIL NIL) (-197 354646 355104 355610 "DDFACT" 356678 NIL DDFACT (NIL T T) -7 NIL NIL) (-196 354242 354285 354436 "DBLRESP" 354597 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-195 351917 352251 352620 "DBASE" 354000 NIL DBASE (NIL T) -8 NIL NIL) (-194 351052 351876 351904 "D03FAFA" 351909 T D03FAFA (NIL) -8 NIL NIL) (-193 350188 351011 351039 "D03EEFA" 351044 T D03EEFA (NIL) -8 NIL NIL) (-192 348138 348604 349093 "D03AGNT" 349719 T D03AGNT (NIL) -7 NIL NIL) (-191 347456 348097 348125 "D02EJFA" 348130 T D02EJFA (NIL) -8 NIL NIL) (-190 346774 347415 347443 "D02CJFA" 347448 T D02CJFA (NIL) -8 NIL NIL) (-189 346092 346733 346761 "D02BHFA" 346766 T D02BHFA (NIL) -8 NIL NIL) (-188 345410 346051 346079 "D02BBFA" 346084 T D02BBFA (NIL) -8 NIL NIL) (-187 338608 340196 341802 "D02AGNT" 343824 T D02AGNT (NIL) -7 NIL NIL) (-186 336377 336899 337445 "D01WGTS" 338082 T D01WGTS (NIL) -7 NIL NIL) (-185 335480 336336 336364 "D01TRNS" 336369 T D01TRNS (NIL) -8 NIL NIL) (-184 334583 335439 335467 "D01GBFA" 335472 T D01GBFA (NIL) -8 NIL NIL) (-183 333686 334542 334570 "D01FCFA" 334575 T D01FCFA (NIL) -8 NIL NIL) (-182 332789 333645 333673 "D01ASFA" 333678 T D01ASFA (NIL) -8 NIL NIL) (-181 331892 332748 332776 "D01AQFA" 332781 T D01AQFA (NIL) -8 NIL NIL) (-180 330995 331851 331879 "D01APFA" 331884 T D01APFA (NIL) -8 NIL NIL) (-179 330098 330954 330982 "D01ANFA" 330987 T D01ANFA (NIL) -8 NIL NIL) (-178 329201 330057 330085 "D01AMFA" 330090 T D01AMFA (NIL) -8 NIL NIL) (-177 328304 329160 329188 "D01ALFA" 329193 T D01ALFA (NIL) -8 NIL NIL) (-176 327407 328263 328291 "D01AKFA" 328296 T D01AKFA (NIL) -8 NIL NIL) (-175 326510 327366 327394 "D01AJFA" 327399 T D01AJFA (NIL) -8 NIL NIL) (-174 319814 321363 322922 "D01AGNT" 324971 T D01AGNT (NIL) -7 NIL NIL) (-173 319151 319279 319431 "CYCLOTOM" 319682 T CYCLOTOM (NIL) -7 NIL NIL) (-172 315886 316599 317326 "CYCLES" 318444 T CYCLES (NIL) -7 NIL NIL) (-171 315198 315332 315503 "CVMP" 315747 NIL CVMP (NIL T) -7 NIL NIL) (-170 312979 313237 313612 "CTRIGMNP" 314926 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-169 312584 312667 312772 "CTORCALL" 312894 T CTORCALL (NIL) -8 NIL NIL) (-168 311958 312057 312210 "CSTTOOLS" 312481 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-167 307750 308407 309165 "CRFP" 311270 NIL CRFP (NIL T T) -7 NIL NIL) (-166 306797 306982 307210 "CRAPACK" 307554 NIL CRAPACK (NIL T) -7 NIL NIL) (-165 306181 306282 306486 "CPMATCH" 306673 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-164 305906 305934 306040 "CPIMA" 306147 NIL CPIMA (NIL T T T) -7 NIL NIL) (-163 302270 302942 303660 "COORDSYS" 305241 NIL COORDSYS (NIL T) -7 NIL NIL) (-162 301654 301783 301933 "CONTOUR" 302140 T CONTOUR (NIL) -8 NIL NIL) (-161 297515 299657 300149 "CONTFRAC" 301194 NIL CONTFRAC (NIL T) -8 NIL NIL) (-160 296669 297233 297261 "COMRING" 297266 T COMRING (NIL) -9 NIL 297317) (-159 295750 296027 296211 "COMPPROP" 296505 T COMPPROP (NIL) -8 NIL NIL) (-158 295404 295439 295567 "COMPLPAT" 295709 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-157 285385 295213 295322 "COMPLEX" 295327 NIL COMPLEX (NIL T) -8 NIL NIL) (-156 285021 285078 285185 "COMPLEX2" 285322 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-155 284739 284774 284872 "COMPFACT" 284980 NIL COMPFACT (NIL T T) -7 NIL NIL) (-154 269074 279368 279408 "COMPCAT" 280410 NIL COMPCAT (NIL T) -9 NIL 281803) (-153 258589 261513 265140 "COMPCAT-" 265496 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-152 258320 258348 258450 "COMMUPC" 258555 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-151 258115 258148 258207 "COMMONOP" 258281 T COMMONOP (NIL) -7 NIL NIL) (-150 257698 257866 257953 "COMM" 258048 T COMM (NIL) -8 NIL NIL) (-149 256947 257141 257169 "COMBOPC" 257507 T COMBOPC (NIL) -9 NIL 257682) (-148 255843 256053 256295 "COMBINAT" 256737 NIL COMBINAT (NIL T) -7 NIL NIL) (-147 252041 252614 253254 "COMBF" 255265 NIL COMBF (NIL T T) -7 NIL NIL) (-146 250827 251157 251392 "COLOR" 251826 T COLOR (NIL) -8 NIL NIL) (-145 250467 250514 250639 "CMPLXRT" 250774 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-144 245969 246997 248077 "CLIP" 249407 T CLIP (NIL) -7 NIL NIL) (-143 244303 245073 245311 "CLIF" 245797 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-142 240526 242450 242491 "CLAGG" 243420 NIL CLAGG (NIL T) -9 NIL 243956) (-141 238948 239405 239988 "CLAGG-" 239993 NIL CLAGG- (NIL T T) -8 NIL NIL) (-140 238492 238577 238717 "CINTSLPE" 238857 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-139 235972 236443 236991 "CHVAR" 238020 NIL CHVAR (NIL T T T) -7 NIL NIL) (-138 235195 235759 235787 "CHARZ" 235792 T CHARZ (NIL) -9 NIL 235806) (-137 234949 234989 235067 "CHARPOL" 235149 NIL CHARPOL (NIL T) -7 NIL NIL) (-136 234056 234653 234681 "CHARNZ" 234728 T CHARNZ (NIL) -9 NIL 234783) (-135 232081 232746 233081 "CHAR" 233741 T CHAR (NIL) -8 NIL NIL) (-134 231807 231868 231896 "CFCAT" 232007 T CFCAT (NIL) -9 NIL NIL) (-133 231052 231163 231345 "CDEN" 231691 NIL CDEN (NIL T T T) -7 NIL NIL) (-132 227044 230205 230485 "CCLASS" 230792 T CCLASS (NIL) -8 NIL NIL) (-131 226963 226989 227024 "CATEGORY" 227029 T -10 (NIL) -8 NIL NIL) (-130 221983 222960 223713 "CARTEN" 226266 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-129 221091 221239 221460 "CARTEN2" 221830 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-128 219389 220243 220499 "CARD" 220855 T CARD (NIL) -8 NIL NIL) (-127 218762 219090 219118 "CACHSET" 219250 T CACHSET (NIL) -9 NIL 219327) (-126 218259 218555 218583 "CABMON" 218633 T CABMON (NIL) -9 NIL 218689) (-125 217427 217806 217949 "BYTE" 218136 T BYTE (NIL) -8 NIL NIL) (-124 213375 217374 217408 "BYTEARY" 217413 T BYTEARY (NIL) -8 NIL NIL) (-123 210932 213067 213174 "BTREE" 213301 NIL BTREE (NIL T) -8 NIL NIL) (-122 208430 210580 210702 "BTOURN" 210842 NIL BTOURN (NIL T) -8 NIL NIL) (-121 205849 207902 207943 "BTCAT" 208011 NIL BTCAT (NIL T) -9 NIL 208088) (-120 205516 205596 205745 "BTCAT-" 205750 NIL BTCAT- (NIL T T) -8 NIL NIL) (-119 200737 204608 204636 "BTAGG" 204892 T BTAGG (NIL) -9 NIL 205071) (-118 200160 200304 200534 "BTAGG-" 200539 NIL BTAGG- (NIL T) -8 NIL NIL) (-117 197204 199438 199653 "BSTREE" 199977 NIL BSTREE (NIL T) -8 NIL NIL) (-116 196342 196468 196652 "BRILL" 197060 NIL BRILL (NIL T) -7 NIL NIL) (-115 193044 195071 195112 "BRAGG" 195761 NIL BRAGG (NIL T) -9 NIL 196018) (-114 191573 191979 192534 "BRAGG-" 192539 NIL BRAGG- (NIL T T) -8 NIL NIL) (-113 184773 190911 191095 "BPADICRT" 191421 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-112 183077 184710 184755 "BPADIC" 184760 NIL BPADIC (NIL NIL) -8 NIL NIL) (-111 182773 182803 182916 "BOUNDZRO" 183041 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-110 178288 179379 180246 "BOP" 181926 T BOP (NIL) -8 NIL NIL) (-109 175909 176353 176873 "BOP1" 177801 NIL BOP1 (NIL T) -7 NIL NIL) (-108 174544 175249 175467 "BOOLEAN" 175711 T BOOLEAN (NIL) -8 NIL NIL) (-107 173911 174289 174341 "BMODULE" 174346 NIL BMODULE (NIL T T) -9 NIL 174410) (-106 169721 173709 173782 "BITS" 173858 T BITS (NIL) -8 NIL NIL) (-105 168818 169253 169405 "BINFILE" 169589 T BINFILE (NIL) -8 NIL NIL) (-104 168230 168352 168494 "BINDING" 168696 T BINDING (NIL) -8 NIL NIL) (-103 162064 167674 167839 "BINARY" 168085 T BINARY (NIL) -8 NIL NIL) (-102 159892 161320 161361 "BGAGG" 161621 NIL BGAGG (NIL T) -9 NIL 161758) (-101 159723 159755 159846 "BGAGG-" 159851 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 158821 159107 159312 "BFUNCT" 159538 T BFUNCT (NIL) -8 NIL NIL) (-99 157522 157700 157985 "BEZOUT" 158645 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 154047 156382 156710 "BBTREE" 157225 NIL BBTREE (NIL T) -8 NIL NIL) (-97 153785 153838 153864 "BASTYPE" 153981 T BASTYPE (NIL) -9 NIL NIL) (-96 153640 153669 153739 "BASTYPE-" 153744 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 153078 153154 153304 "BALFACT" 153551 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 151900 152497 152682 "AUTOMOR" 152923 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151626 151631 151657 "ATTREG" 151662 T ATTREG (NIL) -9 NIL NIL) (-92 149905 150323 150675 "ATTRBUT" 151292 T ATTRBUT (NIL) -8 NIL NIL) (-91 149441 149554 149580 "ATRIG" 149781 T ATRIG (NIL) -9 NIL NIL) (-90 149250 149291 149378 "ATRIG-" 149383 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147447 149026 149114 "ASTACK" 149193 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145952 146249 146614 "ASSOCEQ" 147129 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144984 145611 145735 "ASP9" 145859 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144748 144932 144971 "ASP8" 144976 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143617 144353 144495 "ASP80" 144637 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142516 143252 143384 "ASP7" 143516 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141470 142193 142311 "ASP78" 142429 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140439 141150 141267 "ASP77" 141384 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139351 140077 140208 "ASP74" 140339 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 138251 138986 139118 "ASP73" 139250 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 137206 137928 138046 "ASP6" 138164 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136154 136883 137001 "ASP55" 137119 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135104 135828 135947 "ASP50" 136066 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134192 134805 134915 "ASP4" 135025 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 133280 133893 134003 "ASP49" 134113 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 132065 132819 132987 "ASP42" 133169 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130842 131598 131768 "ASP41" 131952 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129792 130519 130637 "ASP35" 130755 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129557 129740 129779 "ASP34" 129784 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 129294 129361 129437 "ASP33" 129512 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 128189 128929 129061 "ASP31" 129193 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127954 128137 128176 "ASP30" 128181 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127689 127758 127834 "ASP29" 127909 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127454 127637 127676 "ASP28" 127681 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 127219 127402 127441 "ASP27" 127446 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 126303 126917 127028 "ASP24" 127139 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 125219 125944 126074 "ASP20" 126204 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124307 124920 125030 "ASP1" 125140 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 123251 123981 124100 "ASP19" 124219 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122988 123055 123131 "ASP12" 123206 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121840 122587 122731 "ASP10" 122875 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119739 121684 121775 "ARRAY2" 121780 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115555 119387 119501 "ARRAY1" 119656 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114587 114760 114981 "ARRAY12" 115378 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108947 110818 110893 "ARR2CAT" 113523 NIL ARR2CAT (NIL T T T) -9 NIL 114281) (-54 106381 107125 108079 "ARR2CAT-" 108084 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 105141 105291 105594 "APPRULE" 106219 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 104794 104842 104960 "APPLYORE" 105087 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 103768 104059 104254 "ANY" 104617 T ANY (NIL) -8 NIL NIL) (-50 103046 103169 103326 "ANY1" 103642 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100578 101496 101821 "ANTISYM" 102771 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100093 100282 100379 "ANON" 100499 T ANON (NIL) -8 NIL NIL) (-47 94170 98638 99089 "AN" 99660 T AN (NIL) -8 NIL NIL) (-46 90524 91922 91972 "AMR" 92711 NIL AMR (NIL T T) -9 NIL 93310) (-45 89637 89858 90220 "AMR-" 90225 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74187 89554 89615 "ALIST" 89620 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71024 73781 73950 "ALGSC" 74105 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 67580 68134 68741 "ALGPKG" 70464 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 66857 66958 67142 "ALGMFACT" 67466 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 62606 63287 63941 "ALGMANIP" 66381 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 53925 62232 62382 "ALGFF" 62539 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53121 53252 53431 "ALGFACT" 53783 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52112 52722 52760 "ALGEBRA" 52820 NIL ALGEBRA (NIL T) -9 NIL 52878) (-36 51830 51889 52021 "ALGEBRA-" 52026 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34091 49834 49886 "ALAGG" 50022 NIL ALAGG (NIL T T) -9 NIL 50183) (-34 33627 33740 33766 "AHYP" 33967 T AHYP (NIL) -9 NIL NIL) (-33 32558 32806 32832 "AGG" 33331 T AGG (NIL) -9 NIL 33610) (-32 31992 32154 32368 "AGG-" 32373 NIL AGG- (NIL T) -8 NIL NIL) (-31 29675 30093 30510 "AF" 31635 NIL AF (NIL T T) -7 NIL NIL) (-30 28944 29202 29358 "ACPLOT" 29537 T ACPLOT (NIL) -8 NIL NIL) (-29 18411 26357 26408 "ACFS" 27119 NIL ACFS (NIL T) -9 NIL 27358) (-28 16425 16915 17690 "ACFS-" 17695 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12693 14649 14675 "ACF" 15554 T ACF (NIL) -9 NIL 15966) (-26 11397 11731 12224 "ACF-" 12229 NIL ACF- (NIL T) -8 NIL NIL) (-25 10996 11165 11191 "ABELSG" 11283 T ABELSG (NIL) -9 NIL 11348) (-24 10863 10888 10954 "ABELSG-" 10959 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10233 10494 10520 "ABELMON" 10690 T ABELMON (NIL) -9 NIL 10802) (-22 9897 9981 10119 "ABELMON-" 10124 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9232 9578 9604 "ABELGRP" 9729 T ABELGRP (NIL) -9 NIL 9811) (-20 8695 8824 9040 "ABELGRP-" 9045 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
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(|partial| -12 (-5 *5 (-1 (-3 (-525) "failed") *4)) (-4 *4 (-976)) + (-5 *2 (-525)) (-5 *1 (-508 *4 *3)) (-4 *3 (-1148 *4))))) +(((*1 *2 *3 *4 *4) + (-12 (-5 *4 (-713)) (-4 *5 (-327)) (-4 *6 (-1148 *5)) + (-5 *2 + (-592 + (-2 (|:| -2499 (-632 *6)) (|:| |basisDen| *6) + (|:| |basisInv| (-632 *6))))) + (-5 *1 (-471 *5 *6 *7)) + (-5 *3 + (-2 (|:| -2499 (-632 *6)) (|:| |basisDen| *6) + (|:| |basisInv| (-632 *6)))) + (-4 *7 (-1148 *6))))) +(((*1 *2 *3) + (-12 (-4 *1 (-320 *4 *3 *5)) (-4 *4 (-1130)) (-4 *3 (-1148 *4)) + (-4 *5 (-1148 (-385 *3))) (-5 *2 (-108)))) + ((*1 *2 *3) + (-12 (-4 *1 (-320 *3 *4 *5)) (-4 *3 (-1130)) (-4 *4 (-1148 *3)) + (-4 *5 (-1148 (-385 *4))) (-5 *2 (-108))))) (((*1 *2 *3) (-12 (-5 *3 (-1090)) (-4 *4 (-13 (-429) (-789) (-967 (-525)) (-588 (-525)))) @@ -28,26 +261,6 @@ (-4 *3 (-13 (-27) (-1112) (-408 *6))) (-4 *6 (-13 (-429) (-789) (-967 (-525)) (-588 (-525)))) (-5 *2 (-51)) (-5 *1 (-293 *6 *3)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 (-525))) (-5 *4 (-273 *6)) - (-4 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*2 *2) @@ -1766,6 +1167,7 @@ ((*1 *2 *2) (-12 (-4 *3 (-37 (-385 (-525)))) (-4 *4 (-1132 *3)) (-5 *1 (-258 *3 *4 *2 *5)) (-4 *2 (-1155 *3 *4)) (-4 *5 (-915 *4)))) + ((*1 *1 *1) (-4 *1 (-466))) ((*1 *2 *2) (-12 (-5 *2 (-1071 *3)) (-4 *3 (-37 (-385 (-525)))) (-5 *1 (-1076 *3)))) @@ -1773,15 +1175,25 @@ (-12 (-5 *2 (-1071 *3)) (-4 *3 (-37 (-385 (-525)))) (-5 *1 (-1077 *3))))) (((*1 *2 *2) - (|partial| -12 (-5 *2 (-1086 *3)) (-4 *3 (-327)) (-5 *1 (-335 *3))))) + (-12 (-4 *3 (-13 (-517) (-138))) (-5 *1 (-502 *3 *2)) + (-4 *2 (-1163 *3)))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-341) (-346) (-567 (-525)))) (-4 *4 (-1148 *3)) + (-4 *5 (-667 *3 *4)) (-5 *1 (-506 *3 *4 *5 *2)) (-4 *2 (-1163 *5)))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-341) (-346) (-567 (-525)))) (-5 *1 (-507 *3 *2)) + (-4 *2 (-1163 *3)))) + ((*1 *2 *2) + (-12 (-5 *2 (-1071 *3)) (-4 *3 (-13 (-517) (-138))) + (-5 *1 (-1067 *3))))) (((*1 *1 *1 *1) (-4 *1 (-21))) ((*1 *1 *1) (-4 *1 (-21))) ((*1 *1 *1 *1) (|partial| -5 *1 (-128))) ((*1 *1 *1 *1) (-12 (-5 *1 (-195 *2)) (-4 *2 (-13 (-789) - (-10 -8 (-15 -1496 ((-1073) $ (-1090))) (-15 -3686 ((-1177) $)) - (-15 -2460 ((-1177) $))))))) + (-10 -8 (-15 -3928 ((-1073) $ (-1090))) (-15 -3303 ((-1177) $)) + (-15 -1558 ((-1177) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-273 *2)) (-4 *2 (-21)) (-4 *2 (-1126)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-273 *2)) (-4 *2 (-21)) (-4 *2 (-1126)))) ((*1 *1 *1 *1) @@ -1801,43 +1213,38 @@ ((*1 *2 *2 *2) (-12 (-5 *2 (-877 (-205))) (-5 *1 (-1123)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1170 *2)) (-4 *2 (-1126)) (-4 *2 (-21)))) ((*1 *1 *1) (-12 (-4 *1 (-1170 *2)) (-4 *2 (-1126)) (-4 *2 (-21))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-995 *4 *5 *6 *3)) (-4 *4 (-429)) (-4 *5 (-735)) - (-4 *6 (-789)) (-4 *3 (-990 *4 *5 *6)) (-5 *2 (-108))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-525)) (-5 *1 (-294 *3)) (-4 *3 (-517)) (-4 *3 (-789))))) -(((*1 *2 *3) (-12 (-5 *3 (-205)) (-5 *2 (-294 (-357))) (-5 *1 (-284))))) -(((*1 *2 *3) (-12 (-5 *3 (-592 (-51))) (-5 *2 (-1177)) (-5 *1 (-798))))) 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(-4 *4 (-1148 *3)) - (-4 *5 (-1148 (-385 *4))) (-5 *2 (-632 (-385 *4)))))) -(((*1 *2 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-855)) (-5 *1 (-728))))) -(((*1 *2 *1) (-12 (-5 *2 (-592 (-1073))) (-5 *1 (-372)))) - ((*1 *2 *1) (-12 (-5 *2 (-592 (-1073))) (-5 *1 (-1107))))) -(((*1 *1 *1) (-4 *1 (-34))) - ((*1 *2 *2) +(((*1 *2 *2 *2 *2 *2 *2) + (-12 (-4 *2 (-13 (-341) (-10 -8 (-15 ** ($ $ (-385 (-525))))))) + (-5 *1 (-1045 *3 *2)) (-4 *3 (-1148 *2))))) +(((*1 *2 *1 *1) (-12 (-4 *1 (-941 *3)) (-4 *3 (-1126)) (-5 *2 (-525))))) +(((*1 *2 *1) (-12 (-5 *2 (-205)) (-5 *1 (-764))))) +(((*1 *2 *2) + (-12 (-5 *2 (-592 *6)) (-4 *6 (-883 *3 *4 *5)) (-4 *3 (-286)) + (-4 *4 (-735)) (-4 *5 (-789)) (-5 *1 (-424 *3 *4 *5 *6)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-592 *7)) (-5 *3 (-1073)) (-4 *7 (-883 *4 *5 *6)) + (-4 *4 (-286)) (-4 *5 (-735)) (-4 *6 (-789)) + (-5 *1 (-424 *4 *5 *6 *7)))) + ((*1 *2 *2 *3 *3) + (-12 (-5 *2 (-592 *7)) (-5 *3 (-1073)) (-4 *7 (-883 *4 *5 *6)) + (-4 *4 (-286)) (-4 *5 (-735)) (-4 *6 (-789)) + (-5 *1 (-424 *4 *5 *6 *7))))) +(((*1 *1 *2 *3) + (-12 (-5 *1 (-897 *2 *3)) (-4 *2 (-1019)) (-4 *3 (-1019))))) +(((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-593 *3)) (-4 *3 (-1019))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-592 *8)) (-5 *4 (-592 *9)) (-4 *8 (-990 *5 *6 *7)) + (-4 *9 (-995 *5 *6 *7 *8)) (-4 *5 (-429)) (-4 *6 (-735)) + (-4 *7 (-789)) (-5 *2 (-713)) (-5 *1 (-993 *5 *6 *7 *8 *9)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-592 *8)) (-5 *4 (-592 *9)) (-4 *8 (-990 *5 *6 *7)) + (-4 *9 (-1028 *5 *6 *7 *8)) (-4 *5 (-429)) (-4 *6 (-735)) + (-4 *7 (-789)) (-5 *2 (-713)) (-5 *1 (-1060 *5 *6 *7 *8 *9))))) +(((*1 *2 *1 *1) + (-12 (-5 *2 (-385 (-886 *3))) (-5 *1 (-430 *3 *4 *5 *6)) + (-4 *3 (-517)) (-4 *3 (-160)) (-14 *4 (-855)) + (-14 *5 (-592 (-1090))) (-14 *6 (-1172 (-632 *3)))))) +(((*1 *2 *2) (-12 (-4 *3 (-13 (-789) (-517))) (-5 *1 (-255 *3 *2)) (-4 *2 (-13 (-408 *3) (-933))))) ((*1 *2 *2) @@ -1846,19 +1253,23 @@ ((*1 *2 *2) (-12 (-4 *3 (-37 (-385 (-525)))) (-4 *4 (-1132 *3)) (-5 *1 (-258 *3 *4 *2 *5)) (-4 *2 (-1155 *3 *4)) (-4 *5 (-915 *4)))) + ((*1 *1 *1) (-4 *1 (-466))) ((*1 *2 *2) (-12 (-5 *2 (-1071 *3)) (-4 *3 (-37 (-385 (-525)))) (-5 *1 (-1076 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1071 *3)) (-4 *3 (-37 (-385 (-525)))) (-5 *1 (-1077 *3))))) +(((*1 *2 *3 *1) + (-12 (-5 *3 (-1055 *4 *5)) (-4 *4 (-13 (-1019) (-33))) + (-4 *5 (-13 (-1019) (-33))) (-5 *2 (-108)) (-5 *1 (-1056 *4 *5))))) (((*1 *1 *1 *1) (-4 *1 (-25))) ((*1 *1 *1 *1) (-5 *1 (-146))) ((*1 *1 *1 *1) (-12 (-5 *1 (-195 *2)) (-4 *2 (-13 (-789) - (-10 -8 (-15 -1496 ((-1073) $ (-1090))) (-15 -3686 ((-1177) $)) - (-15 -2460 ((-1177) $))))))) + (-10 -8 (-15 -3928 ((-1073) $ (-1090))) (-15 -3303 ((-1177) $)) + (-15 -1558 ((-1177) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-273 *2)) (-4 *2 (-25)) (-4 *2 (-1126)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-273 *2)) (-4 *2 (-25)) (-4 *2 (-1126)))) ((*1 *1 *2 *1) @@ -1881,510 +1292,43 @@ (-12 (-5 *2 (-1071 *3)) (-4 *3 (-976)) (-5 *1 (-1075 *3)))) ((*1 *2 *2 *2) (-12 (-5 *2 (-877 (-205))) (-5 *1 (-1123)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1170 *2)) (-4 *2 (-1126)) (-4 *2 (-25))))) -(((*1 *1 *1 *2) - (-12 (-4 *1 (-908 *3 *4 *2 *5)) (-4 *3 (-976)) (-4 *4 (-735)) - (-4 *2 (-789)) (-4 *5 (-990 *3 *4 *2))))) -(((*1 *2 *1) (-12 (-4 *1 (-1013 *2)) (-4 *2 (-1126))))) -(((*1 *2 *1) - (|partial| -12 - (-4 *3 (-13 (-789) (-967 (-525)) (-588 (-525)) (-429))) - (-5 *2 (-782 *4)) (-5 *1 (-291 *3 *4 *5 *6)) - (-4 *4 (-13 (-27) (-1112) (-408 *3))) (-14 *5 (-1090)) - (-14 *6 *4))) - ((*1 *2 *1) - (|partial| -12 - (-4 *3 (-13 (-789) (-967 (-525)) (-588 (-525)) (-429))) - (-5 *2 (-782 *4)) (-5 *1 (-1158 *3 *4 *5 *6)) - (-4 *4 (-13 (-27) (-1112) (-408 *3))) (-14 *5 (-1090)) - (-14 *6 *4)))) -(((*1 *1 *2) (-12 (-5 *2 (-385 (-525))) (-5 *1 (-103)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-592 (-501))) (-5 *1 (-501))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1086 (-525))) (-5 *1 (-876)) (-5 *3 (-525)))) - ((*1 *2 *2) - (-12 (-4 *3 (-286)) (-4 *4 (-351 *3)) (-4 *5 (-351 *3)) - (-5 *1 (-1041 *3 *4 *5 *2)) (-4 *2 (-630 *3 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(-782 (-205)))) (|:| |abserr| (-205)) - (|:| |relerr| (-205))))))) -(((*1 *2 *3) - (-12 (-5 *3 (-713)) (-5 *2 (-1086 *4)) (-5 *1 (-495 *4)) - (-4 *4 (-327))))) -(((*1 *1 *1 *2) (-12 (-4 *1 (-943)) (-5 *2 (-797))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-592 (-1073))) (-5 *1 (-372)))) - ((*1 *2 *1 *2) (-12 (-5 *2 (-592 (-1073))) (-5 *1 (-1107))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1090)) (-5 *4 (-886 (-525))) (-5 *2 (-308)) - (-5 *1 (-310))))) -(((*1 *1 *1) (-4 *1 (-34))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-789) (-517))) (-5 *1 (-255 *3 *2)) - (-4 *2 (-13 (-408 *3) (-933))))) - ((*1 *2 *2) - (-12 (-4 *3 (-37 (-385 (-525)))) (-4 *4 (-1163 *3)) - (-5 *1 (-257 *3 *4 *2)) (-4 *2 (-1134 *3 *4)))) - ((*1 *2 *2) - (-12 (-4 *3 (-37 (-385 (-525)))) (-4 *4 (-1132 *3)) - (-5 *1 (-258 *3 *4 *2 *5)) (-4 *2 (-1155 *3 *4)) (-4 *5 (-915 *4)))) - ((*1 *2 *2) - (-12 (-5 *2 (-1071 *3)) (-4 *3 (-37 (-385 (-525)))) - (-5 *1 (-1076 *3)))) - ((*1 *2 *2) - (-12 (-5 *2 (-1071 *3)) (-4 *3 (-37 (-385 (-525)))) - (-5 *1 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+ (-12 (-5 *3 (-592 (-592 (-877 (-205))))) (-5 *4 (-592 (-242))) + (-5 *2 (-1173)) (-5 *1 (-1176))))) +(((*1 *2 *2) + (-12 (-5 *2 (-1071 *3)) (-4 *3 (-976)) (-5 *1 (-1075 *3)))) + ((*1 *1 *1) + (-12 (-5 *1 (-1164 *2 *3 *4)) (-4 *2 (-976)) (-14 *3 (-1090)) + (-14 *4 *2)))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-713)) (-5 *2 (-108)) (-5 *1 (-543 *3)) (-4 *3 (-510))))) (((*1 *2 *2 *2) - (-12 (-5 *2 (-592 *3)) (-4 *3 (-789)) (-5 *1 (-682 *3))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5) - (-12 (-5 *3 (-1 (-357) (-357))) (-5 *4 (-357)) - (-5 *2 - (-2 (|:| -3067 *4) (|:| -2263 *4) (|:| |totalpts| (-525)) - (|:| |success| (-108)))) - (-5 *1 (-731)) (-5 *5 (-525))))) -(((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-899 *3)) (-4 *3 (-900))))) -(((*1 *2) - (-12 (-4 *1 (-320 *3 *4 *5)) (-4 *3 (-1130)) (-4 *4 (-1148 *3)) - (-4 *5 (-1148 (-385 *4))) (-5 *2 (-108))))) + (-12 (-5 *2 (-1071 *3)) (-4 *3 (-341)) (-4 *3 (-976)) + (-5 *1 (-1075 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-592 (-1090))) (-5 *1 (-767))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-976)) (-5 *1 (-1144 *3 *2)) (-4 *2 (-1148 *3))))) +(((*1 *2 *3) + (|partial| -12 + (-5 *3 + (-2 (|:| |xinit| (-205)) (|:| |xend| (-205)) + (|:| |fn| (-1172 (-294 (-205)))) (|:| |yinit| (-592 (-205))) + (|:| |intvals| (-592 (-205))) (|:| |g| (-294 (-205))) + (|:| |abserr| (-205)) (|:| |relerr| (-205)))) + (-5 *2 + (-2 (|:| |stiffness| (-357)) (|:| |stability| (-357)) + (|:| |expense| (-357)) (|:| |accuracy| (-357)) + (|:| |intermediateResults| (-357)))) + (-5 *1 (-745))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-789) (-517))) (-5 *1 (-255 *3 *2)) (-4 *2 (-13 (-408 *3) (-933))))) @@ -2467,67 +1412,53 @@ ((*1 *2 *2) (-12 (-5 *2 (-1071 *3)) (-4 *3 (-37 (-385 (-525)))) (-5 *1 (-1077 *3))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-592 *6)) (-4 *6 (-990 *3 *4 *5)) (-4 *3 (-138)) - (-4 *3 (-286)) (-4 *3 (-517)) (-4 *4 (-735)) (-4 *5 (-789)) - (-5 *1 (-909 *3 *4 *5 *6))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-97)) (-5 *2 (-108)))) - ((*1 *1 *2 *2) (-12 (-5 *1 (-273 *2)) (-4 *2 (-1126)))) - ((*1 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*2 (-592 *3)) (-4 *3 (-1126)) (-5 *1 (-1071 *3))))) +(((*1 *2 *3 *4 *5 *3 *6 *3) + (-12 (-5 *3 (-525)) (-5 *4 (-205)) (-5 *5 (-157 (-205))) + (-5 *6 (-1073)) (-5 *2 (-965)) (-5 *1 (-701))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-789) (-517))) (-5 *1 (-255 *3 *2)) (-4 *2 (-13 (-408 *3) (-933))))) @@ -2547,46 +1478,63 @@ ((*1 *2 *2) (-12 (-5 *2 (-1071 *3)) (-4 *3 (-37 (-385 (-525)))) (-5 *1 (-1077 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-542 *3)) (-4 *3 (-341))))) +(((*1 *2 *1 *1) (-12 (-4 *1 (-789)) (-5 *2 (-108)))) + ((*1 *1 *1 *1) (-5 *1 (-797)))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-205)) (-5 *4 (-525)) (-5 *2 (-965)) (-5 *1 (-701))))) -(((*1 *2 *2) - (-12 (-5 *2 (-877 *3)) (-4 *3 (-13 (-341) (-1112) (-933))) - (-5 *1 (-163 *3))))) -(((*1 *2 *1) - (-12 (-5 *2 (-807 (-899 *3) (-899 *3))) (-5 *1 (-899 *3)) - (-4 *3 (-900))))) -(((*1 *1 *2) (-12 (-5 *2 (-592 *1)) (-4 *1 (-281)))) - ((*1 *1 *1) (-4 *1 (-281))) ((*1 *1 *1) (-5 *1 (-797)))) -(((*1 *2 *3 *1) (-12 (-5 *3 (-1090)) (-5 *2 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(-5 *1 (-1075 *4)) (-4 *4 (-976)) + (-5 *3 (-525))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1148 *5)) (-4 *5 (-341)) (-5 *2 - (-592 - (-2 (|:| |radval| (-294 (-525))) (|:| |radmult| (-525)) - (|:| |radvect| (-592 (-632 (-294 (-525)))))))) - (-5 *1 (-961))))) -(((*1 *2 *1) - (-12 (-5 *2 (-592 *4)) (-5 *1 (-1056 *3 *4)) - (-4 *3 (-13 (-1019) (-33))) (-4 *4 (-13 (-1019) (-33)))))) -(((*1 *2 *1) (-12 (-5 *2 (-396 *3)) (-5 *1 (-848 *3)) (-4 *3 (-286))))) -(((*1 *2 *2 *3) - (-12 (-4 *3 (-341)) (-5 *1 (-264 *3 *2)) (-4 *2 (-1163 *3))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-995 *4 *5 *6 *3)) (-4 *4 (-429)) (-4 *5 (-735)) - (-4 *6 (-789)) (-4 *3 (-990 *4 *5 *6)) (-5 *2 (-108))))) + (-2 (|:| |ir| (-542 (-385 *6))) (|:| |specpart| (-385 *6)) + (|:| |polypart| *6))) + (-5 *1 (-535 *5 *6)) (-5 *3 (-385 *6))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-713)) (-4 *5 (-976)) (-5 *2 (-525)) + (-5 *1 (-420 *5 *3 *6)) (-4 *3 (-1148 *5)) + (-4 *6 (-13 (-382) (-967 *5) (-341) (-1112) (-263))))) + ((*1 *2 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*5)) (-4 *4 (-351 *5)) + (-5 *2 + (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2499 (-592 *4)))) + (-5 *1 (-1041 *5 *6 *4 *3)) (-4 *3 (-630 *5 *6 *4))))) (((*1 *2 *2 *3) (|partial| -12 (-5 *2 (-592 (-1086 *5))) (-5 *3 (-1086 *5)) (-4 *5 (-154 *4)) (-4 *4 (-510)) (-5 *1 (-140 *4 *5)))) @@ -8794,22 +9287,135 @@ ((*1 *2 *2 *3) (|partial| -12 (-5 *2 (-592 (-1086 *1))) (-5 *3 (-1086 *1)) (-4 *1 (-843))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-205)) (-5 *4 (-525)) (-5 *2 (-965)) (-5 *1 (-701))))) +(((*1 *2 *1) + (-12 (-4 *1 (-55 *3 *4 *5)) (-4 *3 (-1126)) (-4 *4 (-351 *3)) + (-4 *5 (-351 *3)) (-5 *2 (-713)))) + ((*1 *2 *1) + (-12 (-4 *1 (-979 *3 *4 *5 *6 *7)) (-4 *5 (-976)) + (-4 *6 (-218 *4 *5)) (-4 *7 (-218 *3 *5)) (-5 *2 (-713))))) +(((*1 *2 *3 *4 *2 *5 *6 *7 *8 *9 *10) + (|partial| -12 (-5 *2 (-592 (-1086 *13))) (-5 *3 (-1086 *13)) + (-5 *4 (-592 *12)) (-5 *5 (-592 *10)) (-5 *6 (-592 *13)) + (-5 *7 (-592 (-592 (-2 (|:| -3264 (-713)) (|:| |pcoef| *13))))) + (-5 *8 (-592 (-713))) (-5 *9 (-1172 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+ (-5 *1 (-531 *6)) (-5 *3 (-385 (-886 *6)))))) +(((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-592 (-242))) (-5 *4 (-1090)) + (-5 *1 (-241 *2)) (-4 *2 (-1126)))) + ((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-592 (-242))) (-5 *4 (-1090)) (-5 *2 (-51)) + (-5 *1 (-242))))) +(((*1 *2 *1) (-12 (-5 *2 (-1177)) (-5 *1 (-228))))) +(((*1 *2 *3 *3 *4 *3 *4 *4 *4 *5 *5 *5 *5 *4 *4 *6 *7) + (-12 (-5 *3 (-205)) (-5 *4 (-525)) (-5 *5 (-632 (-205))) + (-5 *6 (-3 (|:| |fn| (-366)) (|:| |fp| (-82 FCNF)))) + (-5 *7 (-3 (|:| |fn| (-366)) (|:| |fp| (-83 FCNG)))) (-5 *2 (-965)) + (-5 *1 (-692))))) (((*1 *2 *3) - (-12 (-5 *3 (-205)) (-5 *2 (-108)) (-5 *1 (-278 *4 *5)) (-14 *4 *3) - (-14 *5 *3))) + (-12 (-5 *3 (-205)) (-5 *2 (-108)) (-5 *1 (-278 *4 *5)) + (-14 *4 (-205)) (-14 *5 (-205)))) ((*1 *2 *3 *4) - (-12 (-5 *4 (-1014 (-782 (-205)))) (-5 *3 (-205)) (-5 *2 (-108)) + (-12 (-5 *3 (-205)) (-5 *4 (-1014 (-782 (-205)))) (-5 *2 (-108)) (-5 *1 (-284)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-341)) (-4 *4 (-735)) (-4 *5 (-789)) (-5 *2 (-108)) (-5 *1 (-477 *3 *4 *5 *6)) (-4 *6 (-883 *3 *4 *5))))) +(((*1 *2 *1) + (-12 (-4 *1 (-55 *3 *4 *5)) (-4 *3 (-1126)) (-4 *4 (-351 *3)) + (-4 *5 (-351 *3)) (-5 *2 (-713)))) + ((*1 *2 *1) + (-12 (-4 *1 (-979 *3 *4 *5 *6 *7)) (-4 *5 (-976)) + (-4 *6 (-218 *4 *5)) (-4 *7 (-218 *3 *5)) (-5 *2 (-713))))) +(((*1 *1 *2) + (|partial| -12 (-5 *2 (-1185 *3 *4)) (-4 *3 (-789)) (-4 *4 (-160)) + (-5 *1 (-610 *3 *4)))) + ((*1 *2 *1) + (|partial| -12 (-5 *2 (-610 *3 *4)) (-5 *1 (-1190 *3 *4)) + (-4 *3 (-789)) (-4 *4 (-160))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-915 *2)) (-4 *2 (-1112))))) +(((*1 *2 *1 *2) (-12 (-5 *2 (-108)) (-5 *1 (-1122 *3)) (-4 *3 (-906))))) +(((*1 *2 *3) + (-12 (-5 *3 (-632 (-385 (-886 (-525))))) + (-5 *2 (-592 (-632 (-294 (-525))))) (-5 *1 (-961))))) +(((*1 *2 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1126))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-429)) (-4 *5 (-735)) (-4 *6 (-789)) + (-4 *7 (-990 *4 *5 *6)) (-5 *2 (-108)) (-5 *1 (-920 *4 *5 *6 *7 *3)) + (-4 *3 (-995 *4 *5 *6 *7)))) + ((*1 *2 *3 *3) + (-12 (-4 *4 (-429)) (-4 *5 (-735)) (-4 *6 (-789)) + (-4 *7 (-990 *4 *5 *6)) (-5 *2 (-108)) + (-5 *1 (-1026 *4 *5 *6 *7 *3)) (-4 *3 (-995 *4 *5 *6 *7))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |var| (-1090)) (|:| |fn| (-294 (-205))) + (|:| -4162 (-1014 (-782 (-205)))) (|:| |abserr| (-205)) + (|:| |relerr| (-205)))) + (-5 *2 (-357)) (-5 *1 (-174))))) +(((*1 *2 *2 *3 *2) + (-12 (-5 *3 (-713)) (-4 *4 (-327)) (-5 *1 (-197 *4 *2)) + (-4 *2 (-1148 *4))))) (((*1 *2) (-12 (-4 *4 (-160)) (-5 *2 (-108)) (-5 *1 (-344 *3 *4)) (-4 *3 (-345 *4)))) ((*1 *2) (-12 (-4 *1 (-345 *3)) (-4 *3 (-160)) (-5 *2 (-108))))) +(((*1 *2 *3) (-12 (-5 *3 (-357)) (-5 *2 (-205)) (-5 *1 (-284))))) +(((*1 *2 *2) (-12 (-5 *2 (-294 (-205))) (-5 *1 (-246))))) (((*1 *2 *3) - (-12 (-5 *3 (-826 *4)) (-4 *4 (-1019)) (-5 *2 (-1 (-108) *5)) - (-5 *1 (-824 *4 *5)) (-4 *5 (-1126))))) + (-12 (-4 *4 (-13 (-341) (-787))) (-5 *2 (-157 *4)) + (-5 *1 (-167 *4 *3)) (-4 *3 (-1148 (-157 *4)))))) +(((*1 *1) + (-12 (-5 *1 (-130 *2 *3 *4)) (-14 *2 (-525)) (-14 *3 (-713)) + (-4 *4 (-160))))) +(((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-1095))))) +(((*1 *1 *2) + (-12 (-5 *2 (-592 (-855))) (-5 *1 (-1020 *3 *4)) (-14 *3 (-855)) + (-14 *4 (-855))))) +(((*1 *2 *3) + (-12 (-5 *2 (-110)) (-5 *1 (-109 *3)) (-4 *3 (-789)) (-4 *3 (-1019))))) +(((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-826 *3)) (-4 *3 (-1019)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1022 *3 *4 *5 *6 *7)) (-4 *3 (-1019)) (-4 *4 (-1019)) + (-4 *5 (-1019)) (-4 *6 (-1019)) (-4 *7 (-1019)) (-5 *2 (-108))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-592 (-1090))) (-4 *4 (-1019)) + (-4 *5 (-13 (-976) (-820 *4) (-789) (-567 (-826 *4)))) + (-5 *1 (-53 *4 *5 *2)) + (-4 *2 (-13 (-408 *5) (-820 *4) (-567 (-826 *4))))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-632 *3)) (-4 *3 (-976)) (-5 *1 (-633 *3)))) + ((*1 *2 *2 *2 *2) + (-12 (-5 *2 (-632 *3)) (-4 *3 (-976)) (-5 *1 (-633 *3))))) (((*1 *2 *3 *4 *4 *2 *2 *2) (-12 (-5 *2 (-525)) (-5 *3 @@ -8817,27 +9423,527 @@ (|:| |polj| *4))) (-4 *6 (-735)) (-4 *4 (-883 *5 *6 *7)) (-4 *5 (-429)) (-4 *7 (-789)) (-5 *1 (-426 *5 *6 *7 *4))))) +(((*1 *2 *1) (-12 (-4 *3 (-976)) (-5 *2 (-592 *1)) (-4 *1 (-1051 *3))))) +(((*1 *2 *1 *1) + (-12 (-4 *1 (-990 *3 *4 *5)) (-4 *3 (-976)) (-4 *4 (-735)) + (-4 *5 (-789)) (-5 *2 (-108))))) +(((*1 *1 *2) + (-12 (-5 *2 (-385 (-525))) (-4 *1 (-515 *3)) + (-4 *3 (-13 (-382) (-1112))))) + ((*1 *1 *2) (-12 (-4 *1 (-515 *2)) (-4 *2 (-13 (-382) (-1112))))) + ((*1 *1 *2 *2) (-12 (-4 *1 (-515 *2)) (-4 *2 (-13 (-382) (-1112)))))) +(((*1 *2 *3 *3 *4 *4) + (-12 (-5 *3 (-632 (-205))) (-5 *4 (-525)) (-5 *2 (-965)) + (-5 *1 (-691))))) +(((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-110))))) +(((*1 *2 *2 *3) + (-12 (-4 *3 (-341)) (-5 *1 (-264 *3 *2)) (-4 *2 (-1163 *3))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-525)) (-5 *1 (-305 *3)) (-4 *3 (-1126)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-525)) (-5 *1 (-488 *3 *4)) (-4 *3 (-1126)) + (-14 *4 (-525))))) +(((*1 *2 *2) (|partial| -12 (-5 *2 (-294 (-205))) (-5 *1 (-246))))) +(((*1 *1 *2 *3 *3 *3 *4) + (-12 (-4 *4 (-341)) (-4 *3 (-1148 *4)) (-4 *5 (-1148 (-385 *3))) + (-4 *1 (-313 *4 *3 *5 *2)) (-4 *2 (-320 *4 *3 *5)))) + ((*1 *1 *2 *2 *3) + (-12 (-5 *3 (-525)) (-4 *2 (-341)) (-4 *4 (-1148 *2)) + (-4 *5 (-1148 (-385 *4))) (-4 *1 (-313 *2 *4 *5 *6)) + (-4 *6 (-320 *2 *4 *5)))) + ((*1 *1 *2 *2) + (-12 (-4 *2 (-341)) (-4 *3 (-1148 *2)) (-4 *4 (-1148 (-385 *3))) + (-4 *1 (-313 *2 *3 *4 *5)) (-4 *5 (-320 *2 *3 *4)))) + ((*1 *1 *2) + (-12 (-4 *3 (-341)) (-4 *4 (-1148 *3)) (-4 *5 (-1148 (-385 *4))) + (-4 *1 (-313 *3 *4 *5 *2)) (-4 *2 (-320 *3 *4 *5)))) + ((*1 *1 *2) + (-12 (-5 *2 (-391 *4 (-385 *4) *5 *6)) (-4 *4 (-1148 *3)) + (-4 *5 (-1148 (-385 *4))) (-4 *6 (-320 *3 *4 *5)) (-4 *3 (-341)) + (-4 *1 (-313 *3 *4 *5 *6))))) +(((*1 *2 *1) + (-12 (-4 *1 (-232 *3 *4 *2 *5)) (-4 *3 (-976)) (-4 *4 (-789)) + (-4 *5 (-735)) (-4 *2 (-245 *4))))) (((*1 *2 *3) (-12 (-4 *4 (-517)) (-5 *2 (-713)) (-5 *1 (-42 *4 *3)) (-4 *3 (-395 *4))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-517) (-789) (-967 (-525)))) (-5 *1 (-170 *3 *2)) + (-4 *2 (-13 (-27) (-1112) (-408 (-157 *3)))))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-429) (-789) (-967 (-525)) (-588 (-525)))) + (-5 *1 (-1116 *3 *2)) (-4 *2 (-13 (-27) (-1112) (-408 *3)))))) +(((*1 *1 *2 *1) (-12 (-4 *1 (-102 *2)) (-4 *2 (-1126)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-117 *2)) (-4 *2 (-789)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-122 *2)) (-4 *2 (-789)))) + ((*1 *1 *1 *1 *2) + (-12 (-5 *2 (-525)) (-4 *1 (-261 *3)) (-4 *3 (-1126)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-525)) (-4 *1 (-261 *2)) (-4 *2 (-1126)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| -3946 + (-2 (|:| |var| (-1090)) (|:| |fn| (-294 (-205))) + (|:| -4162 (-1014 (-782 (-205)))) (|:| |abserr| (-205)) + (|:| |relerr| (-205)))) + (|:| -2511 + (-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| (-1071 (-205))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -4162 + (-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 (-520)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-713)) (-4 *1 (-637 *2)) (-4 *2 (-1019)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| -3946 + (-2 (|:| |xinit| (-205)) (|:| |xend| (-205)) + (|:| |fn| (-1172 (-294 (-205)))) (|:| |yinit| (-592 (-205))) + (|:| |intvals| (-592 (-205))) (|:| |g| (-294 (-205))) + (|:| |abserr| (-205)) (|:| |relerr| (-205)))) + (|:| -2511 + (-2 (|:| |stiffness| (-357)) (|:| |stability| (-357)) + (|:| 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55083) (-4050 . 54866) + (-4051 . 54788) (-4052 . 54686) (-4053 . 54561) (-4054 . 54461) + (-4055 . 54196) (-4056 . 54145) (-4057 . 54042) (-4058 . 53744) + (-4059 . 52560) (-4060 . 52415) (-4061 . 51840) (-4062 . 51658) + (-4063 . 51238) (-4064 . 51167) (-4065 . 51087) (-4066 . 50621) + (-4067 . 50569) (-4068 . 50495) (-4069 . 50356) (-4070 . 49178) + (-4071 . 48732) (-4072 . 48157) (-4073 . 47827) (-4074 . 47718) + (-4075 . 47635) (-4076 . 47320) (-4077 . 47292) (-4078 . 47054) + (-4079 . 45435) (-4080 . 45331) (-4081 . 45260) (-4082 . 43062) + (-4083 . 42855) (-4084 . 42280) (-4085 . 42246) (-4086 . 42194) + (-4087 . 42127) (-4088 . 41833) (-4089 . 41778) (-4090 . 41712) + (-4091 . 41351) (-4092 . 40490) (-4093 . 39298) (-4094 . 39238) + (-4095 . 39131) (-4096 . 38557) (-4097 . 38462) (-4098 . 38279) + (-4099 . 38251) (-4100 . 38091) (-4101 . 37723) (-4102 . 37670) + (-4103 . 37445) (-4104 . 36054) (-4105 . 35279) (-4106 . 35153) + (-4107 . 34838) (-4108 . 33832) (-4109 . 33737) (-4110 . 33163) + (-4111 . 32435) (-4112 . 32047) (-4113 . 31981) (-4114 . 31793) + (-4115 . 31577) (-4116 . 31463) (-4117 . 31378) (-4118 . 31191) + (-4119 . 31048) (-4120 . 30886) (-4121 . 30312) (-4122 . 30171) + (-4123 . 30062) (-4124 . 29896) (-4125 . 29822) (-4126 . 29654) + (-4127 . 29406) (-4128 . 29353) (-4129 . 29058) (-4130 . 28973) + (-4131 . 28904) (-4132 . 28580) (-4133 . 28006) (-4134 . 27937) + (-4135 . 27797) (-4136 . 27466) (-4137 . 27414) (-4138 . 27077) + (-4139 . 26947) (-4140 . 26631) (-4141 . 26553) (-4142 . 26263) + (-4143 . 26192) (-4144 . 26133) (-4145 . 26034) (-4146 . 25978) + (-4147 . 25404) (-4148 . 25283) (-4149 . 25094) (-4150 . 24915) + (-4151 . 24859) (-4152 . 24522) (-4153 . 24415) (-4154 . 24217) + (-4155 . 24005) (-4156 . 23692) (-4157 . 23419) (-4158 . 23278) + (-4159 . 22242) (-4160 . 22208) (-4161 . 21991) (-4162 . 21852) + (-4163 . 21473) (-4164 . 21377) (-4165 . 21322) (-4166 . 21256) + (-4167 . 21046) (-4168 . 19218) (-4169 . 18421) (-4170 . 18366) + (-4171 . 18213) (-4172 . 18099) (-4173 . 17928) (-4174 . 17729) + (-4175 . 17296) (-4176 . 16906) (-4177 . 16765) (-4178 . 16547) + (-4179 . 15024) (-4180 . 14946) (-4181 . 14893) (-4182 . 14506) + (-4183 . 14401) (-4184 . 13992) (-4185 . 13665) (-4186 . 12484) + (-4187 . 12410) (-4188 . 12354) (-4189 . 12130) (-4190 . 11974) + (-4191 . 11896) (-4192 . 10356) (-4193 . 10104) (-4194 . 9775) + (-4195 . 9317) (-4196 . 9236) (-4197 . 9184) (-4198 . 9111) + (-4199 . 9024) (-4200 . 8972) (-4201 . 8869) (-4202 . 8591) + (-4203 . 8450) (-4204 . 7909) (-4205 . 7838) (-4206 . 7700) + (-4207 . 7526) (-4208 . 5675) (-4209 . 5490) (-4210 . 5145) + (-4211 . 4409) (-4212 . 4332) (-4213 . 4117) (-4214 . 3865) + (-4215 . 3655) (-4216 . 3112) (-4217 . 2960) (-4218 . 2880) + (-4219 . 2769) (-4220 . 2688) (-4221 . 2527) (-4222 . 2267) + (-4223 . 1893) (-4224 . 1796) (-4225 . 1730) (-4226 . 1502) + (-4227 . 1398) (-4228 . 1079) (-4229 . 981) (-4230 . 798) + (-4231 . 696) (-4232 . 570) (-4233 . 521) (-4234 . 30))
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