diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/share/algebra/browse.daase | 762 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1134 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1283 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8288 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 28536 |
5 files changed, 20002 insertions, 20001 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index cb82cb8b..91aa82b0 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2241087 . 3422100676) +(2241088 . 3424116440) (-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."))) -((-4256 . T) (-4255 . T) (-1355 . T)) +((-4256 . T) (-4255 . T) (-1324 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4252 . T) (-4250 . T) (-4249 . T) ((-4257 "*") . T) (-4248 . T) (-4253 . T) (-4247 . T) (-1355 . T)) +((-4252 . T) (-4250 . T) (-4249 . T) ((-4257 "*") . T) (-4248 . T) (-4253 . T) (-4247 . T) (-1324 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -3855) +(-31 R -3837) ((|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 -968) (QUOTE (-525))))) @@ -62,7 +62,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4255))) (-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|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-1355 . T)) +((-1324 . T)) NIL (-34) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\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| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4255 . T) (-4256 . T) (-1355 . T)) +((-4255 . T) (-4256 . T) (-1324 . T)) NIL (-36 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#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 -3855 UP UPUP -3694) +(-39 -3837 UP UPUP -4179) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4248 |has| (-385 |#2|) (-341)) (-4253 |has| (-385 |#2|) (-341)) (-4247 |has| (-385 |#2|) (-341)) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| (-385 |#2|) (QUOTE (-136))) (|HasCategory| (-385 |#2|) (QUOTE (-138))) (|HasCategory| (-385 |#2|) (QUOTE (-327))) (-3316 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-3316 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-3316 (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-385 |#2|) (QUOTE (-327))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3316 (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341))))) -(-40 R -3855) +((|HasCategory| (-385 |#2|) (QUOTE (-136))) (|HasCategory| (-385 |#2|) (QUOTE (-138))) (|HasCategory| (-385 |#2|) (QUOTE (-327))) (-3204 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-3204 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-3204 (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-385 |#2|) (QUOTE (-327))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3204 (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341))))) +(-40 R -3837) ((|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 -968) (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."))) ((-4255 . T) (-4256 . T)) -((-3316 (-12 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3511) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3631) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3511) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3631) (|devaluate| |#2|))))))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3511) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3631) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3390) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2348) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3390) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2348) (|devaluate| |#2|))))))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3390) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2348) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -140,7 +140,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-53 |Base| R -3855) +(-53 |Base| R -3837) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -150,7 +150,7 @@ NIL NIL (-55 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|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"))) -((-4255 . T) (-4256 . T) (-1355 . T)) +((-4255 . T) (-4256 . T) (-1324 . 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}"))) ((-4256 . T) (-4255 . T)) -((-3316 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3316 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3204 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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}."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) -(-59 -3823) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +(-59 -3245) ((|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 -3823) +(-60 -3245) ((|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 -3823) +(-61 -3245) ((|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 -3823) +(-62 -3245) ((|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 -3823) +(-63 -3245) ((|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 -3823) +(-64 -3245) ((|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 -3823) +(-65 -3245) ((|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 -3823) +(-66 -3245) ((|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 -3823) +(-67 -3245) ((|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 -3823) +(-68 -3245) ((|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 -3823) +(-69 -3245) ((|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 -3823) +(-70 -3245) ((|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 -3823) +(-71 -3245) ((|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 -3823) +(-72 -3245) ((|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 -3823) +(-75 -3245) ((|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 -3823) +(-76 -3245) ((|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 -3823) +(-77 -3245) ((|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 -3823) +(-78 -3245) ((|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 -3823) +(-79 -3245) ((|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 -3823) +(-80 -3245) ((|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 -3823) +(-81 -3245) ((|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 -3823) +(-82 -3245) ((|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 -3823) +(-83 -3245) ((|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 -3823) +(-84 -3245) ((|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 -3823) +(-85 -3245) ((|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 -3823) +(-86 -3245) ((|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 -3823) +(-87 -3245) ((|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}."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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}."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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."))) -((-4256 . T) (-1355 . T)) +((-4256 . T) (-1324 . 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."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| (-525) (QUOTE (-844))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-953))) (|HasCategory| (-525) (QUOTE (-762))) (-3316 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1067))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1091)) (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 (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (|HasCategory| (-525) (QUOTE (-136))))) +((|HasCategory| (-525) (QUOTE (-844))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-953))) (|HasCategory| (-525) (QUOTE (-762))) (-3204 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1067))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1091)) (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 (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (|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 -3855 UP) +(-111 -3837 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}."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| (-112 |#1|) (QUOTE (-844))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| (-112 |#1|) (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-138))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-112 |#1|) (QUOTE (-953))) (|HasCategory| (-112 |#1|) (QUOTE (-762))) (-3316 (|HasCategory| (-112 |#1|) (QUOTE (-762))) (|HasCategory| (-112 |#1|) (QUOTE (-789)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (QUOTE (-1067))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (QUOTE (-213))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -486) (QUOTE (-1091)) (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 (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-844)))) (|HasCategory| (-112 |#1|) (QUOTE (-136))))) +((|HasCategory| (-112 |#1|) (QUOTE (-844))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| (-112 |#1|) (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-138))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-112 |#1|) (QUOTE (-953))) (|HasCategory| (-112 |#1|) (QUOTE (-762))) (-3204 (|HasCategory| (-112 |#1|) (QUOTE (-762))) (|HasCategory| (-112 |#1|) (QUOTE (-789)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (QUOTE (-1067))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (QUOTE (-213))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -486) (QUOTE (-1091)) (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 (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-844)))) (|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| (($ $) "\\spad{left(u)} returns the left child."))) NIL ((|HasAttribute| |#1| (QUOTE -4256))) (-115 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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."))) -((-1355 . T)) +((-1324 . 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"))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-118 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-119) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4256 . T) (-4255 . T) (-1355 . T)) +((-4256 . T) (-4255 . T) (-1324 . T)) NIL (-120 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#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| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4255 . T) (-4256 . T) (-1355 . T)) +((-4255 . T) (-4256 . T) (-1324 . T)) NIL (-122 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-124) ((|constructor| (NIL "ByteArray provides datatype for fix-sized buffer of bytes."))) ((-4256 . T) (-4255 . T)) -((-3316 (-12 (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (-12 (|HasCategory| (-125) (QUOTE (-1020))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125)))))) (-3316 (-12 (|HasCategory| (-125) (QUOTE (-1020))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (|HasCategory| (-125) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-125) (LIST (QUOTE -567) (QUOTE (-501)))) (-3316 (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-125) (QUOTE (-1020)))) (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-125) (QUOTE (-1020))) (-12 (|HasCategory| (-125) (QUOTE (-1020))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (|HasCategory| (-125) (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (-12 (|HasCategory| (-125) (QUOTE (-1020))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125)))))) (-3204 (-12 (|HasCategory| (-125) (QUOTE (-1020))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (|HasCategory| (-125) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-125) (LIST (QUOTE -567) (QUOTE (-501)))) (-3204 (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-125) (QUOTE (-1020)))) (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-125) (QUOTE (-1020))) (-12 (|HasCategory| (-125) (QUOTE (-1020))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (|HasCategory| (-125) (LIST (QUOTE -566) (QUOTE (-798))))) (-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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4257 "*") . T)) NIL -(-129 |minix| -3540 S T$) +(-129 |minix| -1388 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-130 |minix| -3540 R) +(-130 |minix| -1388 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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}."))) ((-4255 . T) (-4245 . T) (-4256 . T)) -((-3316 (-12 (|HasCategory| (-135) (QUOTE (-346))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|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 (-1020))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| (-135) (QUOTE (-346))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|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 (-1020))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-798))))) (-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."))) ((-4252 . T)) NIL -(-139 -3855 UP UPUP) +(-139 -3837 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 (-1020))) (|HasAttribute| |#1| (QUOTE -4255))) (-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."))) -((-1355 . T)) +((-1324 . 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 -3855) +(-147 R -3837) ((|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 (-844))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-986))) (|HasCategory| |#2| (QUOTE (-953))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-341))) (|HasAttribute| |#2| (QUOTE -4251)) (|HasAttribute| |#2| (QUOTE -4254)) (|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})"))) -((-4248 -3316 (|has| |#1| (-517)) (-12 (|has| |#1| (-286)) (|has| |#1| (-844)))) (-4253 |has| |#1| (-341)) (-4247 |has| |#1| (-341)) (-4251 |has| |#1| (-6 -4251)) (-4254 |has| |#1| (-6 -4254)) (-1399 . T) (-1355 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-4248 -3204 (|has| |#1| (-517)) (-12 (|has| |#1| (-286)) (|has| |#1| (-844)))) (-4253 |has| |#1| (-341)) (-4247 |has| |#1| (-341)) (-4251 |has| |#1| (-6 -4251)) (-4254 |has| |#1| (-6 -4254)) (-1368 . T) (-1324 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . 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}."))) -((-4248 -3316 (|has| |#1| (-517)) (-12 (|has| |#1| (-286)) (|has| |#1| (-844)))) (-4253 |has| |#1| (-341)) (-4247 |has| |#1| (-341)) (-4251 |has| |#1| (-6 -4251)) (-4254 |has| |#1| (-6 -4254)) (-1399 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327))) (-3316 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3316 (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -968) (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 -835) (QUOTE (-1091))))) (-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 (-953)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -567) 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T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327))) (-3204 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3204 (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -968) (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 (-1091)) (|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 (-986))) (-12 (|HasCategory| |#1| (QUOTE (-986))) (|HasCategory| |#1| (QUOTE (-1113)))) (|HasCategory| |#1| (QUOTE (-510))) (-3204 (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-341)))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-213))) (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasAttribute| |#1| (QUOTE -4251)) (|HasAttribute| |#1| (QUOTE -4254)) (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341)))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091))))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844)))) (|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|) $) "\\spad{constructorName c} returns the name of the constructor"))) NIL NIL -(-170 R -3855) +(-170 R -3837) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -712,19 +712,19 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|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 -3855 UP UPUP R) +(-196 -3837 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 -3855 FP) +(-197 -3837 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."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| (-525) (QUOTE (-844))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-953))) (|HasCategory| (-525) (QUOTE (-762))) (-3316 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1067))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1091)) (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 (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (|HasCategory| (-525) (QUOTE (-136))))) -(-199 R -3855) +((|HasCategory| (-525) (QUOTE (-844))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-953))) (|HasCategory| (-525) (QUOTE (-762))) (-3204 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1067))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1091)) (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 (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (|HasCategory| (-525) (QUOTE (-136))))) +(-199 R -3837) ((|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}."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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}."))) ((-4252 . T)) NIL -(-204 R -3855) +(-204 R -3837) ((|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}."))) -((-1391 . T) (-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-1360 . T) (-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . 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}"))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4257 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4257 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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."))) -((-4256 . T) (-1355 . T)) +((-4256 . T) (-1324 . 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 -4255))) (-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}."))) -((-4256 . T) (-1355 . T)) +((-4256 . T) (-1324 . 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 -3540 R) +(-217 S -1388 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 -4252)) (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (QUOTE (-346))) (|HasCategory| |#3| (QUOTE (-669))) (|HasCategory| |#3| (QUOTE (-126))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-977))) (|HasCategory| |#3| (QUOTE (-1020)))) -(-218 -3540 R) +(-218 -1388 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"))) -((-4249 |has| |#2| (-977)) (-4250 |has| |#2| (-977)) (-4252 |has| |#2| (-6 -4252)) ((-4257 "*") |has| |#2| (-160)) (-4255 . T) (-1355 . T)) +((-4249 |has| |#2| (-977)) (-4250 |has| |#2| (-977)) (-4252 |has| |#2| (-6 -4252)) ((-4257 "*") |has| |#2| (-160)) (-4255 . T) (-1324 . T)) NIL -(-219 -3540 A B) +(-219 -1388 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.")) 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -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."))) -((-1355 . T)) +((-1324 . 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}"))) ((-4256 . T) (-4255 . T)) -((-3316 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3316 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3204 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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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(|HasCategory| |#3| (QUOTE (-126))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -566) (QUOTE (-798))))) (-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}."))) -((-4255 . T) (-4256 . T) (-1355 . T)) +((-4255 . T) (-4256 . T) (-1324 . 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"))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-6 -4253)) (-4250 . T) (-4249 . T) (-4252 . T)) -((|HasCategory| |#1| (QUOTE (-844))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#3| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#3| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#3| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#3| (LIST (QUOTE -567) (LIST (QUOTE -827) (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 -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#1| (QUOTE (-341))) (-3316 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4253)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-844))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#3| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#3| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#3| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#3| (LIST (QUOTE -567) (LIST (QUOTE -827) (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 -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#1| (QUOTE (-341))) (-3204 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4253)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|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 -3855) +(-255 R -3837) ((|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 -3855) +(-256 R -3837) ((|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 (-1020)))) (-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}."))) -((-4256 . T) (-1355 . T)) +((-4256 . T) (-1324 . 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| -2787 -2727 |exactQuo|) +(-268 S R |Mod| -2054 -1423 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) NIL @@ -1022,21 +1022,21 @@ NIL NIL (-273 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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."))) ((-4255 . T) (-4256 . 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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 -3855 S) +(-276 -3837 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 -3855) +(-277 E -3837) ((|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 -3855) +(-289 -3837) ((|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))}."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-953))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-762))) (-3316 (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-762))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-789)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-1067))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-213))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -486) (QUOTE (-1091)) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -288) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -265) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-286))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-510))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-789))) (-12 (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| $ (QUOTE (-136)))) (-3316 (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (-12 (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| $ (QUOTE (-136)))))) +((|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-953))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-762))) (-3204 (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-762))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-789)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-1067))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-213))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -486) (QUOTE (-1091)) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -288) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (LIST (QUOTE -265) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-286))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-510))) (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-789))) (-12 (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| $ (QUOTE (-136)))) (-3204 (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (-12 (|HasCategory| (-1159 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|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."))) -((-4252 -3316 (-3850 (|has| |#1| (-977)) (|has| |#1| (-588 (-525)))) (-12 (|has| |#1| (-517)) (-3316 (-3850 (|has| |#1| (-977)) (|has| |#1| (-588 (-525)))) (|has| |#1| (-977)) (|has| |#1| (-450)))) (|has| |#1| (-977)) (|has| |#1| (-450))) (-4250 |has| |#1| (-160)) (-4249 |has| |#1| (-160)) ((-4257 "*") |has| |#1| (-517)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-517)) (-4247 |has| |#1| (-517))) -((-3316 (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-517))) (-3316 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-977)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-977))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (-3316 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-1032)))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) 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(QUOTE (-977))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))))) (-3204 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-977)))) (-3204 (-12 (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1032))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| $ (QUOTE (-977))) (|HasCategory| $ (LIST (QUOTE -968) (QUOTE (-525))))) +(-295 R -3837) ((|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."))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-341)) (-4247 |has| |#1| (-341)) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|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 (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3316 (|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 -1278) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3316 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1113))) (|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 -2215) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2192) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|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 (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3204 (|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 -1267) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3204 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1113))) (|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 -4211) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2181) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|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."))) ((-4256 . T) (-4255 . T)) -((-3316 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3316 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) -(-306 S -3855) +((-3204 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3204 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +(-306 S -3837) ((|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 -3855) +(-307 -3837) ((|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."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . 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 -3855 UP UPUP R) +(-312 S -3837 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 -3855 UP UPUP R) +(-313 -3837 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 -3855 UP UPUP R) +(-314 -3837 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 -3855 UP UPUP) +(-319 S -3837 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 -3855 UP UPUP) +(-320 -3837 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."))) ((-4248 |has| (-385 |#2|) (-341)) (-4253 |has| (-385 |#2|) (-341)) (-4247 |has| (-385 |#2|) (-341)) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . 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."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((-3316 (|HasCategory| (-845 |#1|) (QUOTE (-136))) (|HasCategory| (-845 |#1|) (QUOTE (-346)))) (|HasCategory| (-845 |#1|) (QUOTE (-138))) (|HasCategory| (-845 |#1|) (QUOTE (-346))) (|HasCategory| (-845 |#1|) (QUOTE (-136)))) +((-3204 (|HasCategory| (-845 |#1|) (QUOTE (-136))) (|HasCategory| (-845 |#1|) (QUOTE (-346)))) (|HasCategory| (-845 |#1|) (QUOTE (-138))) (|HasCategory| (-845 |#1|) (QUOTE (-346))) (|HasCategory| (-845 |#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."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((-3316 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3204 (|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."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((-3316 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3204 (|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."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) NIL -(-328 R UP -3855) +(-328 R UP -3837) ((|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."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((-3316 (|HasCategory| (-845 |#1|) (QUOTE (-136))) (|HasCategory| (-845 |#1|) (QUOTE (-346)))) (|HasCategory| (-845 |#1|) (QUOTE (-138))) (|HasCategory| (-845 |#1|) (QUOTE (-346))) (|HasCategory| (-845 |#1|) (QUOTE (-136)))) +((-3204 (|HasCategory| (-845 |#1|) (QUOTE (-136))) (|HasCategory| (-845 |#1|) (QUOTE (-346)))) (|HasCategory| (-845 |#1|) (QUOTE (-138))) (|HasCategory| (-845 |#1|) (QUOTE (-346))) (|HasCategory| (-845 |#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."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((-3316 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3204 (|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."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((-3316 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3204 (|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}."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((-3316 (|HasCategory| (-845 |#1|) (QUOTE (-136))) (|HasCategory| (-845 |#1|) (QUOTE (-346)))) (|HasCategory| (-845 |#1|) (QUOTE (-138))) (|HasCategory| (-845 |#1|) (QUOTE (-346))) (|HasCategory| (-845 |#1|) (QUOTE (-136)))) +((-3204 (|HasCategory| (-845 |#1|) (QUOTE (-136))) (|HasCategory| (-845 |#1|) (QUOTE (-346)))) (|HasCategory| (-845 |#1|) (QUOTE (-138))) (|HasCategory| (-845 |#1|) (QUOTE (-346))) (|HasCategory| (-845 |#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."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((-3316 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) -(-334 -3855 GF) +((-3204 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +(-334 -3837 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 -3855 FP FPP) +(-336 -3837 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}."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((-3316 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3204 (|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 -4256)) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020)))) (-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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4255 . T) (-1355 . T)) +((-4255 . T) (-1324 . T)) NIL (-352 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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}."))) -((-4238 . T) (-4246 . T) (-1391 . T) (-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-4238 . T) (-4246 . T) (-1360 . T) (-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . 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}."))) -((-1355 . T)) +((-1324 . 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.}"))) -((-1355 . T)) +((-1324 . 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 -3855 UP UPUP R) +(-370 -3837 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."))) -((-1355 . T)) +((-1324 . 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.}"))) -((-1355 . T)) +((-1324 . 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 -3823 |returnType| -2199 |symbols|) +(-376 -3245 |returnType| -3587 |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 -3855 UP) +(-377 -3837 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-378 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-1355 . T)) +((-1324 . T)) NIL (-379 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1458,7 +1458,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4238)) (|HasAttribute| |#1| (QUOTE -4246))) (-382) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-1391 . T) (-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-1360 . T) (-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . 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."))) ((-4242 -12 (|has| |#1| (-6 -4253)) (|has| |#1| (-429)) (|has| |#1| (-6 -4242))) (-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-953))) (|HasCategory| |#1| (QUOTE (-762))) (-3316 (|HasCategory| |#1| (QUOTE (-762))) (|HasCategory| |#1| (QUOTE (-789)))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-1067))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (-3316 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770))))) (-3316 (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1091)) (|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 -4253)) (|HasAttribute| |#1| (QUOTE -4242)) (|HasCategory| |#1| (QUOTE (-429)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-953))) (|HasCategory| |#1| (QUOTE (-762))) (-3204 (|HasCategory| |#1| (QUOTE (-762))) (|HasCategory| |#1| (QUOTE (-789)))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-1067))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (-3204 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770))))) (-3204 (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1091)) (|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 -4253)) (|HasAttribute| |#1| (QUOTE -4242)) (|HasCategory| |#1| (QUOTE (-429)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1492,11 +1492,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-391 R -3855 UP A) +(-391 R -3837 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4252 . T)) NIL -(-392 R -3855 UP A |ibasis|) +(-392 R -3837 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 -968) (|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."))) ((-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1091)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -288) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -265) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-1131))) (-3316 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-953))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1091)) (|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 -835) (QUOTE (-1091)))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-429)))) +((|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1091)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -288) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -265) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-1131))) (-3204 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-953))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1091)) (|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 -835) (QUOTE (-1091)))) (|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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4255 . T) (-4245 . T) (-4256 . T) (-1355 . T)) +((-4255 . T) (-4245 . T) (-4256 . T) (-1324 . T)) NIL -(-404 R -3855) +(-404 R -3837) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1552,7 +1552,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4242 -12 (|has| |#1| (-6 -4242)) (|has| |#2| (-6 -4242))) (-4249 . T) (-4250 . T) (-4252 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4242)) (|HasAttribute| |#2| (QUOTE -4242)))) -(-406 R -3855) +(-406 R -3837) ((|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 -968) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-977))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-1032))) (|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}."))) -((-4252 -3316 (|has| |#1| (-977)) (|has| |#1| (-450))) (-4250 |has| |#1| (-160)) (-4249 |has| |#1| (-160)) ((-4257 "*") |has| |#1| (-517)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-517)) (-4247 |has| |#1| (-517)) (-1355 . T)) +((-4252 -3204 (|has| |#1| (-977)) (|has| |#1| (-450))) (-4250 |has| |#1| (-160)) (-4249 |has| |#1| (-160)) ((-4257 "*") |has| |#1| (-517)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-517)) (-4247 |has| |#1| (-517)) (-1324 . T)) NIL -(-409 R -3855) +(-409 R -3837) ((|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 -3855) +(-410 R -3837) ((|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 -3855) +(-411 R -3837) ((|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 -3855 UP) +(-413 R -3837 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 -968) (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}."))) -((-1355 . T)) +((-1324 . 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.}"))) -((-1355 . T)) +((-1324 . 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 -3855) +(-420 R UP -3837) ((|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"))) (((-4257 "*") |has| |#2| (-160)) (-4248 |has| |#2| (-517)) (-4253 |has| |#2| (-6 -4253)) (-4250 . T) (-4249 . T) (-4252 . T)) -((|HasCategory| |#2| (QUOTE (-844))) (-3316 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3316 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3316 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3316 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-800 |#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 -968) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (-3316 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#2| (QUOTE -4253)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) +((|HasCategory| |#2| (QUOTE (-844))) (-3204 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3204 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3204 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3204 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-800 |#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 -968) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (-3204 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#2| (QUOTE -4253)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|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| -3855 R) +(-448 |lv| -3837 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."))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-341)) (-4247 |has| |#1| (-341)) (-4249 . T) (-4250 . T) (-4252 . 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T)) -((-12 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3511) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3631) (|devaluate| |#2|)))))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-789))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3390) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2348) (|devaluate| |#2|)))))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-789))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) (-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)}"))) ((-4256 . T) (-4255 . 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."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3511) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3631) (|devaluate| |#2|)))))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3390) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2348) (|devaluate| |#2|)))))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) (-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.")) 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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 -4255)) (|HasAttribute| |#1| (QUOTE -4256)) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (-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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-1355 . T)) +((-1324 . T)) NIL (-465 S) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) @@ -1796,7 +1796,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-467 -3855 UP |AlExt| |AlPol|) +(-467 -3837 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."))) ((-4256 . T) (-4255 . T)) -((-3316 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3316 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3204 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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 -3855) +(-472 R UP -3837) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1836,7 +1836,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-477 -3855 |Expon| |VarSet| |DPoly|) +(-477 -3837 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -567) (QUOTE (-1091))))) @@ -1883,19 +1883,19 @@ NIL (-488 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4256 . T) (-4255 . T)) -((-3316 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3316 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3204 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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}."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((-3316 (|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)))) +((-3204 (|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}."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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."))) ((-4256 . T) (-4255 . T)) -((-3316 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3316 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3204 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4257 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4257 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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 -3855 |Par|) +(-498 K -3837 |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 -3855 |Par|) +(-503 K -3837 |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}."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3511) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3631) (|devaluate| |#2|)))))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) -(-512 R -3855) +((-12 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3390) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2348) (|devaluate| |#2|)))))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) +(-512 R -3837) ((|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 -3855 UP UPUP R) +(-513 R0 -3837 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."))) -((-1391 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-1360 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . 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."))) ((-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) NIL -(-518 R -3855) +(-518 R -3837) ((|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 -3855 L) +(-521 R -3837 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 -3855 UP UPUP R) +(-523 -3837 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 -3855 UP) +(-524 -3837 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 -3855 L) +(-527 R -3837 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 -3855) +(-528 R -3837) ((|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 -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1055)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-578))))) -(-529 -3855 UP) +(-529 -3837 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 -3855) +(-531 -3837) ((|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."))) -((-1391 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-1360 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . 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 -3855) +(-534 R -3837) ((|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 -827) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-263))) (|HasCategory| |#2| (QUOTE (-578))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-263)))) (|HasCategory| |#1| (QUOTE (-517)))) -(-535 -3855 UP) +(-535 -3837 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 -3855) +(-536 R -3837) ((|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 -3855) +(-540 R -3837) ((|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 -3855) +(-541 E -3837) ((|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 -3855) +(-542 -3837) ((|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}."))) ((-4250 . T) (-4249 . T)) ((|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-1091))))) @@ -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"))) ((-4256 . T) (-4255 . T)) -((-3316 (-12 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (-3316 (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -567) (QUOTE (-501)))) (-3316 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1020)))) (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1020))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (-3204 (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -567) (QUOTE (-501)))) (-3204 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1020)))) (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1020))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-798))))) (-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}."))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3316 (|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 -835) (QUOTE (-1091)))) (|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 (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -1278) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|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))) (-3204 (|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 -835) (QUOTE (-1091)))) (|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 (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -1267) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|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.}"))) ((-4250 |has| |#1| (-517)) (-4249 |has| |#1| (-517)) ((-4257 "*") |has| |#1| (-517)) (-4248 |has| |#1| (-517)) (-4252 . 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 -3855 FG) +(-554 R -3837 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."))) ((-4256 . T) (-4255 . T)) -((-3316 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3316 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-977))) (-12 (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-977)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3204 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-977))) (-12 (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-977)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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 -4256)) (|HasCategory| |#2| (QUOTE (-789))) (|HasAttribute| |#1| (QUOTE -4255)) (|HasCategory| |#3| (QUOTE (-1020)))) (-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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-1355 . T)) +((-1324 . T)) NIL (-559) ((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes.")) (|coerce| (($ (|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)."))) -((-4252 -3316 (-3850 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4250 . T) (-4249 . T)) -((-3316 (|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|)))) (-3316 (-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|)))) +((-4252 -3204 (-3833 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4250 . T) (-4249 . T)) +((-3204 (|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|)))) (-3204 (-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."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3511) (QUOTE (-1074))) (LIST (QUOTE |:|) (QUOTE -3631) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| (-1074) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3390) (QUOTE (-1074))) (LIST (QUOTE |:|) (QUOTE -2348) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| (-1074) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (LIST (QUOTE -566) (QUOTE (-798))))) (-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}."))) -((-4256 . T) (-1355 . T)) +((-4256 . T) (-1324 . 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-568 -3855 UP) +(-568 -3837 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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}."))) ((-4249 . T) (-4250 . T) (-4252 . T)) ((|HasCategory| |#1| (QUOTE (-787)))) -(-572 R -3855) +(-572 R -3837) ((|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 -3855) +(-579 R -3837) ((|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| -3855) +(-580 |lv| -3837) ((|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."))) ((-4256 . T)) -((-12 (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3511) (QUOTE (-1074))) (LIST (QUOTE |:|) (QUOTE -3631) (QUOTE (-51))))))) (-3316 (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 (-51))) (QUOTE (-1020))) (|HasCategory| (-51) (QUOTE (-1020)))) (-3316 (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-1074) (QUOTE (-789))) (-3316 (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 (-51))) (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3390) (QUOTE (-1074))) (LIST (QUOTE |:|) (QUOTE -2348) (QUOTE (-51))))))) (-3204 (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 (-51))) (QUOTE (-1020))) (|HasCategory| (-51) (QUOTE (-1020)))) (-3204 (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-1074) (QUOTE (-789))) (-3204 (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 (-51))) (LIST (QUOTE -566) (QUOTE (-798))))) (-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)."))) -((-4252 -3316 (-3850 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4250 . T) (-4249 . T)) -((-3316 (|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|)))) (-3316 (-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|)))) +((-4252 -3204 (-3833 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4250 . T) (-4249 . T)) +((-3204 (|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|)))) (-3204 (-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 -((-1809 (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-341)))) +((-1796 (|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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4252 . T)) @@ -2299,11 +2299,11 @@ NIL (-592 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4256 . T) (-4255 . T)) -((-3316 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3316 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-770))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3204 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-770))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-594 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#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 -4256))) (-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})}."))) -((-1355 . T)) +((-1324 . T)) NIL -(-598 R -3855 L) +(-598 R -3837 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}."))) ((-4249 . T) (-4250 . T) (-4252 . T)) NIL -(-603 -3855 UP) +(-603 -3837 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 -3257) +(-604 A -2420) ((|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}}"))) ((-4249 . T) (-4250 . T) (-4252 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (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}."))) -((-4256 . T) (-4255 . T) (-1355 . T)) +((-4256 . T) (-4255 . T) (-1324 . T)) NIL -(-613 -3855) +(-613 -3837) ((|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 -3855 |Row| |Col| M) +(-614 -3837 |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."))) ((-4252 . T) (-4255 . T) (-4249 . T) (-4250 . T)) -((|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE (-4257 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (-3316 (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|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 -835) (QUOTE (-1091)))))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-517))) (-3316 (|HasAttribute| |#2| (QUOTE (-4257 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#2| (QUOTE (-213)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-160)))) +((|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE (-4257 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (-3204 (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|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 -835) (QUOTE (-1091)))))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-517))) (-3204 (|HasAttribute| |#2| (QUOTE (-4257 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#2| (QUOTE (-213)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|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)]}."))) -((-1355 . T)) +((-1324 . 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 -((-3316 (-12 (|HasCategory| |#1| (QUOTE (-977))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (QUOTE (-977))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| |#1| (QUOTE (-977))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (QUOTE (-977))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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 (-4257 "*"))) (|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"))) -((-4255 . T) (-4256 . T) (-1355 . T)) +((-4255 . T) (-4256 . T) (-1324 . 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."))) ((-4255 . T) (-4256 . T)) -((-3316 (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4257 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4257 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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 -3855 FLAF FLAS) +(-634 S -3837 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"))) -((-4248 . T) (-4253 |has| (-641) (-341)) (-4247 |has| (-641) (-341)) (-1399 . T) (-4254 |has| (-641) (-6 -4254)) (-4251 |has| (-641) (-6 -4251)) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| (-641) (QUOTE (-138))) (|HasCategory| (-641) (QUOTE (-136))) (|HasCategory| (-641) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-641) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-641) (QUOTE (-346))) (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-641) (QUOTE (-213))) (-3316 (|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 (-1091)) (QUOTE (-641)))) (|HasCategory| (-641) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-641) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-641) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-641) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (-3316 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (QUOTE (-327)))) (|HasCategory| (-641) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-641) (QUOTE (-953))) (|HasCategory| (-641) (QUOTE (-1113))) (-12 (|HasCategory| (-641) (QUOTE (-934))) (|HasCategory| (-641) (QUOTE (-1113)))) (-3316 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-341))) (-12 (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (QUOTE (-844))))) (-3316 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (-12 (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (QUOTE (-844)))) (-12 (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (QUOTE (-844))))) (|HasCategory| (-641) (QUOTE (-510))) (-12 (|HasCategory| (-641) (QUOTE (-986))) (|HasCategory| (-641) (QUOTE (-1113)))) (|HasCategory| (-641) (QUOTE (-986))) (-3316 (|HasCategory| (-641) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-641) (QUOTE (-341)))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844))) (-3316 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-341)))) (-3316 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-517)))) (-12 (|HasCategory| (-641) (QUOTE (-213))) (|HasCategory| (-641) (QUOTE (-341)))) (-12 (|HasCategory| (-641) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-641) (QUOTE (-341)))) (|HasCategory| (-641) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-641) (QUOTE (-789))) (|HasCategory| (-641) (QUOTE (-517))) (|HasAttribute| (-641) (QUOTE -4254)) (|HasAttribute| (-641) (QUOTE -4251)) (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-136)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-327))))) +((-4248 . T) (-4253 |has| (-641) (-341)) (-4247 |has| (-641) (-341)) (-1368 . T) (-4254 |has| (-641) (-6 -4254)) (-4251 |has| (-641) (-6 -4251)) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((|HasCategory| (-641) (QUOTE (-138))) (|HasCategory| (-641) (QUOTE (-136))) (|HasCategory| (-641) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-641) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-641) (QUOTE (-346))) (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-641) (QUOTE (-213))) (-3204 (|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 (-1091)) (QUOTE (-641)))) (|HasCategory| (-641) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-641) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-641) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-641) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (-3204 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (QUOTE (-327)))) (|HasCategory| (-641) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-641) (QUOTE (-953))) (|HasCategory| (-641) (QUOTE (-1113))) (-12 (|HasCategory| (-641) (QUOTE (-934))) (|HasCategory| (-641) (QUOTE (-1113)))) (-3204 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-341))) (-12 (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (QUOTE (-844))))) (-3204 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (-12 (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (QUOTE (-844)))) (-12 (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (QUOTE (-844))))) (|HasCategory| (-641) (QUOTE (-510))) (-12 (|HasCategory| (-641) (QUOTE (-986))) (|HasCategory| (-641) (QUOTE (-1113)))) (|HasCategory| (-641) (QUOTE (-986))) (-3204 (|HasCategory| (-641) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-641) (QUOTE (-341)))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844))) (-3204 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-341)))) (-3204 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-517)))) (-12 (|HasCategory| (-641) (QUOTE (-213))) (|HasCategory| (-641) (QUOTE (-341)))) (-12 (|HasCategory| (-641) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-641) (QUOTE (-341)))) (|HasCategory| (-641) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-641) (QUOTE (-789))) (|HasCategory| (-641) (QUOTE (-517))) (|HasAttribute| (-641) (QUOTE -4254)) (|HasAttribute| (-641) (QUOTE -4251)) (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-136)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|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}."))) -((-4256 . T) (-1355 . T)) +((-4256 . T) (-1324 . 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 -3855 PG) +(-640 OV E -3837 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}"))) -((-1391 . T) (-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-1360 . T) (-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . 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 -2004 I) +(-649 S -1514 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| -2787 -2727 |exactQuo|) +(-654 R |Mod| -2054 -1423 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) NIL (-655 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4251 |has| |#1| (-341)) (-4253 |has| |#1| (-6 -4253)) (-4250 . T) (-4249 . T) (-4252 . T)) -((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1005) (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 -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-327))) (-3316 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4253)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1005) (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 -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-327))) (-3204 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4253)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4250 |has| |#1| (-160)) (-4249 |has| |#1| (-160)) (-4252 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138)))) -(-658 R |Mod| -2787 -2727 |exactQuo|) +(-658 R |Mod| -2054 -1423 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4252 . T)) NIL @@ -2572,7 +2572,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4250 . T) (-4249 . T)) NIL -(-661 -3855) +(-661 -3837) ((|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]]}."))) ((-4252 . 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 -3855 UP) +(-670 -3837 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."))) (((-4257 "*") |has| |#2| (-160)) (-4248 |has| |#2| (-517)) (-4253 |has| |#2| (-6 -4253)) (-4250 . T) (-4249 . T) (-4252 . T)) -((|HasCategory| |#2| (QUOTE (-844))) (-3316 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3316 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3316 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3316 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-800 |#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 -968) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (-3316 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#2| (QUOTE -4253)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) +((|HasCategory| |#2| (QUOTE (-844))) (-3204 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3204 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3204 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3204 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-800 |#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 -968) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (-3204 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#2| (QUOTE -4253)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2646,7 +2646,7 @@ NIL ((-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-789)))) (-679 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4245 . T) (-4256 . T) (-1355 . T)) +((-4245 . T) (-4256 . T) (-1324 . T)) NIL (-680 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|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 -3855) +(-708 -3837) ((|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 -3855) +(-709 P -3837) ((|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 -3855) +(-710 UP -3837) ((|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."))) (((-4257 "*") . T)) NIL -(-714 R -3855) +(-714 R -3837) ((|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 -3855 |ExtF| |SUEx| |ExtP| |n|) +(-719 -3837 |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."))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-6 -4253)) (-4250 . T) (-4249 . T) (-4252 . T)) -((|HasCategory| |#1| (QUOTE (-844))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) 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(QUOTE -37) (QUOTE (-525))))) (-1796 (|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 (-1091)))) (-1796 (|HasCategory| |#1| (LIST (QUOTE -925) (QUOTE (-525))))))) (-3204 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4253)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|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)}"))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4251 |has| |#1| (-341)) (-4253 |has| |#1| (-6 -4253)) (-4250 . T) (-4249 . T) (-4252 . T)) -((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1005) (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 -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (-3316 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4253)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1005) (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 -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (-3204 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4253)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|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.}"))) -((-4256 . T) (-4255 . T) (-1355 . T)) +((-4256 . T) (-4255 . T) (-1324 . 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4249 . T) (-4250 . T) (-4252 . T)) NIL -(-740 -3316 R OS S) +(-740 -3204 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-741 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4249 . T) (-4250 . T) (-4252 . 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 (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (-3316 (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3316 (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-986))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (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 (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (-3204 (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3204 (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-986))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (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 -3855 L) +(-743 R -3837 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 -3855) +(-744 R -3837) ((|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 -3855) +(-746 R -3837) ((|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 -3855 UP UPUP R) +(-748 -3837 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 -3855 UP L LQ) +(-749 -3837 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 -3855 UP L LQ) +(-751 -3837 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 -3855 UP) +(-752 -3837 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 -3855 L UP A LO) +(-753 -3837 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 -3855 UP) +(-754 -3837 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 -3855 LO) +(-755 -3837 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 -3855 LODO) +(-756 -3837 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) 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(QUOTE (-977))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1091))))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525))))) (-3204 (|HasCategory| |#2| (QUOTE (-977))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-1020)))) (|HasAttribute| |#2| (QUOTE -4252)) (|HasCategory| |#2| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (-758 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-6 -4253)) (-4250 . T) (-4249 . T) (-4252 . T)) -((|HasCategory| |#1| (QUOTE (-844))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-760 (-1091)) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-760 (-1091)) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-760 (-1091)) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-760 (-1091)) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-760 (-1091)) (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 -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#1| (QUOTE (-341))) (-3316 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4253)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-844))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-760 (-1091)) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-760 (-1091)) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-760 (-1091)) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-760 (-1091)) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-760 (-1091)) (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 -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#1| (QUOTE (-341))) (-3204 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4253)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|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."))) (((-4257 "*") |has| |#2| (-341)) (-4248 |has| |#2| (-341)) (-4253 |has| |#2| (-341)) (-4247 |has| |#2| (-341)) (-4252 . T) (-4250 . T) (-4249 . 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}."))) -((-4255 . T) (-4245 . T) (-4256 . T) (-1355 . T)) +((-4255 . T) (-4245 . T) (-4256 . T) (-1324 . 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."))) ((-4252 |has| |#1| (-787))) -((|HasCategory| |#1| (QUOTE (-787))) (-3316 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-787)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-510))) (-3316 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-787))) (-3204 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-787)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-510))) (-3204 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) (-776 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) ((-4250 |has| |#1| (-160)) (-4249 |has| |#1| (-160)) (-4252 . 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."))) ((-4252 |has| |#1| (-787))) -((|HasCategory| |#1| (QUOTE (-787))) (-3316 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-787)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-510))) (-3316 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-787))) (-3204 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-787)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-510))) (-3204 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) (-783) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-784 -3540 S) +(-784 -1388 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| -1752) +(-793 R |sigma| -1695) ((|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."))) ((-4249 . T) (-4250 . T) (-4252 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-341)))) -(-794 |x| R |sigma| -1752) +(-794 |x| R |sigma| -1695) ((|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."))) ((-4249 . T) (-4250 . T) (-4252 . T)) ((|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-341)))) @@ -3155,15 +3155,15 @@ NIL (-806 |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)."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| (-805 |#1|) (QUOTE (-844))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| (-805 |#1|) (QUOTE (-136))) (|HasCategory| (-805 |#1|) (QUOTE (-138))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-805 |#1|) (QUOTE (-953))) (|HasCategory| (-805 |#1|) (QUOTE (-762))) (-3316 (|HasCategory| (-805 |#1|) (QUOTE (-762))) (|HasCategory| (-805 |#1|) (QUOTE (-789)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-805 |#1|) (QUOTE (-1067))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-805 |#1|) (QUOTE (-213))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -486) (QUOTE (-1091)) (LIST (QUOTE -805) (|devaluate| |#1|)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -288) (LIST (QUOTE -805) (|devaluate| |#1|)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -265) (LIST (QUOTE -805) (|devaluate| |#1|)) (LIST (QUOTE -805) (|devaluate| |#1|)))) (|HasCategory| (-805 |#1|) (QUOTE (-286))) (|HasCategory| (-805 |#1|) (QUOTE (-510))) (|HasCategory| (-805 |#1|) (QUOTE (-789))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-805 |#1|) (QUOTE (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-805 |#1|) (QUOTE (-844)))) (|HasCategory| (-805 |#1|) (QUOTE (-136))))) +((|HasCategory| (-805 |#1|) (QUOTE (-844))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| (-805 |#1|) (QUOTE (-136))) (|HasCategory| (-805 |#1|) (QUOTE (-138))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-805 |#1|) (QUOTE (-953))) (|HasCategory| (-805 |#1|) (QUOTE (-762))) (-3204 (|HasCategory| (-805 |#1|) (QUOTE (-762))) (|HasCategory| (-805 |#1|) (QUOTE (-789)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-805 |#1|) (QUOTE (-1067))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-805 |#1|) (QUOTE (-213))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -486) (QUOTE (-1091)) (LIST (QUOTE -805) (|devaluate| |#1|)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -288) (LIST (QUOTE -805) (|devaluate| |#1|)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -265) (LIST (QUOTE -805) (|devaluate| |#1|)) (LIST (QUOTE -805) (|devaluate| |#1|)))) (|HasCategory| (-805 |#1|) (QUOTE (-286))) (|HasCategory| (-805 |#1|) (QUOTE (-510))) (|HasCategory| (-805 |#1|) (QUOTE (-789))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-805 |#1|) (QUOTE (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-805 |#1|) (QUOTE (-844)))) (|HasCategory| (-805 |#1|) (QUOTE (-136))))) (-807 |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)}."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-953))) (|HasCategory| |#2| (QUOTE (-762))) (-3316 (|HasCategory| |#2| (QUOTE (-762))) (|HasCategory| |#2| (QUOTE (-789)))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#2| (LIST (QUOTE -486) (QUOTE (-1091)) (|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 (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) +((|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-953))) (|HasCategory| |#2| (QUOTE (-762))) (-3204 (|HasCategory| |#2| (QUOTE (-762))) (|HasCategory| |#2| (QUOTE (-789)))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#2| (LIST (QUOTE -486) (QUOTE (-1091)) (|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 (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) (-808 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 (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))))) (-809) ((|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 @@ -3219,7 +3219,7 @@ NIL (-822 |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 (-1809 (|HasCategory| |#2| (QUOTE (-977)))) (-1809 (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1091)))))) (-12 (|HasCategory| |#2| (QUOTE (-977))) (-1809 (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1091)))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1091))))) +((-12 (-1796 (|HasCategory| |#2| (QUOTE (-977)))) (-1796 (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1091)))))) (-12 (|HasCategory| |#2| (QUOTE (-977))) (-1796 (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1091)))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1091))))) (-823 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 @@ -3228,7 +3228,7 @@ 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 -(-825 R -2004) +(-825 R -1514) ((|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 @@ -3252,7 +3252,7 @@ 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 -(-831 UP -3855) +(-831 UP -3837) ((|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 @@ -3275,7 +3275,7 @@ NIL (-836 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 (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-837 |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 @@ -3291,7 +3291,7 @@ NIL (-840 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."))) ((-4252 . T)) -((-3316 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-789)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-789)))) +((-3204 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-789)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-789)))) (-841 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 @@ -3312,7 +3312,7 @@ 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."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) ((|HasCategory| $ (QUOTE (-138))) (|HasCategory| $ (QUOTE (-136))) (|HasCategory| $ (QUOTE (-346)))) -(-846 R0 -3855 UP UPUP R) +(-846 R0 -3837 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 @@ -3340,7 +3340,7 @@ 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 -(-853 -3855) +(-853 -3837) ((|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 @@ -3356,11 +3356,11 @@ 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}."))) (((-4257 "*") . T)) NIL -(-857 -3855 P) +(-857 -3837 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-858 |xx| -3855) +(-858 |xx| -3837) ((|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 @@ -3384,7 +3384,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-864 R -3855) +(-864 R -3837) ((|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 @@ -3396,7 +3396,7 @@ 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 -(-867 S R -3855) +(-867 S R -3837) ((|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 @@ -3416,11 +3416,11 @@ 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 -821) (|devaluate| |#1|)))) -(-872 R -3855 -2004) +(-872 R -3837 -1514) ((|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 -(-873 -2004) +(-873 -1514) ((|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 @@ -3443,7 +3443,7 @@ NIL (-878 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4256 . T) (-4255 . T)) -((-3316 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3316 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-977))) (-12 (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-977)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3204 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-977))) (-12 (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-977)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-879 |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 @@ -3468,7 +3468,7 @@ 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}."))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-6 -4253)) (-4250 . T) (-4249 . T) (-4252 . T)) NIL -(-885 E V R P -3855) +(-885 E V R P -3837) ((|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 @@ -3479,8 +3479,8 @@ NIL (-887 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}."))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-6 -4253)) (-4250 . T) (-4249 . T) (-4252 . T)) -((|HasCategory| |#1| (QUOTE (-844))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1091) (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 -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))) (-3316 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4253)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) -(-888 E V R P -3855) +((|HasCategory| |#1| (QUOTE (-844))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1091) (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 -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))) (-3204 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4253)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +(-888 E V R P -3837) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-429)))) @@ -3499,12 +3499,12 @@ NIL (-892 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4256 . T) (-4255 . T)) -((-3316 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3316 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3204 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-893) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-894 -3855) +(-894 -3837) ((|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 @@ -3519,17 +3519,17 @@ NIL (-897 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}"))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-6 -4253)) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-126)))) (-3316 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4253))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-126)))) (-3204 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4253))) (-898 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"))) ((-4252 -12 (|has| |#2| (-450)) (|has| |#1| (-450)))) -((-3316 (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735)))) (-12 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(|HasCategory| |#2| (QUOTE (-669))))) (-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-346)))) (-3316 (-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))))) +((-3204 (-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)))) (-3204 (-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)))) (-3204 (-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)))) (-3204 (-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)))) (-3204 (-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))))) (-899) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL NIL (-900 T$) -((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|equivOperands| (((|Pair| $ $) $) "\\spad{equivOperands p} extracts the operands to the logical equivalence; otherwise errors.")) (|equiv?| (((|Boolean|) $) "\\spad{equiv? p} is \\spad{true} when \\spad{`p'} is a logical equivalence.")) (|impliesOperands| (((|Pair| $ $) $) "\\spad{impliesOperands p} extracts the operands to the logical implication; otherwise errors.")) (|implies?| (((|Boolean|) $) "\\spad{implies? p} is \\spad{true} when \\spad{`p'} is a logical implication.")) (|orOperands| (((|Pair| $ $) $) "\\spad{orOperands p} extracts the operands to the logical disjunction; otherwise errors.")) (|or?| (((|Boolean|) $) "\\spad{or? p} is \\spad{true} when \\spad{`p'} is a logical disjunction.")) (|andOperands| (((|Pair| $ $) $) "\\spad{andOperands p} extracts the operands of the logical conjunction; otherwise errors.")) (|and?| (((|Boolean|) $) "\\spad{and? p} is \\spad{true} when \\spad{`p'} is a logical conjunction.")) (|notOperand| (($ $) "\\spad{notOperand returns} the operand to the logical `not' operator; otherwise errors.")) (|not?| (((|Boolean|) $) "\\spad{not? p} is \\spad{true} when \\spad{`p'} is a logical negation")) (|variable| (((|Symbol|) $) "\\spad{variable p} extracts the varible name from \\spad{`p'}; otherwise errors.")) (|variable?| (((|Boolean|) $) "variables? \\spad{p} returns \\spad{true} when \\spad{`p'} really is a variable.")) (|term| ((|#1| $) "\\spad{term p} extracts the term value from \\spad{`p'}; otherwise errors.")) (|term?| (((|Boolean|) $) "\\spad{term? p} returns \\spad{true} when \\spad{`p'} really is a term")) (|variables| (((|Set| (|Symbol|)) $) "\\spad{variables(p)} returns the set of propositional variables appearing in the proposition \\spad{`p'}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(t)} turns the term \\spad{`t'} into a propositional variable.") (($ |#1|) "\\spad{coerce(t)} turns the term \\spad{`t'} into a propositional formula"))) +((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|equivOperands| (((|Pair| $ $) $) "\\spad{equivOperands p} extracts the operands to the logical equivalence; otherwise errors.")) (|equiv?| (((|Boolean|) $) "\\spad{equiv? p} is \\spad{true} when \\spad{`p'} is a logical equivalence.")) (|impliesOperands| (((|Pair| $ $) $) "\\spad{impliesOperands p} extracts the operands to the logical implication; otherwise errors.")) (|implies?| (((|Boolean|) $) "\\spad{implies? p} is \\spad{true} when \\spad{`p'} is a logical implication.")) (|orOperands| (((|Pair| $ $) $) "\\spad{orOperands p} extracts the operands to the logical disjunction; otherwise errors.")) (|or?| (((|Boolean|) $) "\\spad{or? p} is \\spad{true} when \\spad{`p'} is a logical disjunction.")) (|andOperands| (((|Pair| $ $) $) "\\spad{andOperands p} extracts the operands of the logical conjunction; otherwise errors.")) (|and?| (((|Boolean|) $) "\\spad{and? p} is \\spad{true} when \\spad{`p'} is a logical conjunction.")) (|notOperand| (($ $) "\\spad{notOperand returns} the operand to the logical `not' operator; otherwise errors.")) (|not?| (((|Boolean|) $) "\\spad{not? p} is \\spad{true} when \\spad{`p'} is a logical negation")) (|variable| (((|Symbol|) $) "\\spad{variable p} extracts the variable name from \\spad{`p'}; otherwise errors.")) (|variable?| (((|Boolean|) $) "variables? \\spad{p} returns \\spad{true} when \\spad{`p'} really is a variable.")) (|term| ((|#1| $) "\\spad{term p} extracts the term value from \\spad{`p'}; otherwise errors.")) (|term?| (((|Boolean|) $) "\\spad{term? p} returns \\spad{true} when \\spad{`p'} really is a term")) (|variables| (((|Set| (|Symbol|)) $) "\\spad{variables(p)} returns the set of propositional variables appearing in the proposition \\spad{`p'}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(t)} turns the term \\spad{`t'} into a propositional variable.") (($ |#1|) "\\spad{coerce(t)} turns the term \\spad{`t'} into a propositional formula"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-901) @@ -3538,7 +3538,7 @@ NIL NIL (-902 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}."))) -((-4255 . T) (-4256 . T) (-1355 . T)) +((-4255 . T) (-4256 . T) (-1324 . T)) NIL (-903 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}}"))) @@ -3566,7 +3566,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-517)))) (-909 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."))) -((-4255 . T) (-1355 . T)) +((-4255 . T) (-1324 . T)) NIL (-910 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."))) @@ -3582,7 +3582,7 @@ NIL NIL (-913 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}."))) -((-4256 . T) (-4255 . T) (-1355 . T)) +((-4256 . T) (-4255 . T) (-1324 . T)) NIL (-914 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3600,7 +3600,7 @@ 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 -(-918 K R UP -3855) +(-918 K R UP -3837) ((|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 @@ -3630,7 +3630,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-953))) (|HasCategory| |#2| (QUOTE (-762))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1067)))) (-925 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}."))) -((-1355 . T) (-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-1324 . T) (-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) NIL (-926 |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}."))) @@ -3638,7 +3638,7 @@ NIL NIL (-927 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."))) -((-4255 . T) (-4256 . T) (-1355 . T)) +((-4255 . T) (-4256 . T) (-1324 . T)) NIL (-928 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}."))) @@ -3655,11 +3655,11 @@ NIL (-931 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.}"))) ((-4248 |has| |#1| (-269)) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-341))) (-3316 (|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 (-1091)) (|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 -835) (QUOTE (-1091)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-986))) (|HasCategory| |#1| (QUOTE (-510))) (-3316 (|HasCategory| |#1| (LIST (QUOTE -968) (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))) (-3204 (|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 (-1091)) (|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 -835) (QUOTE (-1091)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-986))) (|HasCategory| |#1| (QUOTE (-510))) (-3204 (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))))) (-932 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}."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-933 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3668,14 +3668,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-935 -3855 UP UPUP |radicnd| |n|) +(-935 -3837 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4248 |has| (-385 |#2|) (-341)) (-4253 |has| (-385 |#2|) (-341)) (-4247 |has| (-385 |#2|) (-341)) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| (-385 |#2|) (QUOTE (-136))) (|HasCategory| (-385 |#2|) (QUOTE (-138))) (|HasCategory| (-385 |#2|) (QUOTE (-327))) (-3316 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-3316 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-3316 (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-385 |#2|) (QUOTE (-327))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3316 (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|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))) (-3204 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-3204 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-3204 (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-385 |#2|) (QUOTE (-327))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3204 (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341))))) (-936 |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."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| (-525) (QUOTE (-844))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-953))) (|HasCategory| (-525) (QUOTE (-762))) (-3316 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1067))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1091)) (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 (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (|HasCategory| (-525) (QUOTE (-136))))) +((|HasCategory| (-525) (QUOTE (-844))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-1091)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-953))) (|HasCategory| (-525) (QUOTE (-762))) (-3204 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1067))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1091)) (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 (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (|HasCategory| (-525) (QUOTE (-136))))) (-937) ((|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 @@ -3698,7 +3698,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4256)) (|HasCategory| |#2| (QUOTE (-1020)))) (-942 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}."))) -((-1355 . T)) +((-1324 . T)) NIL (-943 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)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|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}}"))) @@ -3708,19 +3708,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4248 . T) (-4253 . T) (-4247 . T) (-4250 . T) (-4249 . T) ((-4257 "*") . T) (-4252 . T)) NIL -(-945 R -3855) +(-945 R -3837) ((|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 -(-946 R -3855) +(-946 R -3837) ((|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 -(-947 -3855 UP) +(-947 -3837 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 -(-948 -3855 UP) +(-948 -3837 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 @@ -3751,8 +3751,8 @@ NIL (-955 |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"))) ((-4248 . T) (-4253 . T) (-4247 . T) (-4250 . T) (-4249 . T) ((-4257 "*") . T) (-4252 . T)) -((-3316 (|HasCategory| (-385 (-525)) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-385 (-525)) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 (-525)) (LIST (QUOTE -968) (QUOTE (-525))))) -(-956 -3855 L) +((-3204 (|HasCategory| (-385 (-525)) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-385 (-525)) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 (-525)) (LIST (QUOTE -968) (QUOTE (-525))))) +(-956 -3837 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 @@ -3788,14 +3788,14 @@ 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 -(-965 -3855 |Expon| |VarSet| |FPol| |LFPol|) +(-965 -3837 |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"))) (((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) NIL (-966) ((|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.}"))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3511) (QUOTE (-1091))) (LIST (QUOTE |:|) (QUOTE -3631) (QUOTE (-51))))))) (-3316 (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (QUOTE (-1020))) (|HasCategory| (-51) (QUOTE (-1020)))) (-3316 (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (QUOTE (-1020))) (|HasCategory| (-1091) (QUOTE (-789))) (|HasCategory| (-51) (QUOTE (-1020))) (-3316 (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3390) (QUOTE (-1091))) (LIST (QUOTE |:|) (QUOTE -2348) (QUOTE (-51))))))) (-3204 (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (QUOTE (-1020))) (|HasCategory| (-51) (QUOTE (-1020)))) (-3204 (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (QUOTE (-1020))) (|HasCategory| (-1091) (QUOTE (-789))) (|HasCategory| (-51) (QUOTE (-1020))) (-3204 (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (LIST (QUOTE -566) (QUOTE (-798))))) (-967 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 @@ -3840,7 +3840,7 @@ 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."))) ((-4252 . T)) NIL -(-978 |xx| -3855) +(-978 |xx| -3837) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -3850,12 +3850,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-286))) (|HasCategory| |#4| (QUOTE (-341))) (|HasCategory| |#4| (QUOTE (-517))) (|HasCategory| |#4| (QUOTE (-160)))) (-980 |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"))) -((-4255 . T) (-1355 . T) (-4250 . T) (-4249 . T)) +((-4255 . T) (-1324 . T) (-4250 . T) (-4249 . T)) NIL (-981 |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}."))) ((-4255 . T) (-4250 . T) (-4249 . T)) -((-3316 (-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 (-1020))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -567) (QUOTE (-501)))) (-3316 (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (QUOTE (-341)))) (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (QUOTE (-286))) (|HasCategory| |#3| (QUOTE (-517))) (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|))))) +((-3204 (-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 (-1020))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -567) (QUOTE (-501)))) (-3204 (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (QUOTE (-341)))) (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (QUOTE (-286))) (|HasCategory| |#3| (QUOTE (-517))) (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|))))) (-982 |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 @@ -3887,7 +3887,7 @@ NIL (-989) ((|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}"))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3511) (QUOTE (-1091))) (LIST (QUOTE |:|) (QUOTE -3631) (QUOTE (-51))))))) (-3316 (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (QUOTE (-1020))) (|HasCategory| (-51) (QUOTE (-1020)))) (-3316 (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (QUOTE (-1020))) (|HasCategory| (-1091) (QUOTE (-789))) (|HasCategory| (-51) (QUOTE (-1020))) (-3316 (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3390) (QUOTE (-1091))) (LIST (QUOTE |:|) (QUOTE -2348) (QUOTE (-51))))))) (-3204 (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (QUOTE (-1020))) (|HasCategory| (-51) (QUOTE (-1020)))) (-3204 (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (QUOTE (-1020))) (|HasCategory| (-1091) (QUOTE (-789))) (|HasCategory| (-51) (QUOTE (-1020))) (-3204 (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (LIST (QUOTE -566) (QUOTE (-798))))) (-990 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 @@ -3914,7 +3914,7 @@ NIL NIL (-996 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}."))) -((-4256 . T) (-4255 . T) (-1355 . T)) +((-4256 . T) (-4255 . T) (-1324 . T)) NIL (-997 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."))) @@ -3924,11 +3924,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-999 |Base| R -3855) +(-999 |Base| R -3837) ((|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 -(-1000 |Base| R -3855) +(-1000 |Base| R -3837) ((|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 @@ -3943,7 +3943,7 @@ NIL (-1003 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."))) ((-4248 |has| |#1| (-341)) (-4253 |has| |#1| (-341)) (-4247 |has| |#1| (-341)) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327))) (-3316 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-327)))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091))))) (-3316 (|HasCategory| |#1| (LIST (QUOTE -968) (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))) (-3204 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-327)))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091))))) (-3204 (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341)))) (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341))))) (-1004 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 @@ -3967,7 +3967,7 @@ NIL (-1009 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"))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-6 -4253)) (-4250 . T) (-4249 . T) (-4252 . 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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 @@ -3986,7 +3986,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-1020)))) (-1014 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."))) -((-1355 . T)) +((-1324 . T)) NIL (-1015 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) @@ -3994,7 +3994,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (QUOTE (-1020)))) (-1016 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| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-1355 . T)) +((-1324 . T)) NIL (-1017 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) @@ -4002,7 +4002,7 @@ NIL NIL (-1018 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) -((-4245 . T) (-1355 . T)) +((-4245 . T) (-1324 . T)) NIL (-1019 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}."))) @@ -4019,7 +4019,7 @@ NIL (-1022 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)}}"))) ((-4255 . T) (-4245 . T) (-4256 . T)) -((-3316 (-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-1023 |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 @@ -4046,7 +4046,7 @@ NIL NIL (-1029 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.}"))) -((-4256 . T) (-4255 . T) (-1355 . T)) +((-4256 . T) (-4255 . T) (-1324 . T)) NIL (-1030) ((|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."))) @@ -4063,12 +4063,12 @@ NIL (-1033 |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 (-213))) (|HasCategory| |#3| (LIST (QUOTE -968) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (LIST (QUOTE -968) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-346))) (|HasCategory| |#3| (LIST (QUOTE -968) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-669))) (|HasCategory| |#3| (LIST (QUOTE -968) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-735))) (|HasCategory| |#3| (LIST (QUOTE -968) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-787))) (|HasCategory| |#3| (LIST (QUOTE -968) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-977))) (|HasCategory| |#3| (LIST (QUOTE -968) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (LIST (QUOTE -968) (QUOTE (-525)))))) (|HasCategory| (-525) (QUOTE (-789))) (-12 (|HasCategory| |#3| (QUOTE (-977))) (|HasCategory| |#3| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-213))) (|HasCategory| |#3| (QUOTE (-977)))) (-12 (|HasCategory| |#3| (QUOTE (-977))) (|HasCategory| |#3| (LIST (QUOTE -835) (QUOTE (-1091))))) (-12 (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (LIST (QUOTE -968) (QUOTE (-525))))) (-3204 (|HasCategory| |#3| (QUOTE (-977))) (-12 (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (LIST (QUOTE -968) (QUOTE (-525)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#3| (QUOTE (-1020)))) (|HasAttribute| |#3| (QUOTE -4252)) (|HasCategory| |#3| (QUOTE (-126))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -566) (QUOTE (-798))))) (-1034 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)))) -(-1035 R -3855) +(-1035 R -3837) ((|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 @@ -4086,7 +4086,7 @@ NIL NIL (-1039 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4255 . T) (-4256 . T) (-1355 . T)) +((-4255 . T) (-4256 . T) (-1324 . T)) NIL (-1040 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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."))) @@ -4094,7 +4094,7 @@ NIL ((|HasCategory| |#3| (QUOTE (-341))) (|HasAttribute| |#3| (QUOTE (-4257 "*"))) (|HasCategory| |#3| (QUOTE (-160)))) (-1041 |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."))) -((-1355 . T) (-4255 . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-1324 . T) (-4255 . T) (-4249 . T) (-4250 . T) (-4252 . T)) NIL (-1042 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}."))) @@ -4103,16 +4103,16 @@ NIL (-1043 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."))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-6 -4253)) (-4250 . T) (-4249 . T) (-4252 . T)) -((|HasCategory| |#1| (QUOTE (-844))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (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 -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))) (-3316 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4253)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-844))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (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 -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))) (-3204 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4253)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) (-1044 |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}."))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4250 . T) (-4249 . T) (-4252 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (-3316 (|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))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341)))) (-1045 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}"))) -((-4256 . T) (-4255 . T) (-1355 . T)) +((-4256 . T) (-4255 . T) (-1324 . T)) NIL -(-1046 UP -3855) +(-1046 UP -3837) ((|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 @@ -4159,18 +4159,18 @@ NIL (-1057 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."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| (-1056 |#1| |#2|) (LIST (QUOTE -288) (LIST (QUOTE -1056) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1056 |#1| |#2|) (QUOTE (-1020)))) (|HasCategory| (-1056 |#1| |#2|) (QUOTE (-1020))) (-3316 (|HasCategory| (-1056 |#1| |#2|) (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| (-1056 |#1| |#2|) (LIST (QUOTE -288) (LIST (QUOTE -1056) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1056 |#1| |#2|) (QUOTE (-1020))))) (|HasCategory| (-1056 |#1| |#2|) (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| (-1056 |#1| |#2|) (LIST (QUOTE -288) (LIST (QUOTE -1056) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1056 |#1| |#2|) (QUOTE (-1020)))) (|HasCategory| (-1056 |#1| |#2|) (QUOTE (-1020))) (-3204 (|HasCategory| (-1056 |#1| |#2|) (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| (-1056 |#1| |#2|) (LIST (QUOTE -288) (LIST (QUOTE -1056) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1056 |#1| |#2|) (QUOTE (-1020))))) (|HasCategory| (-1056 |#1| |#2|) (LIST (QUOTE -566) (QUOTE (-798))))) (-1058 |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}."))) ((-4252 . T) (-4244 |has| |#2| (-6 (-4257 "*"))) (-4255 . T) (-4249 . T) (-4250 . T)) -((|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE (-4257 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (-3316 (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|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 -835) (QUOTE (-1091)))))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-341))) (-3316 (|HasAttribute| |#2| (QUOTE (-4257 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#2| (QUOTE (-213)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-160)))) +((|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE (-4257 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (-3204 (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|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 -835) (QUOTE (-1091)))))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-341))) (-3204 (|HasAttribute| |#2| (QUOTE (-4257 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasCategory| |#2| (QUOTE (-213)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-160)))) (-1059 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1060) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4256 . T) (-4255 . T) (-1355 . T)) +((-4256 . T) (-4255 . T) (-1324 . T)) NIL (-1061 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4183,19 +4183,19 @@ NIL (-1063 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-1064 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 (-1065 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})}."))) -((-1355 . T)) +((-1324 . T)) NIL (-1066 |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."))) ((-4256 . T)) -((-12 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3511) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3631) (|devaluate| |#2|)))))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-789))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3390) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2348) (|devaluate| |#2|)))))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-789))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) (-1067) ((|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 @@ -4219,19 +4219,19 @@ NIL (-1072 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."))) ((-4256 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-1073) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4256 . T) (-4255 . T) (-1355 . T)) +((-4256 . T) (-4255 . T) (-1324 . T)) NIL (-1074) NIL ((-4256 . T) (-4255 . T)) -((-3316 (-12 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|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 (-1020))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|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 (-1020))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-798))))) (-1075 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3511) (QUOTE (-1074))) (LIST (QUOTE |:|) (QUOTE -3631) (|devaluate| |#1|)))))) (-3316 (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-1020)))) (-3316 (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (QUOTE (-1020))) (|HasCategory| (-1074) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3390) (QUOTE (-1074))) (LIST (QUOTE |:|) (QUOTE -2348) (|devaluate| |#1|)))))) (-3204 (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-1020)))) (-3204 (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (QUOTE (-1020))) (|HasCategory| (-1074) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (LIST (QUOTE -566) (QUOTE (-798))))) (-1076 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 @@ -4258,9 +4258,9 @@ NIL NIL (-1082 |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."))) -(((-4257 "*") -3316 (-3850 (|has| |#1| (-341)) (|has| (-1089 |#1| |#2| |#3|) (-762))) (|has| |#1| (-160)) (-3850 (|has| |#1| (-341)) (|has| (-1089 |#1| |#2| |#3|) (-844)))) (-4248 -3316 (-3850 (|has| |#1| (-341)) (|has| (-1089 |#1| |#2| |#3|) (-762))) (|has| |#1| (-517)) (-3850 (|has| |#1| (-341)) (|has| (-1089 |#1| |#2| |#3|) (-844)))) (-4253 |has| |#1| (-341)) (-4247 |has| |#1| (-341)) (-4249 . T) (-4250 . T) (-4252 . 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(-844)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (-3204 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4253)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) (-1088 |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."))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-341)) (-4247 |has| |#1| (-341)) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|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 (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3316 (|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 -1278) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3316 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1113))) (|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 -2215) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2192) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|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 (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3204 (|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 -1267) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3204 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1113))) (|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 -4211) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2181) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|devaluate| |#1|))))))) (-1089 |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}."))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3316 (|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 -835) (QUOTE (-1091)))) (|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 (-1032))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasSignature| |#1| (LIST (QUOTE -1278) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasCategory| |#1| (QUOTE (-341))) (-3316 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1113))) (|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 -2215) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2192) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3204 (|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 -835) (QUOTE (-1091)))) (|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 (-1032))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasSignature| |#1| (LIST (QUOTE -1267) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasCategory| |#1| (QUOTE (-341))) (-3204 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1113))) (|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 -4211) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2181) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|devaluate| |#1|))))))) (-1090) ((|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 @@ -4303,7 +4303,7 @@ NIL (-1093 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-6 -4253)) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| (-904) (QUOTE (-126))) (|HasCategory| |#1| (QUOTE (-517)))) (-3316 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4253))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| (-904) (QUOTE (-126))) (|HasCategory| |#1| (QUOTE (-517)))) (-3204 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4253))) (-1094) ((|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 @@ -4335,7 +4335,7 @@ NIL (-1101 |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}"))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3511) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3631) (|devaluate| |#2|)))))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (-3316 (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3390) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2348) (|devaluate| |#2|)))))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (-3204 (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) (-1102 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 @@ -4346,7 +4346,7 @@ NIL NIL (-1104 |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})}."))) -((-4256 . T) (-1355 . T)) +((-4256 . T) (-1324 . T)) NIL (-1105 |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."))) @@ -4387,7 +4387,7 @@ NIL (-1114 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4256 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-1115 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4396,7 +4396,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1117 R -3855) +(-1117 R -3837) ((|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 @@ -4404,7 +4404,7 @@ 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 -(-1119 R -3855) +(-1119 R -3837) ((|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 -827) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -821) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -821) (|devaluate| |#1|))))) @@ -4414,12 +4414,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-346)))) (-1121 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4256 . T) (-4255 . T) (-1355 . T)) +((-4256 . T) (-4255 . T) (-1324 . T)) NIL (-1122 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4250 . T) (-4249 . T) (-4252 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (-3316 (|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))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341)))) (-1123 |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 @@ -4432,13 +4432,13 @@ 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 (-1020))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) -(-1126 -3855) +(-1126 -3837) ((|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 (-1127) ((|constructor| (NIL "The fundamental Type."))) -((-1355 . T)) +((-1324 . T)) NIL (-1128 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}.}"))) @@ -4470,16 +4470,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-341)))) (-1135 |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 -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3204 (-12 (|HasCategory| (-1165 |#1| |#2| |#3|) (QUOTE (-762))) (|HasCategory| |#1| (QUOTE (-341)))) (-12 (|HasCategory| (-1165 |#1| |#2| |#3|) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-160)))) (-12 (|HasCategory| (-1165 |#1| |#2| |#3|) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-1165 |#1| |#2| |#3|) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-341)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-1165 |#1| |#2| |#3|) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-341)))) (-12 (|HasCategory| (-1165 |#1| |#2| |#3|) (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-136))))) (-1138 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 @@ -4515,7 +4515,7 @@ NIL (-1146 |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."))) (((-4257 "*") |has| |#2| (-160)) (-4248 |has| |#2| (-517)) (-4251 |has| |#2| (-341)) (-4253 |has| |#2| (-6 -4253)) (-4250 . T) (-4249 . T) (-4252 . T)) -((|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3316 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1005) (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 -968) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (-3316 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3316 (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3316 (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1091)))) (-3316 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE -4253)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) +((|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3204 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1005) (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 -968) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (-3204 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3204 (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3204 (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1091)))) (-3204 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE -4253)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (-3204 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) (-1147 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 @@ -4531,7 +4531,7 @@ NIL (-1150 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 -835) (QUOTE (-1091)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1032))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -1278) (LIST (|devaluate| |#2|) (QUOTE (-1091)))))) +((|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1091)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1032))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -1267) (LIST (|devaluate| |#2|) (QUOTE (-1091)))))) (-1151 |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."))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4249 . T) (-4250 . T) (-4252 . T)) @@ -4559,22 +4559,22 @@ NIL (-1157 |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)}."))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-341)) (-4247 |has| |#1| (-341)) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|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 (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3316 (|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 -1278) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3316 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1113))) (|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 -2215) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2192) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) +((|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|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 (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3204 (|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 -1267) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3204 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1113))) (|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 -4211) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2181) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-1158 |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."))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4253 |has| |#1| (-341)) (-4247 |has| |#1| (-341)) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|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 (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-3316 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3316 (|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 -1278) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3316 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1113))) (|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 -2215) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2192) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1091)))) (|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 (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-3204 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3204 (|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 -1267) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3204 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1113))) (|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 -4211) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2181) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|devaluate| |#1|))))))) (-1159 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))}."))) (((-4257 "*") |has| (-1158 |#2| |#3| |#4|) (-160)) (-4248 |has| (-1158 |#2| |#3| |#4|) (-517)) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| (-1158 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-160))) (|HasCategory| (-1158 |#2| |#3| |#4|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-341))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-429))) (-3316 (|HasCategory| (-1158 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-517)))) +((|HasCategory| (-1158 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-160))) (|HasCategory| (-1158 |#2| |#3| |#4|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-341))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-429))) (-3204 (|HasCategory| (-1158 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-517)))) (-1160 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL ((|HasAttribute| |#1| (QUOTE -4256))) (-1161 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-1355 . T)) +((-1324 . T)) NIL (-1162 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) @@ -4583,7 +4583,7 @@ NIL (-1163 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-893))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasSignature| |#2| (LIST (QUOTE -2192) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2215) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1091))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-893))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasSignature| |#2| (LIST (QUOTE -2181) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4211) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1091))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341)))) (-1164 |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."))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4249 . T) (-4250 . T) (-4252 . T)) @@ -4591,18 +4591,18 @@ NIL (-1165 |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}."))) (((-4257 "*") |has| |#1| (-160)) (-4248 |has| |#1| (-517)) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3316 (|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 -835) (QUOTE (-1091)))) (|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 (-1032))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasSignature| |#1| (LIST (QUOTE -1278) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasCategory| |#1| (QUOTE (-341))) (-3316 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1113))) (|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 -2215) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2192) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3204 (|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 -835) (QUOTE (-1091)))) (|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 (-1032))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasSignature| |#1| (LIST (QUOTE -1267) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasCategory| |#1| (QUOTE (-341))) (-3204 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1113))) (|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 -4211) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2181) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|devaluate| |#1|))))))) (-1166 |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 -(-1167 -3855 UP L UTS) +(-1167 -3837 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)))) (-1168) ((|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."))) -((-1355 . T)) +((-1324 . T)) NIL (-1169 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) @@ -4614,7 +4614,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-977))) (|HasCategory| |#2| (QUOTE (-669))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1171 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4256 . T) (-4255 . T) (-1355 . T)) +((-4256 . T) (-4255 . T) (-1324 . T)) NIL (-1172 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4623,7 +4623,7 @@ NIL (-1173 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4256 . T) (-4255 . T)) -((-3316 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3316 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-977))) (-12 (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-977)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-3204 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3204 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3204 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-977))) (-12 (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-977)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-1174) ((|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 @@ -4656,7 +4656,7 @@ 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 -(-1182 K R UP -3855) +(-1182 K R UP -3837) ((|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 @@ -4684,11 +4684,11 @@ 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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4248 |has| |#2| (-6 -4248)) (-4250 . T) (-4249 . T) (-4252 . T)) NIL -(-1189 S -3855) +(-1189 S -3837) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138)))) -(-1190 -3855) +(-1190 -3837) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) NIL @@ -4744,4 +4744,4 @@ NIL NIL NIL NIL -((-3 NIL 2241067 2241072 2241077 2241082) (-2 NIL 2241047 2241052 2241057 2241062) (-1 NIL 2241027 2241032 2241037 2241042) (0 NIL 2241007 2241012 2241017 2241022) (-1199 "ZMOD.spad" 2240816 2240829 2240945 2241002) (-1198 "ZLINDEP.spad" 2239860 2239871 2240806 2240811) (-1197 "ZDSOLVE.spad" 2229709 2229731 2239850 2239855) (-1196 "YSTREAM.spad" 2229202 2229213 2229699 2229704) (-1195 "XRPOLY.spad" 2228422 2228442 2229058 2229127) (-1194 "XPR.spad" 2226151 2226164 2228140 2228239) (-1193 "XPOLY.spad" 2225706 2225717 2226007 2226076) (-1192 "XPOLYC.spad" 2225023 2225039 2225632 2225701) (-1191 "XPBWPOLY.spad" 2223460 2223480 2224803 2224872) (-1190 "XF.spad" 2221921 2221936 2223362 2223455) (-1189 "XF.spad" 2220362 2220379 2221805 2221810) (-1188 "XFALG.spad" 2217386 2217402 2220288 2220357) (-1187 "XEXPPKG.spad" 2216637 2216663 2217376 2217381) (-1186 "XDPOLY.spad" 2216251 2216267 2216493 2216562) (-1185 "XALG.spad" 2215849 2215860 2216207 2216246) (-1184 "WUTSET.spad" 2211688 2211705 2215495 2215522) (-1183 "WP.spad" 2210702 2210746 2211546 2211613) (-1182 "WFFINTBS.spad" 2208265 2208287 2210692 2210697) (-1181 "WEIER.spad" 2206479 2206490 2208255 2208260) (-1180 "VSPACE.spad" 2206152 2206163 2206447 2206474) (-1179 "VSPACE.spad" 2205845 2205858 2206142 2206147) (-1178 "VOID.spad" 2205435 2205444 2205835 2205840) (-1177 "VIEW.spad" 2203057 2203066 2205425 2205430) (-1176 "VIEWDEF.spad" 2198254 2198263 2203047 2203052) (-1175 "VIEW3D.spad" 2182089 2182098 2198244 2198249) (-1174 "VIEW2D.spad" 2169826 2169835 2182079 2182084) (-1173 "VECTOR.spad" 2168503 2168514 2168754 2168781) (-1172 "VECTOR2.spad" 2167130 2167143 2168493 2168498) (-1171 "VECTCAT.spad" 2165018 2165029 2167086 2167125) (-1170 "VECTCAT.spad" 2162727 2162740 2164797 2164802) (-1169 "VARIABLE.spad" 2162507 2162522 2162717 2162722) (-1168 "UTYPE.spad" 2162141 2162150 2162487 2162502) (-1167 "UTSODETL.spad" 2161434 2161458 2162097 2162102) (-1166 "UTSODE.spad" 2159622 2159642 2161424 2161429) (-1165 "UTS.spad" 2154411 2154439 2158089 2158186) (-1164 "UTSCAT.spad" 2151862 2151878 2154309 2154406) (-1163 "UTSCAT.spad" 2148957 2148975 2151406 2151411) (-1162 "UTS2.spad" 2148550 2148585 2148947 2148952) (-1161 "URAGG.spad" 2143172 2143183 2148530 2148545) (-1160 "URAGG.spad" 2137768 2137781 2143128 2143133) (-1159 "UPXSSING.spad" 2135414 2135440 2136852 2136985) (-1158 "UPXS.spad" 2132441 2132469 2133546 2133695) (-1157 "UPXSCONS.spad" 2130198 2130218 2130573 2130722) (-1156 "UPXSCCA.spad" 2128656 2128676 2130044 2130193) (-1155 "UPXSCCA.spad" 2127256 2127278 2128646 2128651) (-1154 "UPXSCAT.spad" 2125837 2125853 2127102 2127251) (-1153 "UPXS2.spad" 2125378 2125431 2125827 2125832) (-1152 "UPSQFREE.spad" 2123790 2123804 2125368 2125373) (-1151 "UPSCAT.spad" 2121383 2121407 2123688 2123785) (-1150 "UPSCAT.spad" 2118682 2118708 2120989 2120994) (-1149 "UPOLYC.spad" 2113660 2113671 2118524 2118677) (-1148 "UPOLYC.spad" 2108530 2108543 2113396 2113401) (-1147 "UPOLYC2.spad" 2107999 2108018 2108520 2108525) (-1146 "UP.spad" 2105044 2105059 2105552 2105705) (-1145 "UPMP.spad" 2103934 2103947 2105034 2105039) (-1144 "UPDIVP.spad" 2103497 2103511 2103924 2103929) (-1143 "UPDECOMP.spad" 2101734 2101748 2103487 2103492) (-1142 "UPCDEN.spad" 2100941 2100957 2101724 2101729) (-1141 "UP2.spad" 2100303 2100324 2100931 2100936) (-1140 "UNISEG.spad" 2099656 2099667 2100222 2100227) (-1139 "UNISEG2.spad" 2099149 2099162 2099612 2099617) (-1138 "UNIFACT.spad" 2098250 2098262 2099139 2099144) (-1137 "ULS.spad" 2088809 2088837 2089902 2090331) (-1136 "ULSCONS.spad" 2082852 2082872 2083224 2083373) (-1135 "ULSCCAT.spad" 2080449 2080469 2082672 2082847) (-1134 "ULSCCAT.spad" 2078180 2078202 2080405 2080410) (-1133 "ULSCAT.spad" 2076396 2076412 2078026 2078175) (-1132 "ULS2.spad" 2075908 2075961 2076386 2076391) (-1131 "UFD.spad" 2074973 2074982 2075834 2075903) (-1130 "UFD.spad" 2074100 2074111 2074963 2074968) (-1129 "UDVO.spad" 2072947 2072956 2074090 2074095) (-1128 "UDPO.spad" 2070374 2070385 2072903 2072908) (-1127 "TYPE.spad" 2070296 2070305 2070354 2070369) (-1126 "TWOFACT.spad" 2068946 2068961 2070286 2070291) (-1125 "TUPLE.spad" 2068332 2068343 2068845 2068850) (-1124 "TUBETOOL.spad" 2065169 2065178 2068322 2068327) (-1123 "TUBE.spad" 2063810 2063827 2065159 2065164) (-1122 "TS.spad" 2062399 2062415 2063375 2063472) (-1121 "TSETCAT.spad" 2049514 2049531 2062355 2062394) (-1120 "TSETCAT.spad" 2036627 2036646 2049470 2049475) (-1119 "TRMANIP.spad" 2030993 2031010 2036333 2036338) (-1118 "TRIMAT.spad" 2029952 2029977 2030983 2030988) (-1117 "TRIGMNIP.spad" 2028469 2028486 2029942 2029947) (-1116 "TRIGCAT.spad" 2027981 2027990 2028459 2028464) (-1115 "TRIGCAT.spad" 2027491 2027502 2027971 2027976) (-1114 "TREE.spad" 2026062 2026073 2027098 2027125) (-1113 "TRANFUN.spad" 2025893 2025902 2026052 2026057) (-1112 "TRANFUN.spad" 2025722 2025733 2025883 2025888) (-1111 "TOPSP.spad" 2025396 2025405 2025712 2025717) (-1110 "TOOLSIGN.spad" 2025059 2025070 2025386 2025391) (-1109 "TEXTFILE.spad" 2023616 2023625 2025049 2025054) (-1108 "TEX.spad" 2020633 2020642 2023606 2023611) (-1107 "TEX1.spad" 2020189 2020200 2020623 2020628) (-1106 "TEMUTL.spad" 2019744 2019753 2020179 2020184) (-1105 "TBCMPPK.spad" 2017837 2017860 2019734 2019739) (-1104 "TBAGG.spad" 2016861 2016884 2017805 2017832) (-1103 "TBAGG.spad" 2015905 2015930 2016851 2016856) (-1102 "TANEXP.spad" 2015281 2015292 2015895 2015900) (-1101 "TABLE.spad" 2013692 2013715 2013962 2013989) (-1100 "TABLEAU.spad" 2013173 2013184 2013682 2013687) (-1099 "TABLBUMP.spad" 2009956 2009967 2013163 2013168) (-1098 "SYSTEM.spad" 2009230 2009239 2009946 2009951) (-1097 "SYSSOLP.spad" 2006703 2006714 2009220 2009225) (-1096 "SYNTAX.spad" 2002895 2002904 2006693 2006698) (-1095 "SYMTAB.spad" 2000951 2000960 2002885 2002890) (-1094 "SYMS.spad" 1996936 1996945 2000941 2000946) (-1093 "SYMPOLY.spad" 1995946 1995957 1996028 1996155) (-1092 "SYMFUNC.spad" 1995421 1995432 1995936 1995941) (-1091 "SYMBOL.spad" 1992757 1992766 1995411 1995416) (-1090 "SWITCH.spad" 1989514 1989523 1992747 1992752) (-1089 "SUTS.spad" 1986413 1986441 1987981 1988078) (-1088 "SUPXS.spad" 1983427 1983455 1984545 1984694) (-1087 "SUP.spad" 1980199 1980210 1980980 1981133) (-1086 "SUPFRACF.spad" 1979304 1979322 1980189 1980194) (-1085 "SUP2.spad" 1978694 1978707 1979294 1979299) (-1084 "SUMRF.spad" 1977660 1977671 1978684 1978689) (-1083 "SUMFS.spad" 1977293 1977310 1977650 1977655) (-1082 "SULS.spad" 1967839 1967867 1968945 1969374) (-1081 "SUCH.spad" 1967519 1967534 1967829 1967834) (-1080 "SUBSPACE.spad" 1959526 1959541 1967509 1967514) (-1079 "SUBRESP.spad" 1958686 1958700 1959482 1959487) (-1078 "STTF.spad" 1954785 1954801 1958676 1958681) (-1077 "STTFNC.spad" 1951253 1951269 1954775 1954780) (-1076 "STTAYLOR.spad" 1943651 1943662 1951134 1951139) (-1075 "STRTBL.spad" 1942156 1942173 1942305 1942332) (-1074 "STRING.spad" 1941565 1941574 1941579 1941606) (-1073 "STRICAT.spad" 1941341 1941350 1941521 1941560) (-1072 "STREAM.spad" 1938109 1938120 1940866 1940881) (-1071 "STREAM3.spad" 1937654 1937669 1938099 1938104) (-1070 "STREAM2.spad" 1936722 1936735 1937644 1937649) (-1069 "STREAM1.spad" 1936426 1936437 1936712 1936717) (-1068 "STINPROD.spad" 1935332 1935348 1936416 1936421) (-1067 "STEP.spad" 1934533 1934542 1935322 1935327) (-1066 "STBL.spad" 1933059 1933087 1933226 1933241) (-1065 "STAGG.spad" 1932124 1932135 1933039 1933054) (-1064 "STAGG.spad" 1931197 1931210 1932114 1932119) (-1063 "STACK.spad" 1930548 1930559 1930804 1930831) (-1062 "SREGSET.spad" 1928252 1928269 1930194 1930221) (-1061 "SRDCMPK.spad" 1926797 1926817 1928242 1928247) (-1060 "SRAGG.spad" 1921882 1921891 1926753 1926792) (-1059 "SRAGG.spad" 1916999 1917010 1921872 1921877) (-1058 "SQMATRIX.spad" 1914625 1914643 1915533 1915620) (-1057 "SPLTREE.spad" 1909177 1909190 1914061 1914088) (-1056 "SPLNODE.spad" 1905765 1905778 1909167 1909172) (-1055 "SPFCAT.spad" 1904542 1904551 1905755 1905760) (-1054 "SPECOUT.spad" 1903092 1903101 1904532 1904537) (-1053 "spad-parser.spad" 1902557 1902566 1903082 1903087) (-1052 "SPACEC.spad" 1886570 1886581 1902547 1902552) (-1051 "SPACE3.spad" 1886346 1886357 1886560 1886565) (-1050 "SORTPAK.spad" 1885891 1885904 1886302 1886307) (-1049 "SOLVETRA.spad" 1883648 1883659 1885881 1885886) (-1048 "SOLVESER.spad" 1882168 1882179 1883638 1883643) (-1047 "SOLVERAD.spad" 1878178 1878189 1882158 1882163) (-1046 "SOLVEFOR.spad" 1876598 1876616 1878168 1878173) (-1045 "SNTSCAT.spad" 1876186 1876203 1876554 1876593) (-1044 "SMTS.spad" 1874446 1874472 1875751 1875848) (-1043 "SMP.spad" 1871888 1871908 1872278 1872405) (-1042 "SMITH.spad" 1870731 1870756 1871878 1871883) (-1041 "SMATCAT.spad" 1868829 1868859 1870663 1870726) (-1040 "SMATCAT.spad" 1866871 1866903 1868707 1868712) (-1039 "SKAGG.spad" 1865820 1865831 1866827 1866866) (-1038 "SINT.spad" 1864128 1864137 1865686 1865815) (-1037 "SIMPAN.spad" 1863856 1863865 1864118 1864123) (-1036 "SIGNRF.spad" 1862964 1862975 1863846 1863851) (-1035 "SIGNEF.spad" 1862233 1862250 1862954 1862959) (-1034 "SHP.spad" 1860151 1860166 1862189 1862194) (-1033 "SHDP.spad" 1851187 1851214 1851696 1851825) (-1032 "SGROUP.spad" 1850653 1850662 1851177 1851182) (-1031 "SGROUP.spad" 1850117 1850128 1850643 1850648) (-1030 "SGCF.spad" 1842998 1843007 1850107 1850112) (-1029 "SFRTCAT.spad" 1841914 1841931 1842954 1842993) (-1028 "SFRGCD.spad" 1840977 1840997 1841904 1841909) (-1027 "SFQCMPK.spad" 1835614 1835634 1840967 1840972) (-1026 "SFORT.spad" 1835049 1835063 1835604 1835609) (-1025 "SEXOF.spad" 1834892 1834932 1835039 1835044) (-1024 "SEX.spad" 1834784 1834793 1834882 1834887) (-1023 "SEXCAT.spad" 1831888 1831928 1834774 1834779) (-1022 "SET.spad" 1830188 1830199 1831309 1831348) (-1021 "SETMN.spad" 1828622 1828639 1830178 1830183) (-1020 "SETCAT.spad" 1828107 1828116 1828612 1828617) (-1019 "SETCAT.spad" 1827590 1827601 1828097 1828102) (-1018 "SETAGG.spad" 1824113 1824124 1827558 1827585) (-1017 "SETAGG.spad" 1820656 1820669 1824103 1824108) (-1016 "SEGXCAT.spad" 1819768 1819781 1820636 1820651) (-1015 "SEG.spad" 1819581 1819592 1819687 1819692) (-1014 "SEGCAT.spad" 1818400 1818411 1819561 1819576) (-1013 "SEGBIND.spad" 1817472 1817483 1818355 1818360) (-1012 "SEGBIND2.spad" 1817168 1817181 1817462 1817467) (-1011 "SEG2.spad" 1816593 1816606 1817124 1817129) (-1010 "SDVAR.spad" 1815869 1815880 1816583 1816588) (-1009 "SDPOL.spad" 1813262 1813273 1813553 1813680) (-1008 "SCPKG.spad" 1811341 1811352 1813252 1813257) (-1007 "SCOPE.spad" 1810486 1810495 1811331 1811336) (-1006 "SCACHE.spad" 1809168 1809179 1810476 1810481) (-1005 "SAOS.spad" 1809040 1809049 1809158 1809163) (-1004 "SAERFFC.spad" 1808753 1808773 1809030 1809035) (-1003 "SAE.spad" 1806931 1806947 1807542 1807677) (-1002 "SAEFACT.spad" 1806632 1806652 1806921 1806926) (-1001 "RURPK.spad" 1804273 1804289 1806622 1806627) (-1000 "RULESET.spad" 1803714 1803738 1804263 1804268) (-999 "RULE.spad" 1801919 1801942 1803704 1803709) (-998 "RULECOLD.spad" 1801772 1801784 1801909 1801914) (-997 "RSETGCD.spad" 1798151 1798170 1801762 1801767) (-996 "RSETCAT.spad" 1787924 1787940 1798107 1798146) (-995 "RSETCAT.spad" 1777729 1777747 1787914 1787919) (-994 "RSDCMPK.spad" 1776182 1776201 1777719 1777724) (-993 "RRCC.spad" 1774567 1774596 1776172 1776177) (-992 "RRCC.spad" 1772950 1772981 1774557 1774562) (-991 "RPOLCAT.spad" 1752311 1752325 1772818 1772945) (-990 "RPOLCAT.spad" 1731387 1731403 1751896 1751901) (-989 "ROUTINE.spad" 1727251 1727259 1730034 1730061) (-988 "ROMAN.spad" 1726484 1726492 1727117 1727246) (-987 "ROIRC.spad" 1725565 1725596 1726474 1726479) (-986 "RNS.spad" 1724469 1724477 1725467 1725560) (-985 "RNS.spad" 1723459 1723469 1724459 1724464) (-984 "RNG.spad" 1723195 1723203 1723449 1723454) (-983 "RMODULE.spad" 1722834 1722844 1723185 1723190) (-982 "RMCAT2.spad" 1722243 1722299 1722824 1722829) (-981 "RMATRIX.spad" 1720923 1720941 1721410 1721449) (-980 "RMATCAT.spad" 1716445 1716475 1720867 1720918) (-979 "RMATCAT.spad" 1711869 1711901 1716293 1716298) (-978 "RINTERP.spad" 1711758 1711777 1711859 1711864) (-977 "RING.spad" 1711116 1711124 1711738 1711753) (-976 "RING.spad" 1710482 1710492 1711106 1711111) (-975 "RIDIST.spad" 1709867 1709875 1710472 1710477) (-974 "RGCHAIN.spad" 1708447 1708462 1709352 1709379) (-973 "RF.spad" 1706062 1706072 1708437 1708442) (-972 "RFFACTOR.spad" 1705525 1705535 1706052 1706057) (-971 "RFFACT.spad" 1705261 1705272 1705515 1705520) (-970 "RFDIST.spad" 1704250 1704258 1705251 1705256) (-969 "RETSOL.spad" 1703668 1703680 1704240 1704245) (-968 "RETRACT.spad" 1703018 1703028 1703658 1703663) (-967 "RETRACT.spad" 1702366 1702378 1703008 1703013) (-966 "RESULT.spad" 1700427 1700435 1701013 1701040) (-965 "RESRING.spad" 1699775 1699821 1700365 1700422) (-964 "RESLATC.spad" 1699100 1699110 1699765 1699770) (-963 "REPSQ.spad" 1698830 1698840 1699090 1699095) (-962 "REP.spad" 1696383 1696391 1698820 1698825) (-961 "REPDB.spad" 1696089 1696099 1696373 1696378) (-960 "REP2.spad" 1685662 1685672 1695931 1695936) (-959 "REP1.spad" 1679653 1679663 1685612 1685617) (-958 "REGSET.spad" 1677451 1677467 1679299 1679326) (-957 "REF.spad" 1676781 1676791 1677406 1677411) (-956 "REDORDER.spad" 1675958 1675974 1676771 1676776) (-955 "RECLOS.spad" 1674748 1674767 1675451 1675544) (-954 "REALSOLV.spad" 1673881 1673889 1674738 1674743) (-953 "REAL.spad" 1673754 1673762 1673871 1673876) (-952 "REAL0Q.spad" 1671037 1671051 1673744 1673749) (-951 "REAL0.spad" 1667866 1667880 1671027 1671032) (-950 "RDIV.spad" 1667518 1667542 1667856 1667861) (-949 "RDIST.spad" 1667082 1667092 1667508 1667513) (-948 "RDETRS.spad" 1665879 1665896 1667072 1667077) (-947 "RDETR.spad" 1663987 1664004 1665869 1665874) (-946 "RDEEFS.spad" 1663061 1663077 1663977 1663982) (-945 "RDEEF.spad" 1662058 1662074 1663051 1663056) (-944 "RCFIELD.spad" 1659245 1659253 1661960 1662053) (-943 "RCFIELD.spad" 1656518 1656528 1659235 1659240) (-942 "RCAGG.spad" 1654421 1654431 1656498 1656513) (-941 "RCAGG.spad" 1652261 1652273 1654340 1654345) (-940 "RATRET.spad" 1651622 1651632 1652251 1652256) (-939 "RATFACT.spad" 1651315 1651326 1651612 1651617) (-938 "RANDSRC.spad" 1650635 1650643 1651305 1651310) (-937 "RADUTIL.spad" 1650390 1650398 1650625 1650630) (-936 "RADIX.spad" 1647183 1647196 1648860 1648953) (-935 "RADFF.spad" 1645600 1645636 1645718 1645874) (-934 "RADCAT.spad" 1645194 1645202 1645590 1645595) (-933 "RADCAT.spad" 1644786 1644796 1645184 1645189) (-932 "QUEUE.spad" 1644129 1644139 1644393 1644420) (-931 "QUAT.spad" 1642715 1642725 1643057 1643122) (-930 "QUATCT2.spad" 1642334 1642352 1642705 1642710) (-929 "QUATCAT.spad" 1640499 1640509 1642264 1642329) (-928 "QUATCAT.spad" 1638416 1638428 1640183 1640188) (-927 "QUAGG.spad" 1637230 1637240 1638372 1638411) (-926 "QFORM.spad" 1636693 1636707 1637220 1637225) (-925 "QFCAT.spad" 1635384 1635394 1636583 1636688) (-924 "QFCAT.spad" 1633681 1633693 1634882 1634887) (-923 "QFCAT2.spad" 1633372 1633388 1633671 1633676) (-922 "QEQUAT.spad" 1632929 1632937 1633362 1633367) (-921 "QCMPACK.spad" 1627676 1627695 1632919 1632924) (-920 "QALGSET.spad" 1623751 1623783 1627590 1627595) (-919 "QALGSET2.spad" 1621747 1621765 1623741 1623746) (-918 "PWFFINTB.spad" 1619057 1619078 1621737 1621742) (-917 "PUSHVAR.spad" 1618386 1618405 1619047 1619052) (-916 "PTRANFN.spad" 1614512 1614522 1618376 1618381) (-915 "PTPACK.spad" 1611600 1611610 1614502 1614507) (-914 "PTFUNC2.spad" 1611421 1611435 1611590 1611595) (-913 "PTCAT.spad" 1610503 1610513 1611377 1611416) (-912 "PSQFR.spad" 1609810 1609834 1610493 1610498) (-911 "PSEUDLIN.spad" 1608668 1608678 1609800 1609805) (-910 "PSETPK.spad" 1594101 1594117 1608546 1608551) (-909 "PSETCAT.spad" 1588009 1588032 1594069 1594096) (-908 "PSETCAT.spad" 1581903 1581928 1587965 1587970) (-907 "PSCURVE.spad" 1580886 1580894 1581893 1581898) (-906 "PSCAT.spad" 1579653 1579682 1580784 1580881) (-905 "PSCAT.spad" 1578510 1578541 1579643 1579648) (-904 "PRTITION.spad" 1577353 1577361 1578500 1578505) (-903 "PRS.spad" 1566915 1566932 1577309 1577314) (-902 "PRQAGG.spad" 1566334 1566344 1566871 1566910) (-901 "PROPLOG.spad" 1565737 1565745 1566324 1566329) (-900 "PROPFRML.spad" 1563602 1563613 1565673 1565678) (-899 "PROPERTY.spad" 1563096 1563104 1563592 1563597) (-898 "PRODUCT.spad" 1560776 1560788 1561062 1561117) (-897 "PR.spad" 1559165 1559177 1559870 1559997) (-896 "PRINT.spad" 1558917 1558925 1559155 1559160) (-895 "PRIMES.spad" 1557168 1557178 1558907 1558912) (-894 "PRIMELT.spad" 1555149 1555163 1557158 1557163) (-893 "PRIMCAT.spad" 1554772 1554780 1555139 1555144) (-892 "PRIMARR.spad" 1553777 1553787 1553955 1553982) (-891 "PRIMARR2.spad" 1552500 1552512 1553767 1553772) (-890 "PREASSOC.spad" 1551872 1551884 1552490 1552495) (-889 "PPCURVE.spad" 1551009 1551017 1551862 1551867) (-888 "POLYROOT.spad" 1549781 1549803 1550965 1550970) (-887 "POLY.spad" 1547081 1547091 1547598 1547725) (-886 "POLYLIFT.spad" 1546342 1546365 1547071 1547076) (-885 "POLYCATQ.spad" 1544444 1544466 1546332 1546337) (-884 "POLYCAT.spad" 1537850 1537871 1544312 1544439) (-883 "POLYCAT.spad" 1530558 1530581 1537022 1537027) (-882 "POLY2UP.spad" 1530006 1530020 1530548 1530553) (-881 "POLY2.spad" 1529601 1529613 1529996 1530001) (-880 "POLUTIL.spad" 1528542 1528571 1529557 1529562) (-879 "POLTOPOL.spad" 1527290 1527305 1528532 1528537) (-878 "POINT.spad" 1526131 1526141 1526218 1526245) (-877 "PNTHEORY.spad" 1522797 1522805 1526121 1526126) (-876 "PMTOOLS.spad" 1521554 1521568 1522787 1522792) (-875 "PMSYM.spad" 1521099 1521109 1521544 1521549) (-874 "PMQFCAT.spad" 1520686 1520700 1521089 1521094) (-873 "PMPRED.spad" 1520155 1520169 1520676 1520681) (-872 "PMPREDFS.spad" 1519599 1519621 1520145 1520150) (-871 "PMPLCAT.spad" 1518669 1518687 1519531 1519536) (-870 "PMLSAGG.spad" 1518250 1518264 1518659 1518664) (-869 "PMKERNEL.spad" 1517817 1517829 1518240 1518245) (-868 "PMINS.spad" 1517393 1517403 1517807 1517812) (-867 "PMFS.spad" 1516966 1516984 1517383 1517388) (-866 "PMDOWN.spad" 1516252 1516266 1516956 1516961) (-865 "PMASS.spad" 1515264 1515272 1516242 1516247) (-864 "PMASSFS.spad" 1514233 1514249 1515254 1515259) (-863 "PLOTTOOL.spad" 1514013 1514021 1514223 1514228) (-862 "PLOT.spad" 1508844 1508852 1514003 1514008) (-861 "PLOT3D.spad" 1505264 1505272 1508834 1508839) (-860 "PLOT1.spad" 1504405 1504415 1505254 1505259) (-859 "PLEQN.spad" 1491621 1491648 1504395 1504400) (-858 "PINTERP.spad" 1491237 1491256 1491611 1491616) (-857 "PINTERPA.spad" 1491019 1491035 1491227 1491232) (-856 "PI.spad" 1490626 1490634 1490993 1491014) (-855 "PID.spad" 1489582 1489590 1490552 1490621) (-854 "PICOERCE.spad" 1489239 1489249 1489572 1489577) (-853 "PGROEB.spad" 1487836 1487850 1489229 1489234) (-852 "PGE.spad" 1479089 1479097 1487826 1487831) (-851 "PGCD.spad" 1477971 1477988 1479079 1479084) (-850 "PFRPAC.spad" 1477114 1477124 1477961 1477966) (-849 "PFR.spad" 1473771 1473781 1477016 1477109) (-848 "PFOTOOLS.spad" 1473029 1473045 1473761 1473766) (-847 "PFOQ.spad" 1472399 1472417 1473019 1473024) (-846 "PFO.spad" 1471818 1471845 1472389 1472394) (-845 "PF.spad" 1471392 1471404 1471623 1471716) (-844 "PFECAT.spad" 1469058 1469066 1471318 1471387) (-843 "PFECAT.spad" 1466752 1466762 1469014 1469019) (-842 "PFBRU.spad" 1464622 1464634 1466742 1466747) (-841 "PFBR.spad" 1462160 1462183 1464612 1464617) (-840 "PERM.spad" 1457841 1457851 1461990 1462005) (-839 "PERMGRP.spad" 1452577 1452587 1457831 1457836) (-838 "PERMCAT.spad" 1451129 1451139 1452557 1452572) (-837 "PERMAN.spad" 1449661 1449675 1451119 1451124) (-836 "PENDTREE.spad" 1448934 1448944 1449290 1449295) (-835 "PDRING.spad" 1447425 1447435 1448914 1448929) (-834 "PDRING.spad" 1445924 1445936 1447415 1447420) (-833 "PDEPROB.spad" 1444881 1444889 1445914 1445919) (-832 "PDEPACK.spad" 1438883 1438891 1444871 1444876) (-831 "PDECOMP.spad" 1438345 1438362 1438873 1438878) (-830 "PDECAT.spad" 1436699 1436707 1438335 1438340) (-829 "PCOMP.spad" 1436550 1436563 1436689 1436694) (-828 "PBWLB.spad" 1435132 1435149 1436540 1436545) (-827 "PATTERN.spad" 1429563 1429573 1435122 1435127) (-826 "PATTERN2.spad" 1429299 1429311 1429553 1429558) (-825 "PATTERN1.spad" 1427601 1427617 1429289 1429294) (-824 "PATRES.spad" 1425148 1425160 1427591 1427596) (-823 "PATRES2.spad" 1424810 1424824 1425138 1425143) (-822 "PATMATCH.spad" 1422972 1423003 1424523 1424528) (-821 "PATMAB.spad" 1422397 1422407 1422962 1422967) (-820 "PATLRES.spad" 1421481 1421495 1422387 1422392) (-819 "PATAB.spad" 1421245 1421255 1421471 1421476) (-818 "PARTPERM.spad" 1418607 1418615 1421235 1421240) (-817 "PARSURF.spad" 1418035 1418063 1418597 1418602) (-816 "PARSU2.spad" 1417830 1417846 1418025 1418030) (-815 "script-parser.spad" 1417350 1417358 1417820 1417825) (-814 "PARSCURV.spad" 1416778 1416806 1417340 1417345) (-813 "PARSC2.spad" 1416567 1416583 1416768 1416773) (-812 "PARPCURV.spad" 1416025 1416053 1416557 1416562) (-811 "PARPC2.spad" 1415814 1415830 1416015 1416020) (-810 "PAN2EXPR.spad" 1415226 1415234 1415804 1415809) (-809 "PALETTE.spad" 1414196 1414204 1415216 1415221) (-808 "PAIR.spad" 1413179 1413192 1413784 1413789) (-807 "PADICRC.spad" 1410512 1410530 1411687 1411780) (-806 "PADICRAT.spad" 1408530 1408542 1408751 1408844) (-805 "PADIC.spad" 1408225 1408237 1408456 1408525) (-804 "PADICCT.spad" 1406766 1406778 1408151 1408220) (-803 "PADEPAC.spad" 1405445 1405464 1406756 1406761) (-802 "PADE.spad" 1404185 1404201 1405435 1405440) (-801 "OWP.spad" 1403169 1403199 1404043 1404110) (-800 "OVAR.spad" 1402950 1402973 1403159 1403164) (-799 "OUT.spad" 1402034 1402042 1402940 1402945) (-798 "OUTFORM.spad" 1391448 1391456 1402024 1402029) (-797 "OSI.spad" 1390923 1390931 1391438 1391443) (-796 "OSGROUP.spad" 1390841 1390849 1390913 1390918) (-795 "ORTHPOL.spad" 1389302 1389312 1390758 1390763) (-794 "OREUP.spad" 1388662 1388690 1388984 1389023) (-793 "ORESUP.spad" 1387963 1387987 1388344 1388383) (-792 "OREPCTO.spad" 1385782 1385794 1387883 1387888) (-791 "OREPCAT.spad" 1379839 1379849 1385738 1385777) (-790 "OREPCAT.spad" 1373786 1373798 1379687 1379692) (-789 "ORDSET.spad" 1372952 1372960 1373776 1373781) (-788 "ORDSET.spad" 1372116 1372126 1372942 1372947) (-787 "ORDRING.spad" 1371506 1371514 1372096 1372111) (-786 "ORDRING.spad" 1370904 1370914 1371496 1371501) (-785 "ORDMON.spad" 1370759 1370767 1370894 1370899) (-784 "ORDFUNS.spad" 1369885 1369901 1370749 1370754) (-783 "ORDFIN.spad" 1369819 1369827 1369875 1369880) (-782 "ORDCOMP.spad" 1368287 1368297 1369369 1369398) (-781 "ORDCOMP2.spad" 1367572 1367584 1368277 1368282) (-780 "OPTPROB.spad" 1366152 1366160 1367562 1367567) (-779 "OPTPACK.spad" 1358537 1358545 1366142 1366147) (-778 "OPTCAT.spad" 1356212 1356220 1358527 1358532) (-777 "OPQUERY.spad" 1355761 1355769 1356202 1356207) (-776 "OP.spad" 1355503 1355513 1355583 1355650) (-775 "ONECOMP.spad" 1354251 1354261 1355053 1355082) (-774 "ONECOMP2.spad" 1353669 1353681 1354241 1354246) (-773 "OMSERVER.spad" 1352671 1352679 1353659 1353664) (-772 "OMSAGG.spad" 1352447 1352457 1352615 1352666) (-771 "OMPKG.spad" 1351059 1351067 1352437 1352442) (-770 "OM.spad" 1350024 1350032 1351049 1351054) (-769 "OMLO.spad" 1349449 1349461 1349910 1349949) (-768 "OMEXPR.spad" 1349283 1349293 1349439 1349444) (-767 "OMERR.spad" 1348826 1348834 1349273 1349278) (-766 "OMERRK.spad" 1347860 1347868 1348816 1348821) (-765 "OMENC.spad" 1347204 1347212 1347850 1347855) (-764 "OMDEV.spad" 1341493 1341501 1347194 1347199) (-763 "OMCONN.spad" 1340902 1340910 1341483 1341488) (-762 "OINTDOM.spad" 1340665 1340673 1340828 1340897) (-761 "OFMONOID.spad" 1336852 1336862 1340655 1340660) (-760 "ODVAR.spad" 1336113 1336123 1336842 1336847) (-759 "ODR.spad" 1335561 1335587 1335925 1336074) (-758 "ODPOL.spad" 1332910 1332920 1333250 1333377) (-757 "ODP.spad" 1324082 1324102 1324455 1324584) (-756 "ODETOOLS.spad" 1322665 1322684 1324072 1324077) (-755 "ODESYS.spad" 1320315 1320332 1322655 1322660) (-754 "ODERTRIC.spad" 1316256 1316273 1320272 1320277) (-753 "ODERED.spad" 1315643 1315667 1316246 1316251) (-752 "ODERAT.spad" 1313194 1313211 1315633 1315638) (-751 "ODEPRRIC.spad" 1310085 1310107 1313184 1313189) (-750 "ODEPROB.spad" 1309284 1309292 1310075 1310080) (-749 "ODEPRIM.spad" 1306558 1306580 1309274 1309279) (-748 "ODEPAL.spad" 1305934 1305958 1306548 1306553) (-747 "ODEPACK.spad" 1292536 1292544 1305924 1305929) (-746 "ODEINT.spad" 1291967 1291983 1292526 1292531) (-745 "ODEIFTBL.spad" 1289362 1289370 1291957 1291962) (-744 "ODEEF.spad" 1284729 1284745 1289352 1289357) (-743 "ODECONST.spad" 1284248 1284266 1284719 1284724) (-742 "ODECAT.spad" 1282844 1282852 1284238 1284243) (-741 "OCT.spad" 1280991 1281001 1281707 1281746) (-740 "OCTCT2.spad" 1280635 1280656 1280981 1280986) (-739 "OC.spad" 1278409 1278419 1280591 1280630) (-738 "OC.spad" 1275909 1275921 1278093 1278098) (-737 "OCAMON.spad" 1275757 1275765 1275899 1275904) (-736 "OASGP.spad" 1275572 1275580 1275747 1275752) (-735 "OAMONS.spad" 1275092 1275100 1275562 1275567) (-734 "OAMON.spad" 1274953 1274961 1275082 1275087) (-733 "OAGROUP.spad" 1274815 1274823 1274943 1274948) (-732 "NUMTUBE.spad" 1274402 1274418 1274805 1274810) (-731 "NUMQUAD.spad" 1262264 1262272 1274392 1274397) (-730 "NUMODE.spad" 1253400 1253408 1262254 1262259) (-729 "NUMINT.spad" 1250958 1250966 1253390 1253395) (-728 "NUMFMT.spad" 1249798 1249806 1250948 1250953) (-727 "NUMERIC.spad" 1241871 1241881 1249604 1249609) (-726 "NTSCAT.spad" 1240361 1240377 1241827 1241866) (-725 "NTPOLFN.spad" 1239906 1239916 1240278 1240283) (-724 "NSUP.spad" 1232919 1232929 1237459 1237612) (-723 "NSUP2.spad" 1232311 1232323 1232909 1232914) (-722 "NSMP.spad" 1228510 1228529 1228818 1228945) (-721 "NREP.spad" 1226882 1226896 1228500 1228505) (-720 "NPCOEF.spad" 1226128 1226148 1226872 1226877) (-719 "NORMRETR.spad" 1225726 1225765 1226118 1226123) (-718 "NORMPK.spad" 1223628 1223647 1225716 1225721) (-717 "NORMMA.spad" 1223316 1223342 1223618 1223623) (-716 "NONE.spad" 1223057 1223065 1223306 1223311) (-715 "NONE1.spad" 1222733 1222743 1223047 1223052) (-714 "NODE1.spad" 1222202 1222218 1222723 1222728) (-713 "NNI.spad" 1221089 1221097 1222176 1222197) (-712 "NLINSOL.spad" 1219711 1219721 1221079 1221084) (-711 "NIPROB.spad" 1218194 1218202 1219701 1219706) (-710 "NFINTBAS.spad" 1215654 1215671 1218184 1218189) (-709 "NCODIV.spad" 1213852 1213868 1215644 1215649) (-708 "NCNTFRAC.spad" 1213494 1213508 1213842 1213847) (-707 "NCEP.spad" 1211654 1211668 1213484 1213489) (-706 "NASRING.spad" 1211250 1211258 1211644 1211649) (-705 "NASRING.spad" 1210844 1210854 1211240 1211245) (-704 "NARNG.spad" 1210188 1210196 1210834 1210839) (-703 "NARNG.spad" 1209530 1209540 1210178 1210183) (-702 "NAGSP.spad" 1208603 1208611 1209520 1209525) (-701 "NAGS.spad" 1198128 1198136 1208593 1208598) (-700 "NAGF07.spad" 1196521 1196529 1198118 1198123) (-699 "NAGF04.spad" 1190753 1190761 1196511 1196516) (-698 "NAGF02.spad" 1184562 1184570 1190743 1190748) (-697 "NAGF01.spad" 1180165 1180173 1184552 1184557) (-696 "NAGE04.spad" 1173625 1173633 1180155 1180160) (-695 "NAGE02.spad" 1163967 1163975 1173615 1173620) (-694 "NAGE01.spad" 1159851 1159859 1163957 1163962) (-693 "NAGD03.spad" 1157771 1157779 1159841 1159846) (-692 "NAGD02.spad" 1150302 1150310 1157761 1157766) (-691 "NAGD01.spad" 1144415 1144423 1150292 1150297) (-690 "NAGC06.spad" 1140202 1140210 1144405 1144410) (-689 "NAGC05.spad" 1138671 1138679 1140192 1140197) (-688 "NAGC02.spad" 1137926 1137934 1138661 1138666) (-687 "NAALG.spad" 1137461 1137471 1137894 1137921) (-686 "NAALG.spad" 1137016 1137028 1137451 1137456) (-685 "MULTSQFR.spad" 1133974 1133991 1137006 1137011) (-684 "MULTFACT.spad" 1133357 1133374 1133964 1133969) (-683 "MTSCAT.spad" 1131391 1131412 1133255 1133352) (-682 "MTHING.spad" 1131048 1131058 1131381 1131386) (-681 "MSYSCMD.spad" 1130482 1130490 1131038 1131043) (-680 "MSET.spad" 1128424 1128434 1130188 1130227) (-679 "MSETAGG.spad" 1128257 1128267 1128380 1128419) (-678 "MRING.spad" 1125228 1125240 1127965 1128032) (-677 "MRF2.spad" 1124796 1124810 1125218 1125223) (-676 "MRATFAC.spad" 1124342 1124359 1124786 1124791) (-675 "MPRFF.spad" 1122372 1122391 1124332 1124337) (-674 "MPOLY.spad" 1119810 1119825 1120169 1120296) (-673 "MPCPF.spad" 1119074 1119093 1119800 1119805) (-672 "MPC3.spad" 1118889 1118929 1119064 1119069) (-671 "MPC2.spad" 1118531 1118564 1118879 1118884) (-670 "MONOTOOL.spad" 1116866 1116883 1118521 1118526) (-669 "MONOID.spad" 1116040 1116048 1116856 1116861) (-668 "MONOID.spad" 1115212 1115222 1116030 1116035) (-667 "MONOGEN.spad" 1113958 1113971 1115072 1115207) (-666 "MONOGEN.spad" 1112726 1112741 1113842 1113847) (-665 "MONADWU.spad" 1110740 1110748 1112716 1112721) (-664 "MONADWU.spad" 1108752 1108762 1110730 1110735) (-663 "MONAD.spad" 1107896 1107904 1108742 1108747) (-662 "MONAD.spad" 1107038 1107048 1107886 1107891) (-661 "MOEBIUS.spad" 1105724 1105738 1107018 1107033) (-660 "MODULE.spad" 1105594 1105604 1105692 1105719) (-659 "MODULE.spad" 1105484 1105496 1105584 1105589) (-658 "MODRING.spad" 1104815 1104854 1105464 1105479) (-657 "MODOP.spad" 1103474 1103486 1104637 1104704) (-656 "MODMONOM.spad" 1103006 1103024 1103464 1103469) (-655 "MODMON.spad" 1099711 1099727 1100487 1100640) (-654 "MODFIELD.spad" 1099069 1099108 1099613 1099706) (-653 "MMLFORM.spad" 1097929 1097937 1099059 1099064) (-652 "MMAP.spad" 1097669 1097703 1097919 1097924) (-651 "MLO.spad" 1096096 1096106 1097625 1097664) (-650 "MLIFT.spad" 1094668 1094685 1096086 1096091) (-649 "MKUCFUNC.spad" 1094201 1094219 1094658 1094663) (-648 "MKRECORD.spad" 1093803 1093816 1094191 1094196) (-647 "MKFUNC.spad" 1093184 1093194 1093793 1093798) (-646 "MKFLCFN.spad" 1092140 1092150 1093174 1093179) (-645 "MKCHSET.spad" 1091916 1091926 1092130 1092135) (-644 "MKBCFUNC.spad" 1091401 1091419 1091906 1091911) (-643 "MINT.spad" 1090840 1090848 1091303 1091396) (-642 "MHROWRED.spad" 1089341 1089351 1090830 1090835) (-641 "MFLOAT.spad" 1087786 1087794 1089231 1089336) (-640 "MFINFACT.spad" 1087186 1087208 1087776 1087781) (-639 "MESH.spad" 1084918 1084926 1087176 1087181) (-638 "MDDFACT.spad" 1083111 1083121 1084908 1084913) (-637 "MDAGG.spad" 1082386 1082396 1083079 1083106) (-636 "MCMPLX.spad" 1078366 1078374 1078980 1079181) (-635 "MCDEN.spad" 1077574 1077586 1078356 1078361) (-634 "MCALCFN.spad" 1074676 1074702 1077564 1077569) (-633 "MATSTOR.spad" 1071952 1071962 1074666 1074671) (-632 "MATRIX.spad" 1070656 1070666 1071140 1071167) (-631 "MATLIN.spad" 1067982 1068006 1070540 1070545) (-630 "MATCAT.spad" 1059555 1059577 1067938 1067977) (-629 "MATCAT.spad" 1051012 1051036 1059397 1059402) (-628 "MATCAT2.spad" 1050280 1050328 1051002 1051007) (-627 "MAPPKG3.spad" 1049179 1049193 1050270 1050275) (-626 "MAPPKG2.spad" 1048513 1048525 1049169 1049174) (-625 "MAPPKG1.spad" 1047331 1047341 1048503 1048508) (-624 "MAPHACK3.spad" 1047139 1047153 1047321 1047326) (-623 "MAPHACK2.spad" 1046904 1046916 1047129 1047134) (-622 "MAPHACK1.spad" 1046534 1046544 1046894 1046899) (-621 "MAGMA.spad" 1044324 1044341 1046524 1046529) (-620 "M3D.spad" 1042022 1042032 1043704 1043709) (-619 "LZSTAGG.spad" 1039240 1039250 1042002 1042017) (-618 "LZSTAGG.spad" 1036466 1036478 1039230 1039235) (-617 "LWORD.spad" 1033171 1033188 1036456 1036461) (-616 "LSQM.spad" 1031399 1031413 1031797 1031848) (-615 "LSPP.spad" 1030932 1030949 1031389 1031394) (-614 "LSMP.spad" 1029772 1029800 1030922 1030927) (-613 "LSMP1.spad" 1027576 1027590 1029762 1029767) (-612 "LSAGG.spad" 1027233 1027243 1027532 1027571) (-611 "LSAGG.spad" 1026922 1026934 1027223 1027228) (-610 "LPOLY.spad" 1025876 1025895 1026778 1026847) (-609 "LPEFRAC.spad" 1025133 1025143 1025866 1025871) (-608 "LO.spad" 1024534 1024548 1025067 1025094) (-607 "LOGIC.spad" 1024136 1024144 1024524 1024529) (-606 "LOGIC.spad" 1023736 1023746 1024126 1024131) (-605 "LODOOPS.spad" 1022654 1022666 1023726 1023731) (-604 "LODO.spad" 1022040 1022056 1022336 1022375) (-603 "LODOF.spad" 1021084 1021101 1021997 1022002) (-602 "LODOCAT.spad" 1019742 1019752 1021040 1021079) (-601 "LODOCAT.spad" 1018398 1018410 1019698 1019703) (-600 "LODO2.spad" 1017673 1017685 1018080 1018119) (-599 "LODO1.spad" 1017075 1017085 1017355 1017394) (-598 "LODEEF.spad" 1015847 1015865 1017065 1017070) (-597 "LNAGG.spad" 1011639 1011649 1015827 1015842) (-596 "LNAGG.spad" 1007405 1007417 1011595 1011600) (-595 "LMOPS.spad" 1004141 1004158 1007395 1007400) (-594 "LMODULE.spad" 1003783 1003793 1004131 1004136) (-593 "LMDICT.spad" 1003066 1003076 1003334 1003361) (-592 "LIST.spad" 1000784 1000794 1002213 1002240) (-591 "LIST3.spad" 1000075 1000089 1000774 1000779) (-590 "LIST2.spad" 998715 998727 1000065 1000070) (-589 "LIST2MAP.spad" 995592 995604 998705 998710) (-588 "LINEXP.spad" 995024 995034 995572 995587) (-587 "LINDEP.spad" 993801 993813 994936 994941) (-586 "LIMITRF.spad" 991715 991725 993791 993796) (-585 "LIMITPS.spad" 990598 990611 991705 991710) (-584 "LIE.spad" 988612 988624 989888 990033) (-583 "LIECAT.spad" 988088 988098 988538 988607) (-582 "LIECAT.spad" 987592 987604 988044 988049) (-581 "LIB.spad" 985640 985648 986251 986266) (-580 "LGROBP.spad" 982993 983012 985630 985635) (-579 "LF.spad" 981912 981928 982983 982988) (-578 "LFCAT.spad" 980931 980939 981902 981907) (-577 "LEXTRIPK.spad" 976434 976449 980921 980926) (-576 "LEXP.spad" 974437 974464 976414 976429) (-575 "LEADCDET.spad" 972821 972838 974427 974432) (-574 "LAZM3PK.spad" 971525 971547 972811 972816) (-573 "LAUPOL.spad" 970216 970229 971120 971189) (-572 "LAPLACE.spad" 969789 969805 970206 970211) (-571 "LA.spad" 969229 969243 969711 969750) (-570 "LALG.spad" 969005 969015 969209 969224) (-569 "LALG.spad" 968789 968801 968995 969000) (-568 "KOVACIC.spad" 967502 967519 968779 968784) (-567 "KONVERT.spad" 967224 967234 967492 967497) (-566 "KOERCE.spad" 966961 966971 967214 967219) (-565 "KERNEL.spad" 965496 965506 966745 966750) (-564 "KERNEL2.spad" 965199 965211 965486 965491) (-563 "KDAGG.spad" 964290 964312 965167 965194) (-562 "KDAGG.spad" 963401 963425 964280 964285) (-561 "KAFILE.spad" 962364 962380 962599 962626) (-560 "JORDAN.spad" 960191 960203 961654 961799) (-559 "JAVACODE.spad" 959957 959965 960181 960186) (-558 "IXAGG.spad" 958070 958094 959937 959952) (-557 "IXAGG.spad" 956048 956074 957917 957922) (-556 "IVECTOR.spad" 954821 954836 954976 955003) (-555 "ITUPLE.spad" 953966 953976 954811 954816) (-554 "ITRIGMNP.spad" 952777 952796 953956 953961) (-553 "ITFUN3.spad" 952271 952285 952767 952772) (-552 "ITFUN2.spad" 952001 952013 952261 952266) (-551 "ITAYLOR.spad" 949793 949808 951837 951962) (-550 "ISUPS.spad" 942204 942219 948767 948864) (-549 "ISUMP.spad" 941701 941717 942194 942199) (-548 "ISTRING.spad" 940704 940717 940870 940897) (-547 "IRURPK.spad" 939417 939436 940694 940699) (-546 "IRSN.spad" 937377 937385 939407 939412) (-545 "IRRF2F.spad" 935852 935862 937333 937338) (-544 "IRREDFFX.spad" 935453 935464 935842 935847) (-543 "IROOT.spad" 933784 933794 935443 935448) (-542 "IR.spad" 931574 931588 933640 933667) (-541 "IR2.spad" 930594 930610 931564 931569) (-540 "IR2F.spad" 929794 929810 930584 930589) (-539 "IPRNTPK.spad" 929554 929562 929784 929789) (-538 "IPF.spad" 929119 929131 929359 929452) (-537 "IPADIC.spad" 928880 928906 929045 929114) (-536 "INVLAPLA.spad" 928525 928541 928870 928875) (-535 "INTTR.spad" 921771 921788 928515 928520) (-534 "INTTOOLS.spad" 919483 919499 921346 921351) (-533 "INTSLPE.spad" 918789 918797 919473 919478) (-532 "INTRVL.spad" 918355 918365 918703 918784) (-531 "INTRF.spad" 916719 916733 918345 918350) (-530 "INTRET.spad" 916151 916161 916709 916714) (-529 "INTRAT.spad" 914826 914843 916141 916146) (-528 "INTPM.spad" 913189 913205 914469 914474) (-527 "INTPAF.spad" 910957 910975 913121 913126) (-526 "INTPACK.spad" 901267 901275 910947 910952) (-525 "INT.spad" 900628 900636 901121 901262) (-524 "INTHERTR.spad" 899894 899911 900618 900623) (-523 "INTHERAL.spad" 899560 899584 899884 899889) (-522 "INTHEORY.spad" 895973 895981 899550 899555) (-521 "INTG0.spad" 889436 889454 895905 895910) (-520 "INTFTBL.spad" 883465 883473 889426 889431) (-519 "INTFACT.spad" 882524 882534 883455 883460) (-518 "INTEF.spad" 880839 880855 882514 882519) (-517 "INTDOM.spad" 879454 879462 880765 880834) (-516 "INTDOM.spad" 878131 878141 879444 879449) (-515 "INTCAT.spad" 876384 876394 878045 878126) (-514 "INTBIT.spad" 875887 875895 876374 876379) (-513 "INTALG.spad" 875069 875096 875877 875882) (-512 "INTAF.spad" 874561 874577 875059 875064) (-511 "INTABL.spad" 873079 873110 873242 873269) (-510 "INS.spad" 870475 870483 872981 873074) (-509 "INS.spad" 867957 867967 870465 870470) (-508 "INPSIGN.spad" 867391 867404 867947 867952) (-507 "INPRODPF.spad" 866457 866476 867381 867386) (-506 "INPRODFF.spad" 865515 865539 866447 866452) (-505 "INNMFACT.spad" 864486 864503 865505 865510) (-504 "INMODGCD.spad" 863970 864000 864476 864481) (-503 "INFSP.spad" 862255 862277 863960 863965) (-502 "INFPROD0.spad" 861305 861324 862245 862250) (-501 "INFORM.spad" 858573 858581 861295 861300) (-500 "INFORM1.spad" 858198 858208 858563 858568) (-499 "INFINITY.spad" 857750 857758 858188 858193) (-498 "INEP.spad" 856282 856304 857740 857745) (-497 "INDE.spad" 856188 856205 856272 856277) (-496 "INCRMAPS.spad" 855609 855619 856178 856183) (-495 "INBFF.spad" 851379 851390 855599 855604) (-494 "IMATRIX.spad" 850324 850350 850836 850863) (-493 "IMATQF.spad" 849418 849462 850280 850285) (-492 "IMATLIN.spad" 848023 848047 849374 849379) (-491 "ILIST.spad" 846679 846694 847206 847233) (-490 "IIARRAY2.spad" 846067 846105 846286 846313) (-489 "IFF.spad" 845477 845493 845748 845841) (-488 "IFARRAY.spad" 842964 842979 844660 844687) (-487 "IFAMON.spad" 842826 842843 842920 842925) (-486 "IEVALAB.spad" 842215 842227 842816 842821) (-485 "IEVALAB.spad" 841602 841616 842205 842210) (-484 "IDPO.spad" 841400 841412 841592 841597) (-483 "IDPOAMS.spad" 841156 841168 841390 841395) (-482 "IDPOAM.spad" 840876 840888 841146 841151) (-481 "IDPC.spad" 839810 839822 840866 840871) (-480 "IDPAM.spad" 839555 839567 839800 839805) (-479 "IDPAG.spad" 839302 839314 839545 839550) (-478 "IDECOMP.spad" 836539 836557 839292 839297) (-477 "IDEAL.spad" 831462 831501 836474 836479) (-476 "ICDEN.spad" 830613 830629 831452 831457) (-475 "ICARD.spad" 829802 829810 830603 830608) (-474 "IBPTOOLS.spad" 828395 828412 829792 829797) (-473 "IBITS.spad" 827594 827607 828031 828058) (-472 "IBATOOL.spad" 824469 824488 827584 827589) (-471 "IBACHIN.spad" 822956 822971 824459 824464) (-470 "IARRAY2.spad" 821944 821970 822563 822590) (-469 "IARRAY1.spad" 820989 821004 821127 821154) (-468 "IAN.spad" 819204 819212 820807 820900) (-467 "IALGFACT.spad" 818805 818838 819194 819199) (-466 "HYPCAT.spad" 818229 818237 818795 818800) (-465 "HYPCAT.spad" 817651 817661 818219 818224) (-464 "HOAGG.spad" 814909 814919 817631 817646) (-463 "HOAGG.spad" 811952 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(-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 +((-3 NIL 2241068 2241073 2241078 2241083) (-2 NIL 2241048 2241053 2241058 2241063) (-1 NIL 2241028 2241033 2241038 2241043) (0 NIL 2241008 2241013 2241018 2241023) (-1199 "ZMOD.spad" 2240817 2240830 2240946 2241003) (-1198 "ZLINDEP.spad" 2239861 2239872 2240807 2240812) (-1197 "ZDSOLVE.spad" 2229710 2229732 2239851 2239856) (-1196 "YSTREAM.spad" 2229203 2229214 2229700 2229705) (-1195 "XRPOLY.spad" 2228423 2228443 2229059 2229128) (-1194 "XPR.spad" 2226152 2226165 2228141 2228240) (-1193 "XPOLY.spad" 2225707 2225718 2226008 2226077) (-1192 "XPOLYC.spad" 2225024 2225040 2225633 2225702) (-1191 "XPBWPOLY.spad" 2223461 2223481 2224804 2224873) (-1190 "XF.spad" 2221922 2221937 2223363 2223456) (-1189 "XF.spad" 2220363 2220380 2221806 2221811) (-1188 "XFALG.spad" 2217387 2217403 2220289 2220358) (-1187 "XEXPPKG.spad" 2216638 2216664 2217377 2217382) (-1186 "XDPOLY.spad" 2216252 2216268 2216494 2216563) (-1185 "XALG.spad" 2215850 2215861 2216208 2216247) (-1184 "WUTSET.spad" 2211689 2211706 2215496 2215523) (-1183 "WP.spad" 2210703 2210747 2211547 2211614) (-1182 "WFFINTBS.spad" 2208266 2208288 2210693 2210698) (-1181 "WEIER.spad" 2206480 2206491 2208256 2208261) (-1180 "VSPACE.spad" 2206153 2206164 2206448 2206475) (-1179 "VSPACE.spad" 2205846 2205859 2206143 2206148) (-1178 "VOID.spad" 2205436 2205445 2205836 2205841) (-1177 "VIEW.spad" 2203058 2203067 2205426 2205431) (-1176 "VIEWDEF.spad" 2198255 2198264 2203048 2203053) (-1175 "VIEW3D.spad" 2182090 2182099 2198245 2198250) (-1174 "VIEW2D.spad" 2169827 2169836 2182080 2182085) (-1173 "VECTOR.spad" 2168504 2168515 2168755 2168782) (-1172 "VECTOR2.spad" 2167131 2167144 2168494 2168499) (-1171 "VECTCAT.spad" 2165019 2165030 2167087 2167126) (-1170 "VECTCAT.spad" 2162728 2162741 2164798 2164803) (-1169 "VARIABLE.spad" 2162508 2162523 2162718 2162723) (-1168 "UTYPE.spad" 2162142 2162151 2162488 2162503) (-1167 "UTSODETL.spad" 2161435 2161459 2162098 2162103) (-1166 "UTSODE.spad" 2159623 2159643 2161425 2161430) (-1165 "UTS.spad" 2154412 2154440 2158090 2158187) (-1164 "UTSCAT.spad" 2151863 2151879 2154310 2154407) (-1163 "UTSCAT.spad" 2148958 2148976 2151407 2151412) (-1162 "UTS2.spad" 2148551 2148586 2148948 2148953) (-1161 "URAGG.spad" 2143173 2143184 2148531 2148546) (-1160 "URAGG.spad" 2137769 2137782 2143129 2143134) (-1159 "UPXSSING.spad" 2135415 2135441 2136853 2136986) (-1158 "UPXS.spad" 2132442 2132470 2133547 2133696) (-1157 "UPXSCONS.spad" 2130199 2130219 2130574 2130723) (-1156 "UPXSCCA.spad" 2128657 2128677 2130045 2130194) (-1155 "UPXSCCA.spad" 2127257 2127279 2128647 2128652) (-1154 "UPXSCAT.spad" 2125838 2125854 2127103 2127252) (-1153 "UPXS2.spad" 2125379 2125432 2125828 2125833) (-1152 "UPSQFREE.spad" 2123791 2123805 2125369 2125374) (-1151 "UPSCAT.spad" 2121384 2121408 2123689 2123786) (-1150 "UPSCAT.spad" 2118683 2118709 2120990 2120995) (-1149 "UPOLYC.spad" 2113661 2113672 2118525 2118678) (-1148 "UPOLYC.spad" 2108531 2108544 2113397 2113402) (-1147 "UPOLYC2.spad" 2108000 2108019 2108521 2108526) (-1146 "UP.spad" 2105045 2105060 2105553 2105706) (-1145 "UPMP.spad" 2103935 2103948 2105035 2105040) (-1144 "UPDIVP.spad" 2103498 2103512 2103925 2103930) (-1143 "UPDECOMP.spad" 2101735 2101749 2103488 2103493) (-1142 "UPCDEN.spad" 2100942 2100958 2101725 2101730) (-1141 "UP2.spad" 2100304 2100325 2100932 2100937) (-1140 "UNISEG.spad" 2099657 2099668 2100223 2100228) (-1139 "UNISEG2.spad" 2099150 2099163 2099613 2099618) (-1138 "UNIFACT.spad" 2098251 2098263 2099140 2099145) (-1137 "ULS.spad" 2088810 2088838 2089903 2090332) (-1136 "ULSCONS.spad" 2082853 2082873 2083225 2083374) (-1135 "ULSCCAT.spad" 2080450 2080470 2082673 2082848) (-1134 "ULSCCAT.spad" 2078181 2078203 2080406 2080411) (-1133 "ULSCAT.spad" 2076397 2076413 2078027 2078176) (-1132 "ULS2.spad" 2075909 2075962 2076387 2076392) (-1131 "UFD.spad" 2074974 2074983 2075835 2075904) (-1130 "UFD.spad" 2074101 2074112 2074964 2074969) (-1129 "UDVO.spad" 2072948 2072957 2074091 2074096) (-1128 "UDPO.spad" 2070375 2070386 2072904 2072909) (-1127 "TYPE.spad" 2070297 2070306 2070355 2070370) (-1126 "TWOFACT.spad" 2068947 2068962 2070287 2070292) (-1125 "TUPLE.spad" 2068333 2068344 2068846 2068851) (-1124 "TUBETOOL.spad" 2065170 2065179 2068323 2068328) (-1123 "TUBE.spad" 2063811 2063828 2065160 2065165) (-1122 "TS.spad" 2062400 2062416 2063376 2063473) (-1121 "TSETCAT.spad" 2049515 2049532 2062356 2062395) (-1120 "TSETCAT.spad" 2036628 2036647 2049471 2049476) (-1119 "TRMANIP.spad" 2030994 2031011 2036334 2036339) (-1118 "TRIMAT.spad" 2029953 2029978 2030984 2030989) (-1117 "TRIGMNIP.spad" 2028470 2028487 2029943 2029948) (-1116 "TRIGCAT.spad" 2027982 2027991 2028460 2028465) (-1115 "TRIGCAT.spad" 2027492 2027503 2027972 2027977) (-1114 "TREE.spad" 2026063 2026074 2027099 2027126) (-1113 "TRANFUN.spad" 2025894 2025903 2026053 2026058) (-1112 "TRANFUN.spad" 2025723 2025734 2025884 2025889) (-1111 "TOPSP.spad" 2025397 2025406 2025713 2025718) (-1110 "TOOLSIGN.spad" 2025060 2025071 2025387 2025392) (-1109 "TEXTFILE.spad" 2023617 2023626 2025050 2025055) (-1108 "TEX.spad" 2020634 2020643 2023607 2023612) (-1107 "TEX1.spad" 2020190 2020201 2020624 2020629) (-1106 "TEMUTL.spad" 2019745 2019754 2020180 2020185) (-1105 "TBCMPPK.spad" 2017838 2017861 2019735 2019740) (-1104 "TBAGG.spad" 2016862 2016885 2017806 2017833) (-1103 "TBAGG.spad" 2015906 2015931 2016852 2016857) (-1102 "TANEXP.spad" 2015282 2015293 2015896 2015901) (-1101 "TABLE.spad" 2013693 2013716 2013963 2013990) (-1100 "TABLEAU.spad" 2013174 2013185 2013683 2013688) (-1099 "TABLBUMP.spad" 2009957 2009968 2013164 2013169) (-1098 "SYSTEM.spad" 2009231 2009240 2009947 2009952) (-1097 "SYSSOLP.spad" 2006704 2006715 2009221 2009226) (-1096 "SYNTAX.spad" 2002896 2002905 2006694 2006699) (-1095 "SYMTAB.spad" 2000952 2000961 2002886 2002891) (-1094 "SYMS.spad" 1996937 1996946 2000942 2000947) (-1093 "SYMPOLY.spad" 1995947 1995958 1996029 1996156) (-1092 "SYMFUNC.spad" 1995422 1995433 1995937 1995942) (-1091 "SYMBOL.spad" 1992758 1992767 1995412 1995417) (-1090 "SWITCH.spad" 1989515 1989524 1992748 1992753) (-1089 "SUTS.spad" 1986414 1986442 1987982 1988079) (-1088 "SUPXS.spad" 1983428 1983456 1984546 1984695) (-1087 "SUP.spad" 1980200 1980211 1980981 1981134) (-1086 "SUPFRACF.spad" 1979305 1979323 1980190 1980195) (-1085 "SUP2.spad" 1978695 1978708 1979295 1979300) (-1084 "SUMRF.spad" 1977661 1977672 1978685 1978690) (-1083 "SUMFS.spad" 1977294 1977311 1977651 1977656) (-1082 "SULS.spad" 1967840 1967868 1968946 1969375) (-1081 "SUCH.spad" 1967520 1967535 1967830 1967835) (-1080 "SUBSPACE.spad" 1959527 1959542 1967510 1967515) (-1079 "SUBRESP.spad" 1958687 1958701 1959483 1959488) (-1078 "STTF.spad" 1954786 1954802 1958677 1958682) (-1077 "STTFNC.spad" 1951254 1951270 1954776 1954781) (-1076 "STTAYLOR.spad" 1943652 1943663 1951135 1951140) (-1075 "STRTBL.spad" 1942157 1942174 1942306 1942333) (-1074 "STRING.spad" 1941566 1941575 1941580 1941607) (-1073 "STRICAT.spad" 1941342 1941351 1941522 1941561) (-1072 "STREAM.spad" 1938110 1938121 1940867 1940882) (-1071 "STREAM3.spad" 1937655 1937670 1938100 1938105) (-1070 "STREAM2.spad" 1936723 1936736 1937645 1937650) (-1069 "STREAM1.spad" 1936427 1936438 1936713 1936718) (-1068 "STINPROD.spad" 1935333 1935349 1936417 1936422) (-1067 "STEP.spad" 1934534 1934543 1935323 1935328) (-1066 "STBL.spad" 1933060 1933088 1933227 1933242) (-1065 "STAGG.spad" 1932125 1932136 1933040 1933055) (-1064 "STAGG.spad" 1931198 1931211 1932115 1932120) (-1063 "STACK.spad" 1930549 1930560 1930805 1930832) (-1062 "SREGSET.spad" 1928253 1928270 1930195 1930222) (-1061 "SRDCMPK.spad" 1926798 1926818 1928243 1928248) (-1060 "SRAGG.spad" 1921883 1921892 1926754 1926793) (-1059 "SRAGG.spad" 1917000 1917011 1921873 1921878) (-1058 "SQMATRIX.spad" 1914626 1914644 1915534 1915621) (-1057 "SPLTREE.spad" 1909178 1909191 1914062 1914089) (-1056 "SPLNODE.spad" 1905766 1905779 1909168 1909173) (-1055 "SPFCAT.spad" 1904543 1904552 1905756 1905761) (-1054 "SPECOUT.spad" 1903093 1903102 1904533 1904538) (-1053 "spad-parser.spad" 1902558 1902567 1903083 1903088) (-1052 "SPACEC.spad" 1886571 1886582 1902548 1902553) (-1051 "SPACE3.spad" 1886347 1886358 1886561 1886566) (-1050 "SORTPAK.spad" 1885892 1885905 1886303 1886308) (-1049 "SOLVETRA.spad" 1883649 1883660 1885882 1885887) (-1048 "SOLVESER.spad" 1882169 1882180 1883639 1883644) (-1047 "SOLVERAD.spad" 1878179 1878190 1882159 1882164) (-1046 "SOLVEFOR.spad" 1876599 1876617 1878169 1878174) (-1045 "SNTSCAT.spad" 1876187 1876204 1876555 1876594) (-1044 "SMTS.spad" 1874447 1874473 1875752 1875849) (-1043 "SMP.spad" 1871889 1871909 1872279 1872406) (-1042 "SMITH.spad" 1870732 1870757 1871879 1871884) (-1041 "SMATCAT.spad" 1868830 1868860 1870664 1870727) (-1040 "SMATCAT.spad" 1866872 1866904 1868708 1868713) (-1039 "SKAGG.spad" 1865821 1865832 1866828 1866867) (-1038 "SINT.spad" 1864129 1864138 1865687 1865816) (-1037 "SIMPAN.spad" 1863857 1863866 1864119 1864124) (-1036 "SIGNRF.spad" 1862965 1862976 1863847 1863852) (-1035 "SIGNEF.spad" 1862234 1862251 1862955 1862960) (-1034 "SHP.spad" 1860152 1860167 1862190 1862195) (-1033 "SHDP.spad" 1851188 1851215 1851697 1851826) (-1032 "SGROUP.spad" 1850654 1850663 1851178 1851183) (-1031 "SGROUP.spad" 1850118 1850129 1850644 1850649) (-1030 "SGCF.spad" 1842999 1843008 1850108 1850113) (-1029 "SFRTCAT.spad" 1841915 1841932 1842955 1842994) (-1028 "SFRGCD.spad" 1840978 1840998 1841905 1841910) (-1027 "SFQCMPK.spad" 1835615 1835635 1840968 1840973) (-1026 "SFORT.spad" 1835050 1835064 1835605 1835610) (-1025 "SEXOF.spad" 1834893 1834933 1835040 1835045) (-1024 "SEX.spad" 1834785 1834794 1834883 1834888) (-1023 "SEXCAT.spad" 1831889 1831929 1834775 1834780) (-1022 "SET.spad" 1830189 1830200 1831310 1831349) (-1021 "SETMN.spad" 1828623 1828640 1830179 1830184) (-1020 "SETCAT.spad" 1828108 1828117 1828613 1828618) (-1019 "SETCAT.spad" 1827591 1827602 1828098 1828103) (-1018 "SETAGG.spad" 1824114 1824125 1827559 1827586) (-1017 "SETAGG.spad" 1820657 1820670 1824104 1824109) (-1016 "SEGXCAT.spad" 1819769 1819782 1820637 1820652) (-1015 "SEG.spad" 1819582 1819593 1819688 1819693) (-1014 "SEGCAT.spad" 1818401 1818412 1819562 1819577) (-1013 "SEGBIND.spad" 1817473 1817484 1818356 1818361) (-1012 "SEGBIND2.spad" 1817169 1817182 1817463 1817468) (-1011 "SEG2.spad" 1816594 1816607 1817125 1817130) (-1010 "SDVAR.spad" 1815870 1815881 1816584 1816589) (-1009 "SDPOL.spad" 1813263 1813274 1813554 1813681) (-1008 "SCPKG.spad" 1811342 1811353 1813253 1813258) (-1007 "SCOPE.spad" 1810487 1810496 1811332 1811337) (-1006 "SCACHE.spad" 1809169 1809180 1810477 1810482) (-1005 "SAOS.spad" 1809041 1809050 1809159 1809164) (-1004 "SAERFFC.spad" 1808754 1808774 1809031 1809036) (-1003 "SAE.spad" 1806932 1806948 1807543 1807678) (-1002 "SAEFACT.spad" 1806633 1806653 1806922 1806927) (-1001 "RURPK.spad" 1804274 1804290 1806623 1806628) (-1000 "RULESET.spad" 1803715 1803739 1804264 1804269) (-999 "RULE.spad" 1801920 1801943 1803705 1803710) (-998 "RULECOLD.spad" 1801773 1801785 1801910 1801915) (-997 "RSETGCD.spad" 1798152 1798171 1801763 1801768) (-996 "RSETCAT.spad" 1787925 1787941 1798108 1798147) (-995 "RSETCAT.spad" 1777730 1777748 1787915 1787920) (-994 "RSDCMPK.spad" 1776183 1776202 1777720 1777725) (-993 "RRCC.spad" 1774568 1774597 1776173 1776178) (-992 "RRCC.spad" 1772951 1772982 1774558 1774563) (-991 "RPOLCAT.spad" 1752312 1752326 1772819 1772946) (-990 "RPOLCAT.spad" 1731388 1731404 1751897 1751902) (-989 "ROUTINE.spad" 1727252 1727260 1730035 1730062) (-988 "ROMAN.spad" 1726485 1726493 1727118 1727247) (-987 "ROIRC.spad" 1725566 1725597 1726475 1726480) (-986 "RNS.spad" 1724470 1724478 1725468 1725561) (-985 "RNS.spad" 1723460 1723470 1724460 1724465) (-984 "RNG.spad" 1723196 1723204 1723450 1723455) (-983 "RMODULE.spad" 1722835 1722845 1723186 1723191) (-982 "RMCAT2.spad" 1722244 1722300 1722825 1722830) (-981 "RMATRIX.spad" 1720924 1720942 1721411 1721450) (-980 "RMATCAT.spad" 1716446 1716476 1720868 1720919) (-979 "RMATCAT.spad" 1711870 1711902 1716294 1716299) (-978 "RINTERP.spad" 1711759 1711778 1711860 1711865) (-977 "RING.spad" 1711117 1711125 1711739 1711754) (-976 "RING.spad" 1710483 1710493 1711107 1711112) (-975 "RIDIST.spad" 1709868 1709876 1710473 1710478) (-974 "RGCHAIN.spad" 1708448 1708463 1709353 1709380) (-973 "RF.spad" 1706063 1706073 1708438 1708443) (-972 "RFFACTOR.spad" 1705526 1705536 1706053 1706058) (-971 "RFFACT.spad" 1705262 1705273 1705516 1705521) (-970 "RFDIST.spad" 1704251 1704259 1705252 1705257) (-969 "RETSOL.spad" 1703669 1703681 1704241 1704246) (-968 "RETRACT.spad" 1703019 1703029 1703659 1703664) (-967 "RETRACT.spad" 1702367 1702379 1703009 1703014) (-966 "RESULT.spad" 1700428 1700436 1701014 1701041) (-965 "RESRING.spad" 1699776 1699822 1700366 1700423) (-964 "RESLATC.spad" 1699101 1699111 1699766 1699771) (-963 "REPSQ.spad" 1698831 1698841 1699091 1699096) (-962 "REP.spad" 1696384 1696392 1698821 1698826) (-961 "REPDB.spad" 1696090 1696100 1696374 1696379) (-960 "REP2.spad" 1685663 1685673 1695932 1695937) (-959 "REP1.spad" 1679654 1679664 1685613 1685618) (-958 "REGSET.spad" 1677452 1677468 1679300 1679327) (-957 "REF.spad" 1676782 1676792 1677407 1677412) (-956 "REDORDER.spad" 1675959 1675975 1676772 1676777) (-955 "RECLOS.spad" 1674749 1674768 1675452 1675545) (-954 "REALSOLV.spad" 1673882 1673890 1674739 1674744) (-953 "REAL.spad" 1673755 1673763 1673872 1673877) (-952 "REAL0Q.spad" 1671038 1671052 1673745 1673750) (-951 "REAL0.spad" 1667867 1667881 1671028 1671033) (-950 "RDIV.spad" 1667519 1667543 1667857 1667862) (-949 "RDIST.spad" 1667083 1667093 1667509 1667514) (-948 "RDETRS.spad" 1665880 1665897 1667073 1667078) (-947 "RDETR.spad" 1663988 1664005 1665870 1665875) (-946 "RDEEFS.spad" 1663062 1663078 1663978 1663983) (-945 "RDEEF.spad" 1662059 1662075 1663052 1663057) (-944 "RCFIELD.spad" 1659246 1659254 1661961 1662054) (-943 "RCFIELD.spad" 1656519 1656529 1659236 1659241) (-942 "RCAGG.spad" 1654422 1654432 1656499 1656514) (-941 "RCAGG.spad" 1652262 1652274 1654341 1654346) (-940 "RATRET.spad" 1651623 1651633 1652252 1652257) (-939 "RATFACT.spad" 1651316 1651327 1651613 1651618) (-938 "RANDSRC.spad" 1650636 1650644 1651306 1651311) (-937 "RADUTIL.spad" 1650391 1650399 1650626 1650631) (-936 "RADIX.spad" 1647184 1647197 1648861 1648954) (-935 "RADFF.spad" 1645601 1645637 1645719 1645875) (-934 "RADCAT.spad" 1645195 1645203 1645591 1645596) (-933 "RADCAT.spad" 1644787 1644797 1645185 1645190) (-932 "QUEUE.spad" 1644130 1644140 1644394 1644421) (-931 "QUAT.spad" 1642716 1642726 1643058 1643123) (-930 "QUATCT2.spad" 1642335 1642353 1642706 1642711) (-929 "QUATCAT.spad" 1640500 1640510 1642265 1642330) (-928 "QUATCAT.spad" 1638417 1638429 1640184 1640189) (-927 "QUAGG.spad" 1637231 1637241 1638373 1638412) (-926 "QFORM.spad" 1636694 1636708 1637221 1637226) (-925 "QFCAT.spad" 1635385 1635395 1636584 1636689) (-924 "QFCAT.spad" 1633682 1633694 1634883 1634888) (-923 "QFCAT2.spad" 1633373 1633389 1633672 1633677) (-922 "QEQUAT.spad" 1632930 1632938 1633363 1633368) (-921 "QCMPACK.spad" 1627677 1627696 1632920 1632925) (-920 "QALGSET.spad" 1623752 1623784 1627591 1627596) (-919 "QALGSET2.spad" 1621748 1621766 1623742 1623747) (-918 "PWFFINTB.spad" 1619058 1619079 1621738 1621743) (-917 "PUSHVAR.spad" 1618387 1618406 1619048 1619053) (-916 "PTRANFN.spad" 1614513 1614523 1618377 1618382) (-915 "PTPACK.spad" 1611601 1611611 1614503 1614508) (-914 "PTFUNC2.spad" 1611422 1611436 1611591 1611596) (-913 "PTCAT.spad" 1610504 1610514 1611378 1611417) (-912 "PSQFR.spad" 1609811 1609835 1610494 1610499) (-911 "PSEUDLIN.spad" 1608669 1608679 1609801 1609806) (-910 "PSETPK.spad" 1594102 1594118 1608547 1608552) (-909 "PSETCAT.spad" 1588010 1588033 1594070 1594097) (-908 "PSETCAT.spad" 1581904 1581929 1587966 1587971) (-907 "PSCURVE.spad" 1580887 1580895 1581894 1581899) (-906 "PSCAT.spad" 1579654 1579683 1580785 1580882) (-905 "PSCAT.spad" 1578511 1578542 1579644 1579649) (-904 "PRTITION.spad" 1577354 1577362 1578501 1578506) (-903 "PRS.spad" 1566916 1566933 1577310 1577315) (-902 "PRQAGG.spad" 1566335 1566345 1566872 1566911) (-901 "PROPLOG.spad" 1565738 1565746 1566325 1566330) (-900 "PROPFRML.spad" 1563602 1563613 1565674 1565679) (-899 "PROPERTY.spad" 1563096 1563104 1563592 1563597) (-898 "PRODUCT.spad" 1560776 1560788 1561062 1561117) (-897 "PR.spad" 1559165 1559177 1559870 1559997) (-896 "PRINT.spad" 1558917 1558925 1559155 1559160) (-895 "PRIMES.spad" 1557168 1557178 1558907 1558912) (-894 "PRIMELT.spad" 1555149 1555163 1557158 1557163) (-893 "PRIMCAT.spad" 1554772 1554780 1555139 1555144) (-892 "PRIMARR.spad" 1553777 1553787 1553955 1553982) (-891 "PRIMARR2.spad" 1552500 1552512 1553767 1553772) (-890 "PREASSOC.spad" 1551872 1551884 1552490 1552495) (-889 "PPCURVE.spad" 1551009 1551017 1551862 1551867) (-888 "POLYROOT.spad" 1549781 1549803 1550965 1550970) (-887 "POLY.spad" 1547081 1547091 1547598 1547725) (-886 "POLYLIFT.spad" 1546342 1546365 1547071 1547076) (-885 "POLYCATQ.spad" 1544444 1544466 1546332 1546337) (-884 "POLYCAT.spad" 1537850 1537871 1544312 1544439) (-883 "POLYCAT.spad" 1530558 1530581 1537022 1537027) (-882 "POLY2UP.spad" 1530006 1530020 1530548 1530553) (-881 "POLY2.spad" 1529601 1529613 1529996 1530001) (-880 "POLUTIL.spad" 1528542 1528571 1529557 1529562) (-879 "POLTOPOL.spad" 1527290 1527305 1528532 1528537) (-878 "POINT.spad" 1526131 1526141 1526218 1526245) (-877 "PNTHEORY.spad" 1522797 1522805 1526121 1526126) (-876 "PMTOOLS.spad" 1521554 1521568 1522787 1522792) (-875 "PMSYM.spad" 1521099 1521109 1521544 1521549) (-874 "PMQFCAT.spad" 1520686 1520700 1521089 1521094) (-873 "PMPRED.spad" 1520155 1520169 1520676 1520681) (-872 "PMPREDFS.spad" 1519599 1519621 1520145 1520150) (-871 "PMPLCAT.spad" 1518669 1518687 1519531 1519536) (-870 "PMLSAGG.spad" 1518250 1518264 1518659 1518664) (-869 "PMKERNEL.spad" 1517817 1517829 1518240 1518245) (-868 "PMINS.spad" 1517393 1517403 1517807 1517812) (-867 "PMFS.spad" 1516966 1516984 1517383 1517388) (-866 "PMDOWN.spad" 1516252 1516266 1516956 1516961) (-865 "PMASS.spad" 1515264 1515272 1516242 1516247) (-864 "PMASSFS.spad" 1514233 1514249 1515254 1515259) (-863 "PLOTTOOL.spad" 1514013 1514021 1514223 1514228) (-862 "PLOT.spad" 1508844 1508852 1514003 1514008) (-861 "PLOT3D.spad" 1505264 1505272 1508834 1508839) (-860 "PLOT1.spad" 1504405 1504415 1505254 1505259) (-859 "PLEQN.spad" 1491621 1491648 1504395 1504400) (-858 "PINTERP.spad" 1491237 1491256 1491611 1491616) (-857 "PINTERPA.spad" 1491019 1491035 1491227 1491232) (-856 "PI.spad" 1490626 1490634 1490993 1491014) (-855 "PID.spad" 1489582 1489590 1490552 1490621) (-854 "PICOERCE.spad" 1489239 1489249 1489572 1489577) (-853 "PGROEB.spad" 1487836 1487850 1489229 1489234) (-852 "PGE.spad" 1479089 1479097 1487826 1487831) (-851 "PGCD.spad" 1477971 1477988 1479079 1479084) (-850 "PFRPAC.spad" 1477114 1477124 1477961 1477966) (-849 "PFR.spad" 1473771 1473781 1477016 1477109) (-848 "PFOTOOLS.spad" 1473029 1473045 1473761 1473766) (-847 "PFOQ.spad" 1472399 1472417 1473019 1473024) (-846 "PFO.spad" 1471818 1471845 1472389 1472394) (-845 "PF.spad" 1471392 1471404 1471623 1471716) (-844 "PFECAT.spad" 1469058 1469066 1471318 1471387) (-843 "PFECAT.spad" 1466752 1466762 1469014 1469019) (-842 "PFBRU.spad" 1464622 1464634 1466742 1466747) (-841 "PFBR.spad" 1462160 1462183 1464612 1464617) (-840 "PERM.spad" 1457841 1457851 1461990 1462005) (-839 "PERMGRP.spad" 1452577 1452587 1457831 1457836) (-838 "PERMCAT.spad" 1451129 1451139 1452557 1452572) (-837 "PERMAN.spad" 1449661 1449675 1451119 1451124) (-836 "PENDTREE.spad" 1448934 1448944 1449290 1449295) (-835 "PDRING.spad" 1447425 1447435 1448914 1448929) (-834 "PDRING.spad" 1445924 1445936 1447415 1447420) (-833 "PDEPROB.spad" 1444881 1444889 1445914 1445919) (-832 "PDEPACK.spad" 1438883 1438891 1444871 1444876) (-831 "PDECOMP.spad" 1438345 1438362 1438873 1438878) (-830 "PDECAT.spad" 1436699 1436707 1438335 1438340) (-829 "PCOMP.spad" 1436550 1436563 1436689 1436694) (-828 "PBWLB.spad" 1435132 1435149 1436540 1436545) (-827 "PATTERN.spad" 1429563 1429573 1435122 1435127) (-826 "PATTERN2.spad" 1429299 1429311 1429553 1429558) (-825 "PATTERN1.spad" 1427601 1427617 1429289 1429294) (-824 "PATRES.spad" 1425148 1425160 1427591 1427596) (-823 "PATRES2.spad" 1424810 1424824 1425138 1425143) (-822 "PATMATCH.spad" 1422972 1423003 1424523 1424528) (-821 "PATMAB.spad" 1422397 1422407 1422962 1422967) (-820 "PATLRES.spad" 1421481 1421495 1422387 1422392) (-819 "PATAB.spad" 1421245 1421255 1421471 1421476) (-818 "PARTPERM.spad" 1418607 1418615 1421235 1421240) (-817 "PARSURF.spad" 1418035 1418063 1418597 1418602) (-816 "PARSU2.spad" 1417830 1417846 1418025 1418030) (-815 "script-parser.spad" 1417350 1417358 1417820 1417825) (-814 "PARSCURV.spad" 1416778 1416806 1417340 1417345) (-813 "PARSC2.spad" 1416567 1416583 1416768 1416773) (-812 "PARPCURV.spad" 1416025 1416053 1416557 1416562) (-811 "PARPC2.spad" 1415814 1415830 1416015 1416020) (-810 "PAN2EXPR.spad" 1415226 1415234 1415804 1415809) (-809 "PALETTE.spad" 1414196 1414204 1415216 1415221) (-808 "PAIR.spad" 1413179 1413192 1413784 1413789) (-807 "PADICRC.spad" 1410512 1410530 1411687 1411780) (-806 "PADICRAT.spad" 1408530 1408542 1408751 1408844) (-805 "PADIC.spad" 1408225 1408237 1408456 1408525) (-804 "PADICCT.spad" 1406766 1406778 1408151 1408220) (-803 "PADEPAC.spad" 1405445 1405464 1406756 1406761) (-802 "PADE.spad" 1404185 1404201 1405435 1405440) (-801 "OWP.spad" 1403169 1403199 1404043 1404110) (-800 "OVAR.spad" 1402950 1402973 1403159 1403164) (-799 "OUT.spad" 1402034 1402042 1402940 1402945) (-798 "OUTFORM.spad" 1391448 1391456 1402024 1402029) (-797 "OSI.spad" 1390923 1390931 1391438 1391443) (-796 "OSGROUP.spad" 1390841 1390849 1390913 1390918) (-795 "ORTHPOL.spad" 1389302 1389312 1390758 1390763) (-794 "OREUP.spad" 1388662 1388690 1388984 1389023) (-793 "ORESUP.spad" 1387963 1387987 1388344 1388383) (-792 "OREPCTO.spad" 1385782 1385794 1387883 1387888) (-791 "OREPCAT.spad" 1379839 1379849 1385738 1385777) (-790 "OREPCAT.spad" 1373786 1373798 1379687 1379692) (-789 "ORDSET.spad" 1372952 1372960 1373776 1373781) (-788 "ORDSET.spad" 1372116 1372126 1372942 1372947) (-787 "ORDRING.spad" 1371506 1371514 1372096 1372111) (-786 "ORDRING.spad" 1370904 1370914 1371496 1371501) (-785 "ORDMON.spad" 1370759 1370767 1370894 1370899) (-784 "ORDFUNS.spad" 1369885 1369901 1370749 1370754) (-783 "ORDFIN.spad" 1369819 1369827 1369875 1369880) (-782 "ORDCOMP.spad" 1368287 1368297 1369369 1369398) (-781 "ORDCOMP2.spad" 1367572 1367584 1368277 1368282) (-780 "OPTPROB.spad" 1366152 1366160 1367562 1367567) (-779 "OPTPACK.spad" 1358537 1358545 1366142 1366147) (-778 "OPTCAT.spad" 1356212 1356220 1358527 1358532) (-777 "OPQUERY.spad" 1355761 1355769 1356202 1356207) (-776 "OP.spad" 1355503 1355513 1355583 1355650) (-775 "ONECOMP.spad" 1354251 1354261 1355053 1355082) (-774 "ONECOMP2.spad" 1353669 1353681 1354241 1354246) (-773 "OMSERVER.spad" 1352671 1352679 1353659 1353664) (-772 "OMSAGG.spad" 1352447 1352457 1352615 1352666) (-771 "OMPKG.spad" 1351059 1351067 1352437 1352442) (-770 "OM.spad" 1350024 1350032 1351049 1351054) (-769 "OMLO.spad" 1349449 1349461 1349910 1349949) (-768 "OMEXPR.spad" 1349283 1349293 1349439 1349444) (-767 "OMERR.spad" 1348826 1348834 1349273 1349278) (-766 "OMERRK.spad" 1347860 1347868 1348816 1348821) (-765 "OMENC.spad" 1347204 1347212 1347850 1347855) (-764 "OMDEV.spad" 1341493 1341501 1347194 1347199) (-763 "OMCONN.spad" 1340902 1340910 1341483 1341488) (-762 "OINTDOM.spad" 1340665 1340673 1340828 1340897) (-761 "OFMONOID.spad" 1336852 1336862 1340655 1340660) (-760 "ODVAR.spad" 1336113 1336123 1336842 1336847) (-759 "ODR.spad" 1335561 1335587 1335925 1336074) (-758 "ODPOL.spad" 1332910 1332920 1333250 1333377) (-757 "ODP.spad" 1324082 1324102 1324455 1324584) (-756 "ODETOOLS.spad" 1322665 1322684 1324072 1324077) (-755 "ODESYS.spad" 1320315 1320332 1322655 1322660) (-754 "ODERTRIC.spad" 1316256 1316273 1320272 1320277) (-753 "ODERED.spad" 1315643 1315667 1316246 1316251) (-752 "ODERAT.spad" 1313194 1313211 1315633 1315638) (-751 "ODEPRRIC.spad" 1310085 1310107 1313184 1313189) (-750 "ODEPROB.spad" 1309284 1309292 1310075 1310080) (-749 "ODEPRIM.spad" 1306558 1306580 1309274 1309279) (-748 "ODEPAL.spad" 1305934 1305958 1306548 1306553) (-747 "ODEPACK.spad" 1292536 1292544 1305924 1305929) (-746 "ODEINT.spad" 1291967 1291983 1292526 1292531) (-745 "ODEIFTBL.spad" 1289362 1289370 1291957 1291962) (-744 "ODEEF.spad" 1284729 1284745 1289352 1289357) (-743 "ODECONST.spad" 1284248 1284266 1284719 1284724) (-742 "ODECAT.spad" 1282844 1282852 1284238 1284243) (-741 "OCT.spad" 1280991 1281001 1281707 1281746) (-740 "OCTCT2.spad" 1280635 1280656 1280981 1280986) (-739 "OC.spad" 1278409 1278419 1280591 1280630) (-738 "OC.spad" 1275909 1275921 1278093 1278098) (-737 "OCAMON.spad" 1275757 1275765 1275899 1275904) (-736 "OASGP.spad" 1275572 1275580 1275747 1275752) (-735 "OAMONS.spad" 1275092 1275100 1275562 1275567) (-734 "OAMON.spad" 1274953 1274961 1275082 1275087) (-733 "OAGROUP.spad" 1274815 1274823 1274943 1274948) (-732 "NUMTUBE.spad" 1274402 1274418 1274805 1274810) (-731 "NUMQUAD.spad" 1262264 1262272 1274392 1274397) (-730 "NUMODE.spad" 1253400 1253408 1262254 1262259) (-729 "NUMINT.spad" 1250958 1250966 1253390 1253395) (-728 "NUMFMT.spad" 1249798 1249806 1250948 1250953) (-727 "NUMERIC.spad" 1241871 1241881 1249604 1249609) (-726 "NTSCAT.spad" 1240361 1240377 1241827 1241866) (-725 "NTPOLFN.spad" 1239906 1239916 1240278 1240283) (-724 "NSUP.spad" 1232919 1232929 1237459 1237612) (-723 "NSUP2.spad" 1232311 1232323 1232909 1232914) (-722 "NSMP.spad" 1228510 1228529 1228818 1228945) (-721 "NREP.spad" 1226882 1226896 1228500 1228505) (-720 "NPCOEF.spad" 1226128 1226148 1226872 1226877) (-719 "NORMRETR.spad" 1225726 1225765 1226118 1226123) (-718 "NORMPK.spad" 1223628 1223647 1225716 1225721) (-717 "NORMMA.spad" 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1022056 1022336 1022375) (-603 "LODOF.spad" 1021084 1021101 1021997 1022002) (-602 "LODOCAT.spad" 1019742 1019752 1021040 1021079) (-601 "LODOCAT.spad" 1018398 1018410 1019698 1019703) (-600 "LODO2.spad" 1017673 1017685 1018080 1018119) (-599 "LODO1.spad" 1017075 1017085 1017355 1017394) (-598 "LODEEF.spad" 1015847 1015865 1017065 1017070) (-597 "LNAGG.spad" 1011639 1011649 1015827 1015842) (-596 "LNAGG.spad" 1007405 1007417 1011595 1011600) (-595 "LMOPS.spad" 1004141 1004158 1007395 1007400) (-594 "LMODULE.spad" 1003783 1003793 1004131 1004136) (-593 "LMDICT.spad" 1003066 1003076 1003334 1003361) (-592 "LIST.spad" 1000784 1000794 1002213 1002240) (-591 "LIST3.spad" 1000075 1000089 1000774 1000779) (-590 "LIST2.spad" 998715 998727 1000065 1000070) (-589 "LIST2MAP.spad" 995592 995604 998705 998710) (-588 "LINEXP.spad" 995024 995034 995572 995587) (-587 "LINDEP.spad" 993801 993813 994936 994941) (-586 "LIMITRF.spad" 991715 991725 993791 993796) (-585 "LIMITPS.spad" 990598 990611 991705 991710) (-584 "LIE.spad" 988612 988624 989888 990033) (-583 "LIECAT.spad" 988088 988098 988538 988607) (-582 "LIECAT.spad" 987592 987604 988044 988049) (-581 "LIB.spad" 985640 985648 986251 986266) (-580 "LGROBP.spad" 982993 983012 985630 985635) (-579 "LF.spad" 981912 981928 982983 982988) (-578 "LFCAT.spad" 980931 980939 981902 981907) (-577 "LEXTRIPK.spad" 976434 976449 980921 980926) (-576 "LEXP.spad" 974437 974464 976414 976429) (-575 "LEADCDET.spad" 972821 972838 974427 974432) (-574 "LAZM3PK.spad" 971525 971547 972811 972816) (-573 "LAUPOL.spad" 970216 970229 971120 971189) (-572 "LAPLACE.spad" 969789 969805 970206 970211) (-571 "LA.spad" 969229 969243 969711 969750) (-570 "LALG.spad" 969005 969015 969209 969224) (-569 "LALG.spad" 968789 968801 968995 969000) (-568 "KOVACIC.spad" 967502 967519 968779 968784) (-567 "KONVERT.spad" 967224 967234 967492 967497) (-566 "KOERCE.spad" 966961 966971 967214 967219) (-565 "KERNEL.spad" 965496 965506 966745 966750) (-564 "KERNEL2.spad" 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(-421 "GALPOLYU.spad" 730637 730650 732181 732186) (-420 "GALFACTU.spad" 728802 728821 730627 730632) (-419 "GALFACT.spad" 718935 718946 728792 728797) (-418 "FVFUN.spad" 715948 715956 718915 718930) (-417 "FVC.spad" 714990 714998 715928 715943) (-416 "FUNCTION.spad" 714839 714851 714980 714985) (-415 "FT.spad" 713051 713059 714829 714834) (-414 "FTEM.spad" 712214 712222 713041 713046) (-413 "FSUPFACT.spad" 711115 711134 712151 712156) (-412 "FST.spad" 709201 709209 711105 711110) (-411 "FSRED.spad" 708679 708695 709191 709196) (-410 "FSPRMELT.spad" 707503 707519 708636 708641) (-409 "FSPECF.spad" 705580 705596 707493 707498) (-408 "FS.spad" 699631 699641 705344 705575) (-407 "FS.spad" 693473 693485 699188 699193) (-406 "FSINT.spad" 693131 693147 693463 693468) (-405 "FSERIES.spad" 692318 692330 692951 693050) (-404 "FSCINT.spad" 691631 691647 692308 692313) (-403 "FSAGG.spad" 690736 690746 691575 691626) (-402 "FSAGG.spad" 689815 689827 690656 690661) (-401 "FSAGG2.spad" 688514 688530 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"FPC.spad" 646448 646456 647308 647401) (-379 "FPC.spad" 645576 645586 646438 646443) (-378 "FPATMAB.spad" 645328 645338 645556 645571) (-377 "FPARFRAC.spad" 643801 643818 645318 645323) (-376 "FORTRAN.spad" 642307 642350 643791 643796) (-375 "FORT.spad" 641236 641244 642297 642302) (-374 "FORTFN.spad" 638396 638404 641216 641231) (-373 "FORTCAT.spad" 638070 638078 638376 638391) (-372 "FORMULA.spad" 635408 635416 638060 638065) (-371 "FORMULA1.spad" 634887 634897 635398 635403) (-370 "FORDER.spad" 634578 634602 634877 634882) (-369 "FOP.spad" 633779 633787 634568 634573) (-368 "FNLA.spad" 633203 633225 633747 633774) (-367 "FNCAT.spad" 631531 631539 633193 633198) (-366 "FNAME.spad" 631423 631431 631521 631526) (-365 "FMTC.spad" 631221 631229 631349 631418) (-364 "FMONOID.spad" 628276 628286 631177 631182) (-363 "FM.spad" 627971 627983 628210 628237) (-362 "FMFUN.spad" 624991 624999 627951 627966) (-361 "FMC.spad" 624033 624041 624971 624986) (-360 "FMCAT.spad" 621687 621705 624001 624028) (-359 "FM1.spad" 621044 621056 621621 621648) (-358 "FLOATRP.spad" 618765 618779 621034 621039) (-357 "FLOAT.spad" 611929 611937 618631 618760) (-356 "FLOATCP.spad" 609346 609360 611919 611924) (-355 "FLINEXP.spad" 609058 609068 609326 609341) (-354 "FLINEXP.spad" 608724 608736 608994 608999) (-353 "FLASORT.spad" 608044 608056 608714 608719) (-352 "FLALG.spad" 605690 605709 607970 608039) (-351 "FLAGG.spad" 602696 602706 605658 605685) (-350 "FLAGG.spad" 599615 599627 602579 602584) (-349 "FLAGG2.spad" 598296 598312 599605 599610) (-348 "FINRALG.spad" 596325 596338 598252 598291) (-347 "FINRALG.spad" 594280 594295 596209 596214) (-346 "FINITE.spad" 593432 593440 594270 594275) (-345 "FINAALG.spad" 582413 582423 593374 593427) (-344 "FINAALG.spad" 571406 571418 582369 582374) (-343 "FILE.spad" 570989 570999 571396 571401) (-342 "FILECAT.spad" 569507 569524 570979 570984) (-341 "FIELD.spad" 568913 568921 569409 569502) (-340 "FIELD.spad" 568405 568415 568903 568908) (-339 "FGROUP.spad" 567014 567024 568385 568400) (-338 "FGLMICPK.spad" 565801 565816 567004 567009) (-337 "FFX.spad" 565176 565191 565517 565610) (-336 "FFSLPE.spad" 564665 564686 565166 565171) (-335 "FFPOLY.spad" 555917 555928 564655 564660) (-334 "FFPOLY2.spad" 554977 554994 555907 555912) (-333 "FFP.spad" 554374 554394 554693 554786) (-332 "FF.spad" 553822 553838 554055 554148) (-331 "FFNBX.spad" 552334 552354 553538 553631) (-330 "FFNBP.spad" 550847 550864 552050 552143) (-329 "FFNB.spad" 549312 549333 550528 550621) (-328 "FFINTBAS.spad" 546726 546745 549302 549307) (-327 "FFIELDC.spad" 544301 544309 546628 546721) (-326 "FFIELDC.spad" 541962 541972 544291 544296) (-325 "FFHOM.spad" 540710 540727 541952 541957) (-324 "FFF.spad" 538145 538156 540700 540705) (-323 "FFCGX.spad" 536992 537012 537861 537954) (-322 "FFCGP.spad" 535881 535901 536708 536801) (-321 "FFCG.spad" 534673 534694 535562 535655) (-320 "FFCAT.spad" 527574 527596 534512 534668) (-319 "FFCAT.spad" 520554 520578 527494 527499) (-318 "FFCAT2.spad" 520299 520339 520544 520549) (-317 "FEXPR.spad" 512012 512058 520059 520098) (-316 "FEVALAB.spad" 511718 511728 512002 512007) (-315 "FEVALAB.spad" 511209 511221 511495 511500) (-314 "FDIV.spad" 510651 510675 511199 511204) (-313 "FDIVCAT.spad" 508693 508717 510641 510646) (-312 "FDIVCAT.spad" 506733 506759 508683 508688) (-311 "FDIV2.spad" 506387 506427 506723 506728) (-310 "FCPAK1.spad" 504940 504948 506377 506382) (-309 "FCOMP.spad" 504319 504329 504930 504935) (-308 "FC.spad" 494144 494152 504309 504314) (-307 "FAXF.spad" 487079 487093 494046 494139) (-306 "FAXF.spad" 480066 480082 487035 487040) (-305 "FARRAY.spad" 478212 478222 479249 479276) (-304 "FAMR.spad" 476332 476344 478110 478207) (-303 "FAMR.spad" 474436 474450 476216 476221) (-302 "FAMONOID.spad" 474086 474096 474390 474395) (-301 "FAMONC.spad" 472308 472320 474076 474081) (-300 "FAGROUP.spad" 471914 471924 472204 472231) (-299 "FACUTIL.spad" 470110 470127 471904 471909) (-298 "FACTFUNC.spad" 469286 469296 470100 470105) (-297 "EXPUPXS.spad" 466119 466142 467418 467567) (-296 "EXPRTUBE.spad" 463347 463355 466109 466114) (-295 "EXPRODE.spad" 460219 460235 463337 463342) (-294 "EXPR.spad" 455521 455531 456235 456638) (-293 "EXPR2UPS.spad" 451613 451626 455511 455516) (-292 "EXPR2.spad" 451316 451328 451603 451608) (-291 "EXPEXPAN.spad" 448257 448282 448891 448984) (-290 "EXIT.spad" 447928 447936 448247 448252) (-289 "EVALCYC.spad" 447386 447400 447918 447923) (-288 "EVALAB.spad" 446950 446960 447376 447381) (-287 "EVALAB.spad" 446512 446524 446940 446945) (-286 "EUCDOM.spad" 444054 444062 446438 446507) (-285 "EUCDOM.spad" 441658 441668 444044 444049) (-284 "ESTOOLS.spad" 433498 433506 441648 441653) (-283 "ESTOOLS2.spad" 433099 433113 433488 433493) (-282 "ESTOOLS1.spad" 432784 432795 433089 433094) (-281 "ES.spad" 425331 425339 432774 432779) (-280 "ES.spad" 417786 417796 425231 425236) (-279 "ESCONT.spad" 414559 414567 417776 417781) (-278 "ESCONT1.spad" 414308 414320 414549 414554) (-277 "ES2.spad" 413803 413819 414298 414303) (-276 "ES1.spad" 413369 413385 413793 413798) (-275 "ERROR.spad" 410690 410698 413359 413364) (-274 "EQTBL.spad" 409162 409184 409371 409398) (-273 "EQ.spad" 404046 404056 406845 406954) (-272 "EQ2.spad" 403762 403774 404036 404041) (-271 "EP.spad" 400076 400086 403752 403757) (-270 "ENV.spad" 398778 398786 400066 400071) (-269 "ENTIRER.spad" 398446 398454 398722 398773) (-268 "EMR.spad" 397647 397688 398372 398441) (-267 "ELTAGG.spad" 395887 395906 397637 397642) (-266 "ELTAGG.spad" 394091 394112 395843 395848) (-265 "ELTAB.spad" 393538 393556 394081 394086) (-264 "ELFUTS.spad" 392917 392936 393528 393533) (-263 "ELEMFUN.spad" 392606 392614 392907 392912) (-262 "ELEMFUN.spad" 392293 392303 392596 392601) (-261 "ELAGG.spad" 390224 390234 392261 392288) (-260 "ELAGG.spad" 388104 388116 390143 390148) (-259 "ELABEXPR.spad" 387035 387043 388094 388099) (-258 "EFUPXS.spad" 383811 383841 386991 386996) (-257 "EFULS.spad" 380647 380670 383767 383772) (-256 "EFSTRUC.spad" 378602 378618 380637 380642) (-255 "EF.spad" 373368 373384 378592 378597) (-254 "EAB.spad" 371644 371652 373358 373363) (-253 "E04UCFA.spad" 371180 371188 371634 371639) (-252 "E04NAFA.spad" 370757 370765 371170 371175) (-251 "E04MBFA.spad" 370337 370345 370747 370752) (-250 "E04JAFA.spad" 369873 369881 370327 370332) (-249 "E04GCFA.spad" 369409 369417 369863 369868) (-248 "E04FDFA.spad" 368945 368953 369399 369404) (-247 "E04DGFA.spad" 368481 368489 368935 368940) (-246 "E04AGNT.spad" 364323 364331 368471 368476) (-245 "DVARCAT.spad" 361008 361018 364313 364318) (-244 "DVARCAT.spad" 357691 357703 360998 361003) (-243 "DSMP.spad" 355125 355139 355430 355557) (-242 "DROPT.spad" 349070 349078 355115 355120) (-241 "DROPT1.spad" 348733 348743 349060 349065) (-240 "DROPT0.spad" 343560 343568 348723 348728) (-239 "DRAWPT.spad" 341715 341723 343550 343555) (-238 "DRAW.spad" 334315 334328 341705 341710) (-237 "DRAWHACK.spad" 333623 333633 334305 334310) (-236 "DRAWCX.spad" 331065 331073 333613 333618) (-235 "DRAWCURV.spad" 330602 330617 331055 331060) (-234 "DRAWCFUN.spad" 319774 319782 330592 330597) (-233 "DQAGG.spad" 317930 317940 319730 319769) (-232 "DPOLCAT.spad" 313271 313287 317798 317925) (-231 "DPOLCAT.spad" 308698 308716 313227 313232) (-230 "DPMO.spad" 302048 302064 302186 302482) (-229 "DPMM.spad" 295411 295429 295536 295832) (-228 "DOMAIN.spad" 294682 294690 295401 295406) (-227 "DMP.spad" 291907 291922 292479 292606) (-226 "DLP.spad" 291255 291265 291897 291902) (-225 "DLIST.spad" 289667 289677 290438 290465) (-224 "DLAGG.spad" 288068 288078 289647 289662) (-223 "DIVRING.spad" 287515 287523 288012 288063) (-222 "DIVRING.spad" 287006 287016 287505 287510) (-221 "DISPLAY.spad" 285186 285194 286996 287001) (-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 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index b77c6994..ef81161f 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,14 +1,14 @@ -(143277 . 3422100682) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) #0#) |has| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (-288 (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))))) +(143277 . 3424116449) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) #0#) |has| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (-288 (-2 (|:| -3390 |#1|) (|:| -2348 |#2|))))) (((|#2| |#2|) . T)) ((((-525)) . T)) -((($ $) -3316 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) ((|#2| |#2|) . T) ((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525))))) +((($ $) -3204 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) ((|#2| |#2|) . T) ((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2|) . T)) -((($) -3316 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) ((|#2|) . T) (((-385 (-525))) |has| |#2| (-37 (-385 (-525))))) +((($) -3204 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) ((|#2|) . T) (((-385 (-525))) |has| |#2| (-37 (-385 (-525))))) (|has| |#1| (-844)) ((((-798)) . T)) ((((-798)) . T)) @@ -23,28 +23,28 @@ ((((-205)) . T) (((-798)) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1|) . T)) -(-3316 (|has| |#1| (-21)) (|has| |#1| (-787))) -((($ $) . 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T)) (((|#1|) . T)) ((((-385 (-525))) |has| |#1| (-968 (-385 (-525)))) (((-525)) |has| |#1| (-968 (-525))) ((|#1|) . T)) (((|#1|) . T) (((-525)) |has| |#1| (-588 (-525)))) -(((|#2|) . T) (((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -3390 (-1074)) (|:| -2348 |#1|))) . T)) (|has| |#1| (-517)) (|has| |#1| (-517)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) -(-3316 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-3204 (|has| |#1| (-789)) (|has| |#1| (-1020))) (((|#1|) . T)) (|has| |#1| (-517)) (|has| |#1| (-517)) @@ -218,11 +218,11 @@ (((|#2|) . T) (($) . T) (((-385 (-525))) . T)) (-12 (|has| |#1| (-1020)) (|has| |#2| (-1020))) ((($) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . 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T)) -(((|#3| |#3|) -3316 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-977))) (($ $) |has| |#3| (-160))) -(((|#4| |#4|) -3316 (|has| |#4| (-160)) (|has| |#4| (-341)) (|has| |#4| (-977))) (($ $) |has| |#4| (-160))) +(((|#3| |#3|) -3204 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-977))) (($ $) |has| |#3| (-160))) +(((|#4| |#4|) -3204 (|has| |#4| (-160)) (|has| |#4| (-341)) (|has| |#4| (-977))) (($ $) |has| |#4| (-160))) (((|#1|) . T)) (((|#2|) . T)) ((((-501)) |has| |#2| (-567 (-501))) (((-827 (-357))) |has| |#2| (-567 (-827 (-357)))) (((-827 (-525))) |has| |#2| (-567 (-827 (-525))))) @@ -231,21 +231,21 @@ ((((-798)) . T)) ((((-501)) |has| |#1| (-567 (-501))) (((-827 (-357))) |has| |#1| (-567 (-827 (-357)))) (((-827 (-525))) |has| |#1| (-567 (-827 (-525))))) ((((-798)) . 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T) (((-205)) . T) (((-357)) . T) (((-827 (-357))) . T)) ((((-798)) . T)) -(-3316 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) +(-3204 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) (((|#1|) |has| |#1| (-160))) (((|#1| $) |has| |#1| (-265 |#1| |#1|))) ((((-798)) . T)) @@ -256,15 +256,15 @@ (|has| |#1| (-789)) (|has| |#1| (-1020)) (((|#1|) . T)) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) ((((-501)) |has| |#1| (-567 (-501)))) ((((-125)) . 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T)) (((|#1| (-904)) . T)) (((#0=(-805 |#1|) $) |has| #0# (-265 #0# #0#))) @@ -273,7 +273,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1067)) -((((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) +((((-2 (|:| -3390 (-1074)) (|:| -2348 |#1|))) . T)) (|has| (-1159 |#1| |#2| |#3| |#4|) (-136)) (|has| (-1159 |#1| |#2| |#3| |#4|) (-138)) (|has| |#1| (-136)) @@ -290,20 +290,20 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-977))) ((((-798)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) #0#) |has| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (-288 (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) #0#) |has| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (-288 (-2 (|:| -3390 |#1|) (|:| -2348 |#2|))))) (((|#1|) . 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T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($ $) -3204 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) ((($) . T)) ((($) . T)) ((($) . T)) -((($) -3316 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3204 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-798)) . T)) ((((-798)) . T)) (|has| (-1158 |#2| |#3| |#4|) (-138)) @@ -314,16 +314,16 @@ ((((-798)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3316 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) +(-3204 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) (((|#1|) . T)) ((((-525) |#1|) . 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T)) ((((-525) (-125)) . T)) ((((-798)) . T)) @@ -660,22 +660,22 @@ (|has| |#1| (-1020)) (((|#2|) . T)) ((((-501)) |has| |#2| (-567 (-501))) (((-827 (-357))) |has| |#2| (-567 (-827 (-357)))) (((-827 (-525))) |has| |#2| (-567 (-827 (-525))))) -(((|#4|) -3316 (|has| |#4| (-160)) (|has| |#4| (-341)))) -(((|#3|) -3316 (|has| |#3| (-160)) (|has| |#3| (-341)))) +(((|#4|) -3204 (|has| |#4| (-160)) (|has| |#4| (-341)))) +(((|#3|) -3204 (|has| |#3| (-160)) (|has| |#3| (-341)))) ((((-798)) . T)) (((|#1|) . T)) -(-3316 (|has| |#2| (-429)) (|has| |#2| (-844))) -(-3316 (|has| |#1| (-429)) (|has| |#1| (-844))) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-844))) +(-3204 (|has| |#2| (-429)) (|has| |#2| (-844))) +(-3204 (|has| |#1| (-429)) (|has| |#1| (-844))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-844))) ((($ $) . T) ((#0=(-1091) $) |has| |#1| (-213)) ((#0# |#1|) |has| |#1| (-213)) ((#1=(-760 (-1091)) |#1|) . T) ((#1# $) . 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T)) (|has| (-385 |#2|) (-138)) (|has| (-385 |#2|) (-136)) @@ -688,22 +688,22 @@ (|has| |#1| (-517)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) ((((-798)) . T)) -((((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) +((((-2 (|:| -3390 (-1074)) (|:| -2348 |#1|))) . T)) (|has| |#1| (-37 (-385 (-525)))) -((((-366) (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) +((((-366) (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|))) . T)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#2| (-1067)) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-517))) (((|#1|) . T)) ((((-366) (-1074)) . T)) (|has| |#1| (-517)) ((((-112 |#1|)) . T)) ((((-125)) . T)) ((((-525) |#1|) . T)) -(-3316 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3204 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (((|#2|) . T)) ((((-798)) . T)) ((((-761 |#1|)) . T)) @@ -716,7 +716,7 @@ (((|#1|) |has| |#1| (-160))) ((((-798)) . T)) ((((-501)) |has| |#1| (-567 (-501)))) -(-3316 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-3204 (|has| |#1| (-789)) (|has| |#1| (-1020))) (((|#2|) |has| |#2| (-288 |#2|))) (((#0=(-525) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -726,7 +726,7 @@ (((#0=(-525) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) ((($) . T) (((-525)) . T) (((-385 (-525))) . T)) (|has| |#2| (-346)) -(-3316 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-3204 (|has| |#1| (-789)) (|has| |#1| (-1020))) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) @@ -737,9 +737,9 @@ ((((-1089 |#1| |#2| |#3|) $) -12 (|has| (-1089 |#1| |#2| |#3|) (-265 (-1089 |#1| |#2| |#3|) (-1089 |#1| |#2| |#3|))) (|has| |#1| (-341))) (($ $) . T)) ((((-798)) . T)) ((((-798)) . T)) -((($) . T) (((-385 (-525))) -3316 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) . T) (((-385 (-525))) -3204 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) ((((-501)) |has| |#1| (-567 (-501)))) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) ((($ $) . T)) ((($ $) . T)) ((((-798)) . T)) @@ -749,12 +749,12 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3204 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-385 (-525))) . 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T) (((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) +((($) . T) (((-385 (-525))) -3204 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) (|has| |#1| (-770)) ((((-385 (-525))) |has| |#1| (-968 (-385 (-525)))) (((-525)) |has| |#1| (-968 (-525))) ((|#1|) . T)) (|has| |#1| (-1020)) @@ -819,8 +819,8 @@ (((|#3|) |has| |#3| (-1020))) (|has| |#3| (-346)) (((|#1|) . T) (((-798)) . T)) -((((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3316 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1165 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) -(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3316 (|has| |#1| (-341)) (|has| |#1| (-517)))) +((((-385 (-525))) -3204 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3204 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1165 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) +(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3204 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3204 (|has| |#1| (-341)) (|has| |#1| (-517)))) ((((-798)) . T)) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2|) . T)) @@ -830,30 +830,30 @@ (((|#1|) . T)) (((|#1|) |has| |#1| (-160))) ((((-385 (-525))) . T) (((-525)) . T)) -((($ $) -3316 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) -((($) -3316 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($ $) -3204 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($) -3204 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) ((((-135)) . T)) (((|#1|) . T)) ((((-135)) . T)) -((($) -3316 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((|#2|) -3316 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977)))) +((($) -3204 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((|#2|) -3204 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977)))) ((((-135)) . T)) (((|#1| |#2| |#3|) . T)) -(-3316 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) +(-3204 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) (|has| $ (-138)) (|has| $ (-138)) (|has| |#1| (-1020)) ((((-798)) . T)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3316 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-977)) (|has| |#1| (-1032))) +(-3204 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-977)) (|has| |#1| (-1032))) ((($ $) |has| |#1| (-265 $ $)) ((|#1| $) |has| |#1| (-265 |#1| |#1|))) (((|#1| (-385 (-525))) . T)) (((|#1|) . T)) ((((-1091)) . T)) (|has| |#1| (-517)) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-517)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) @@ -864,7 +864,7 @@ (|has| |#1| (-138)) (|has| |#1| (-136)) (|has| |#4| (-787)) -(((|#2| (-220 (-3674 |#1|) (-713)) (-800 |#1|)) . T)) +(((|#2| (-220 (-3552 |#1|) (-713)) (-800 |#1|)) . T)) (|has| |#3| (-787)) (((|#1| (-497 |#3|) |#3|) . T)) (|has| |#1| (-138)) @@ -878,21 +878,21 @@ (|has| |#1| (-136)) ((((-385 (-525))) |has| |#2| (-341)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) -(-3316 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) -(-3316 (|has| |#1| (-327)) (|has| |#1| (-346))) +(-3204 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-3204 (|has| |#1| (-327)) (|has| |#1| (-346))) ((((-1058 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-160)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-213)) (|has| |#2| (-977))) -(((|#2|) . T) (((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) -(-3316 (|has| |#3| (-735)) (|has| |#3| (-787))) -(-3316 (|has| |#3| (-735)) (|has| |#3| (-787))) +(((|#2|) . T) (((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) +(-3204 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-3204 (|has| |#3| (-735)) (|has| |#3| (-787))) ((((-798)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) . T) (($) . T)) ((((-641)) . T)) -(-3316 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3204 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) (|has| |#1| (-517)) (((|#1|) . T)) (((|#1|) . T)) @@ -914,10 +914,10 @@ (((|#1| (-385 (-525))) . T)) (((|#3|) . T) (((-565 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) ((($ $) . T) ((|#2| $) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((#0=(-1089 |#1| |#2| |#3|) #0#) -12 (|has| (-1089 |#1| |#2| |#3|) (-288 (-1089 |#1| |#2| |#3|))) (|has| |#1| (-341))) (((-1091) #0#) -12 (|has| (-1089 |#1| |#2| |#3|) (-486 (-1091) (-1089 |#1| |#2| |#3|))) (|has| |#1| (-341)))) @@ -925,8 +925,8 @@ ((((-798)) . T)) ((((-798)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) |has| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (-288 (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))))) -(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020))) (((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) |has| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (-288 (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) |has| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (-288 (-2 (|:| -3390 |#1|) (|:| -2348 |#2|))))) +(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020))) (((-2 (|:| -3390 (-1074)) (|:| -2348 |#1|))) |has| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (-288 (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|))))) ((((-798)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -937,10 +937,10 @@ ((($ $) . T) ((#0=(-800 |#1|) $) . T) ((#0# |#2|) . 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T)) (((|#1|) |has| |#1| (-288 |#1|))) (|has| |#1| (-346)) @@ -1021,31 +1021,31 @@ (|has| |#1| (-346)) ((((-1091) $) |has| |#1| (-486 (-1091) $)) (($ $) |has| |#1| (-288 $)) ((|#1| |#1|) |has| |#1| (-288 |#1|)) (((-1091) |#1|) |has| |#1| (-486 (-1091) |#1|))) ((((-1091)) |has| |#1| (-835 (-1091)))) -(-3316 (-12 (|has| |#1| (-213)) (|has| |#1| (-341))) (|has| |#1| (-327))) +(-3204 (-12 (|has| |#1| (-213)) (|has| |#1| (-341))) (|has| |#1| (-327))) ((((-366) (-1038)) . T)) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-366) |#1|) . T)) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-1020)) ((((-798)) . T)) ((((-798)) . T)) ((((-845 |#1|)) . T)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3316 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) -((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) -3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3204 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) +((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) -3204 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844)))) (((|#1| |#2|) . T)) ((($) . T)) (((|#1| |#1|) . T)) (((#0=(-805 |#1|)) |has| #0# (-288 #0#))) (((|#1| |#2|) . T)) -(-3316 (|has| |#2| (-735)) (|has| |#2| (-787))) -(-3316 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3204 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3204 (|has| |#2| (-735)) (|has| |#2| (-787))) (-12 (|has| |#1| (-735)) (|has| |#2| (-735))) (((|#1|) . T)) (-12 (|has| |#1| (-735)) (|has| |#2| (-735))) -(-3316 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3204 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) (|has| |#1| (-1113)) (((#0=(-525) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) ((((-385 (-525))) . T) (($) . T)) @@ -1056,8 +1056,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-385 (-525)) #0#) . T)) (|has| |#1| (-341)) ((((-525)) . T) (((-385 (-525))) . T) (($) . T)) -((($ $) . T) ((#0=(-385 (-525)) #0#) -3316 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1| |#1|) . T)) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((($ $) . T) ((#0=(-385 (-525)) #0#) -3204 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1| |#1|) . T)) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#1|) . T) (($) . T) (((-385 (-525))) . T)) ((((-798)) . T)) ((((-798)) . T)) @@ -1072,14 +1072,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-787)) (|has| |#1| (-787)) -((($) . T) (((-385 (-525))) -3316 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) -(-3316 (|has| |#1| (-160)) (|has| |#1| (-517))) -(((#0=(-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) #0#) |has| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (-288 (-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))))) +((($) . T) (((-385 (-525))) -3204 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +(-3204 (|has| |#1| (-160)) (|has| |#1| (-517))) +(((#0=(-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) #0#) |has| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (-288 (-2 (|:| -3390 (-1091)) (|:| -2348 (-51)))))) ((($) . T)) (|has| |#2| (-789)) ((($) . T)) (((|#2|) |has| |#2| (-1020))) -((((-798)) -3316 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-566 (-798))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (((-1173 |#2|)) . T)) +((((-798)) -3204 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-566 (-798))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (((-1173 |#2|)) . T)) (|has| |#1| (-789)) (|has| |#1| (-789)) ((((-1074) (-51)) . T)) @@ -1087,10 +1087,10 @@ ((((-798)) . T)) ((((-525)) |has| #0=(-385 |#2|) (-588 (-525))) ((#0#) . T)) ((((-525) (-135)) . T)) -((((-525) (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T) ((|#1| |#2|) . T)) +((((-525) (-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T) ((|#1| |#2|) . T)) ((((-385 (-525))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) ((((-798)) . T)) ((((-845 |#1|)) . T)) (|has| |#1| (-341)) @@ -1115,31 +1115,31 @@ ((($) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-160))) -((((-525) (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T) ((|#1| |#2|) . T)) +((((-525) (-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#3|) . 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T)) (|has| |#2| (-787)) (-12 (|has| |#2| (-213)) (|has| |#2| (-977))) (|has| |#1| (-517)) (|has| |#1| (-1067)) ((((-1074) |#1|) . T)) -(-3316 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) -(((#0=(-385 (-525)) #0#) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($ $) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1| |#1|) . T)) +(-3204 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(((#0=(-385 (-525)) #0#) -3204 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($ $) -3204 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1| |#1|) . T)) ((((-385 (-525))) |has| |#1| (-968 (-525))) (((-525)) |has| |#1| (-968 (-525))) (((-1091)) |has| |#1| (-968 (-1091))) ((|#1|) . T)) ((((-525) |#2|) . T)) ((((-385 (-525))) |has| |#1| (-968 (-385 (-525)))) (((-525)) |has| |#1| (-968 (-525))) ((|#1|) . T)) ((((-525)) |has| |#1| (-821 (-525))) (((-357)) |has| |#1| (-821 (-357)))) -((((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1|) . T)) +((((-385 (-525))) -3204 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3204 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1|) . T)) (((|#1|) . T)) ((((-592 |#4|)) . T) (((-798)) . T)) ((((-501)) |has| |#4| (-567 (-501)))) @@ -1152,17 +1152,17 @@ (((|#1|) . T)) (((|#2|) . T)) ((((-1091)) |has| (-385 |#2|) (-835 (-1091)))) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) #0#) |has| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (-288 (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) #0#) |has| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (-288 (-2 (|:| -3390 |#1|) (|:| -2348 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-798)) -3316 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-566 (-798))) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-669)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-977)) (|has| |#3| (-1020))) (((-1173 |#3|)) . T)) +((((-798)) -3204 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-566 (-798))) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-669)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-977)) (|has| |#3| (-1020))) (((-1173 |#3|)) . T)) ((((-525) |#2|) . T)) -(-3316 (|has| |#1| (-789)) (|has| |#1| (-1020))) -(((|#2| |#2|) -3316 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977))) (($ $) |has| |#2| (-160))) +(-3204 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(((|#2| |#2|) -3204 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977))) (($ $) |has| |#2| (-160))) ((((-798)) . T)) ((((-798)) . T)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T) ((|#2|) . T)) ((((-798)) . T)) ((((-798)) . T)) ((((-1074) (-1091) (-525) (-205) (-798)) . T)) @@ -1197,8 +1197,8 @@ (|has| |#1| (-37 (-385 (-525)))) ((((-798)) . T)) ((((-501)) |has| |#1| (-567 (-501)))) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) -(((|#2|) -3316 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977))) (($) |has| |#2| (-160))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +(((|#2|) -3204 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977))) (($) |has| |#2| (-160))) (|has| $ (-138)) ((((-385 |#2|)) . T)) ((((-385 (-525))) |has| #0=(-385 |#2|) (-968 (-385 (-525)))) (((-525)) |has| #0# (-968 (-525))) ((#0#) . T)) @@ -1209,11 +1209,11 @@ (((|#3|) |has| |#3| (-160))) (|has| |#1| (-138)) (|has| |#1| (-136)) -(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3204 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) -(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3204 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) -(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3204 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) (((|#1|) . T)) (((|#2|) . T)) @@ -1244,7 +1244,7 @@ ((((-931 |#1|)) . T) ((|#1|) . T)) ((((-798)) . T)) ((((-798)) . T)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) ((((-385 (-525))) . T) (((-385 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1087 |#1|)) . T)) ((((-525)) . T) (($) . T) (((-385 (-525))) . T)) @@ -1252,9 +1252,9 @@ (|has| |#1| (-789)) (((|#2|) . T)) ((((-525)) . T) (($) . T) (((-385 (-525))) . T)) -((((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) +((((-2 (|:| -3390 (-1074)) (|:| -2348 |#1|))) . T)) ((((-525) |#2|) . T)) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#2|) . T)) ((((-525) |#3|) . T)) (((|#2|) . T)) @@ -1269,7 +1269,7 @@ (((|#3|) -12 (|has| |#3| (-288 |#3|)) (|has| |#3| (-1020)))) (((|#2|) . T)) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) #0#) |has| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (-288 (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) #0#) |has| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (-288 (-2 (|:| -3390 |#1|) (|:| -2348 |#2|))))) (((|#2| |#2|) . T)) (|has| |#2| (-341)) (((|#2|) . T) (((-525)) |has| |#2| (-968 (-525))) (((-385 (-525))) |has| |#2| (-968 (-385 (-525))))) @@ -1299,19 +1299,19 @@ (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1| |#2|) . T)) ((((-525) (-135)) . T)) -(((#0=(-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) #0#) |has| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (-288 (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) -((($) -3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +(((#0=(-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) #0#) |has| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (-288 (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) +((($) -3204 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (|has| |#1| (-789)) (((|#2| (-713) (-1005)) . T)) (((|#1| |#2|) . T)) -(-3316 (|has| |#1| (-160)) (|has| |#1| (-517))) +(-3204 (|has| |#1| (-160)) (|has| |#1| (-517))) (|has| |#1| (-733)) (((|#1|) |has| |#1| (-160))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-3316 (|has| |#1| (-138)) (-12 (|has| |#1| (-341)) (|has| |#2| (-138)))) -(-3316 (|has| |#1| (-136)) (-12 (|has| |#1| (-341)) (|has| |#2| (-136)))) +(-3204 (|has| |#1| (-138)) (-12 (|has| |#1| (-341)) (|has| |#2| (-138)))) +(-3204 (|has| |#1| (-136)) (-12 (|has| |#1| (-341)) (|has| |#2| (-136)))) (((|#4|) . T)) (|has| |#1| (-136)) ((((-1074) |#1|) . T)) @@ -1324,10 +1324,10 @@ (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#3|) . T)) ((((-1165 |#1| |#2| |#3|)) |has| |#1| (-341))) -(-3316 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-3204 (|has| |#1| (-789)) (|has| |#1| (-1020))) (((|#1|) . T)) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020))) (((-892 |#1|)) . T)) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020))) (((-892 |#1|)) . T)) (|has| |#1| (-787)) (|has| |#1| (-787)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) @@ -1340,8 +1340,8 @@ ((($) . T)) ((((-366) (-1074)) . T)) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) -((((-798)) -3316 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-566 (-798))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (((-1173 |#2|)) . T)) -(((#0=(-51)) . T) (((-2 (|:| -3511 (-1074)) (|:| -3631 #0#))) . T)) +((((-798)) -3204 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-566 (-798))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (((-1173 |#2|)) . T)) +(((#0=(-51)) . T) (((-2 (|:| -3390 (-1074)) (|:| -2348 #0#))) . T)) (((|#1|) . T)) ((((-798)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) @@ -1349,7 +1349,7 @@ (|has| |#2| (-136)) (|has| |#2| (-138)) (|has| |#1| (-450)) -(-3316 (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) +(-3204 (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) (|has| |#1| (-341)) ((((-798)) . T)) (|has| |#1| (-37 (-385 (-525)))) @@ -1358,8 +1358,8 @@ (|has| |#1| (-787)) (|has| |#1| (-787)) ((((-798)) . T)) -((((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3316 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1165 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) -(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3316 (|has| |#1| (-341)) (|has| |#1| (-517)))) +((((-385 (-525))) -3204 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3204 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1165 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) +(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3204 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3204 (|has| |#1| (-341)) (|has| |#1| (-517)))) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1| |#2|) . T)) ((((-1091)) |has| |#1| (-835 (-1091)))) @@ -1367,7 +1367,7 @@ ((((-798)) . T)) ((((-798)) . T)) (|has| |#1| (-1020)) -(((|#2| (-458 (-3674 |#1|) (-713)) (-800 |#1|)) . T)) +(((|#2| (-458 (-3552 |#1|) (-713)) (-800 |#1|)) . T)) ((((-385 (-525))) . #0=(|has| |#2| (-341))) (($) . #0#)) (((|#1| (-497 (-1091)) (-1091)) . T)) (((|#1|) . T)) @@ -1387,16 +1387,16 @@ (|has| |#1| (-138)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) -((((-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))) . T)) +(((|#1|) . T) (((-2 (|:| -3390 (-1074)) (|:| -2348 |#1|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) +((((-2 (|:| -3390 (-1091)) (|:| -2348 (-51)))) . T)) ((((-1089 |#1| |#2| |#3|)) |has| |#1| (-341))) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) ((((-1091) (-51)) . T)) ((($ $) . T)) (((|#1| (-525)) . T)) ((((-845 |#1|)) . T)) -(((|#1|) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977))) (($) -3316 (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)))) +(((|#1|) -3204 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977))) (($) -3204 (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)))) (((|#1|) . T) (((-525)) |has| |#1| (-968 (-525))) (((-385 (-525))) |has| |#1| (-968 (-385 (-525))))) (|has| |#1| (-789)) (|has| |#1| (-789)) @@ -1411,13 +1411,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1020)))) (((|#1|) |has| |#1| (-160))) (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1020)))) -(((|#3|) -3316 (|has| |#3| (-160)) (|has| |#3| (-341)))) +(((|#3|) -3204 (|has| |#3| (-160)) (|has| |#3| (-341)))) (|has| |#2| (-789)) (|has| |#1| (-789)) -(-3316 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-844))) +(-3204 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-844))) ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) ((((-525) |#2|) . T)) -(((|#2|) -3316 (|has| |#2| (-160)) (|has| |#2| (-341)))) +(((|#2|) -3204 (|has| |#2| (-160)) (|has| |#2| (-341)))) (|has| |#1| (-327)) (((|#3| |#3|) -12 (|has| |#3| (-288 |#3|)) (|has| |#3| (-1020)))) ((($) . T) (((-385 (-525))) . T)) @@ -1425,7 +1425,7 @@ (|has| |#1| (-762)) (|has| |#1| (-762)) (((|#1|) . T)) -(-3316 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3204 (|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)))) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-37 (-385 (-525)))) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) ((((-1091)) |has| |#1| (-835 (-1091))) (((-1005)) . T)) (((|#1|) . T)) (|has| |#1| (-787)) -(((#0=(-2 (|:| -3511 (-1074)) (|:| -3631 (-51))) #0#) |has| (-2 (|:| -3511 (-1074)) (|:| -3631 (-51))) (-288 (-2 (|:| -3511 (-1074)) (|:| -3631 (-51)))))) +(((#0=(-2 (|:| -3390 (-1074)) (|:| -2348 (-51))) #0#) |has| (-2 (|:| -3390 (-1074)) (|:| -2348 (-51))) (-288 (-2 (|:| -3390 (-1074)) (|:| -2348 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (|has| |#1| (-1020)) (((|#1|) . T)) @@ -1459,7 +1459,7 @@ (((|#1|) . T)) ((((-135)) . T)) (((|#2|) |has| |#2| (-160))) -(-3316 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) +(-3204 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (((|#1|) . T)) (|has| |#1| (-136)) (|has| |#1| (-138)) @@ -1481,32 +1481,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020))) ((#0=(-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) #0#) |has| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (-288 (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))))) -(-3316 (|has| |#2| (-429)) (|has| |#2| (-844))) -(-3316 (|has| |#1| (-429)) (|has| |#1| (-844))) +(((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020))) ((#0=(-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) #0#) |has| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (-288 (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|))))) +(-3204 (|has| |#2| (-429)) (|has| |#2| (-844))) +(-3204 (|has| |#1| (-429)) (|has| |#1| (-844))) (((|#1|) . T) (($) . T)) (((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) (((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(((|#3|) -3316 (|has| |#3| (-160)) (|has| |#3| (-341)))) +(((|#3|) -3204 (|has| |#3| (-160)) (|has| |#3| (-341)))) (|has| |#1| (-789)) (|has| |#1| (-517)) ((((-538 |#1|)) . T)) ((($) . T)) (((|#2|) . T)) -(-3316 (-12 (|has| |#1| (-341)) (|has| |#2| (-762))) (-12 (|has| |#1| (-341)) (|has| |#2| (-789)))) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3204 (-12 (|has| |#1| (-341)) (|has| |#2| (-762))) (-12 (|has| |#1| (-341)) (|has| |#2| (-789)))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-517))) ((((-845 |#1|)) . T)) (((|#1| (-469 |#1| |#3|) (-469 |#1| |#2|)) . T)) (((|#1| |#4| |#5|) . T)) (((|#1| (-713)) . T)) ((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) |has| |#1| (-517))) -((((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3316 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1089 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) -(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3316 (|has| |#1| (-341)) (|has| |#1| (-517)))) +((((-385 (-525))) -3204 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3204 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1089 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) +(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3204 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3204 (|has| |#1| (-341)) (|has| |#1| (-517)))) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) -((((-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))) . T)) +((((-2 (|:| -3390 (-1091)) (|:| -2348 (-51)))) . T)) ((((-385 |#2|)) . T) (((-385 (-525))) . T) (($) . T)) ((((-617 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1514,17 +1514,17 @@ ((((-798)) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) ((((-798)) . T)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3316 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3204 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) ((((-798)) . T)) ((((-798)) . T)) ((((-798)) . T)) (((|#2|) . T)) -(-3316 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-669)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-977)) (|has| |#3| (-1020))) -(-3316 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3204 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-669)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-977)) (|has| |#3| (-1020))) +(-3204 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((((-385 (-525))) |has| |#1| (-968 (-385 (-525)))) (((-525)) |has| |#1| (-968 (-525))) ((|#1|) . T)) (|has| |#1| (-1113)) (|has| |#1| (-1113)) -(-3316 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) +(-3204 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (|has| |#1| (-1113)) (|has| |#1| (-1113)) (((|#3| |#3|) . T)) @@ -1537,43 +1537,43 @@ (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) ((((-1074) (-51)) . T)) (|has| |#1| (-1020)) -(-3316 (|has| |#2| (-762)) (|has| |#2| (-789))) +(-3204 (|has| |#2| (-762)) (|has| |#2| (-789))) (((|#1|) . T)) -((($) -3316 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -3316 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . 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T)) -(-3316 (|has| |#1| (-429)) (|has| |#1| (-844))) +(-3204 (|has| |#1| (-429)) (|has| |#1| (-844))) (|has| |#2| (-844)) (|has| |#1| (-341)) (((|#2|) |has| |#2| (-1020))) -(-3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3204 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((($) . T) ((|#2|) . T)) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-844))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-844))) (|has| |#1| (-844)) (|has| |#1| (-844)) ((((-501)) . T) (((-385 (-1087 (-525)))) . T) (((-205)) . T) (((-357)) . T)) ((((-357)) . T) (((-205)) . T) (((-798)) . T)) (|has| |#1| (-844)) -(-3316 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-3204 (|has| |#1| (-789)) (|has| |#1| (-1020))) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) ((($ $) . T)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) ((($ $) . T)) ((((-525) (-108)) . T)) ((($) . T)) (((|#1|) . T)) ((((-525)) . T)) ((((-108)) . T)) -(-3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3204 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-37 (-385 (-525)))) (((|#1| (-525)) . T)) ((($) . T)) @@ -1595,7 +1595,7 @@ (((|#1| (-1137 |#1| |#2| |#3|)) . T)) (((|#1| (-713)) . T)) (((|#1|) . T)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) ((((-798)) . T)) (|has| |#1| (-1020)) ((((-1074) |#1|) . T)) @@ -1615,18 +1615,18 @@ (((|#1|) . T)) ((((-525)) . T)) ((((-798)) . T)) -(-3316 (|has| |#1| (-136)) (|has| |#1| (-327))) +(-3204 (|has| |#1| (-136)) (|has| |#1| (-327))) (|has| |#1| (-138)) ((((-798)) . T)) (((|#3|) . T)) -(-3316 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-977))) +(-3204 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-977))) ((((-798)) . T)) ((((-1158 |#2| |#3| |#4|)) . T) (((-1159 |#1| |#2| |#3| |#4|)) . T)) ((((-798)) . T)) -((((-47)) -12 (|has| |#1| (-517)) (|has| |#1| (-968 (-525)))) (((-565 $)) . T) ((|#1|) . T) (((-525)) |has| |#1| (-968 (-525))) (((-385 (-525))) -3316 (-12 (|has| |#1| (-517)) (|has| |#1| (-968 (-525)))) (|has| |#1| (-968 (-385 (-525))))) (((-385 (-887 |#1|))) |has| |#1| (-517)) (((-887 |#1|)) |has| |#1| (-977)) (((-1091)) . T)) +((((-47)) -12 (|has| |#1| (-517)) (|has| |#1| (-968 (-525)))) (((-565 $)) . T) ((|#1|) . T) (((-525)) |has| |#1| (-968 (-525))) (((-385 (-525))) -3204 (-12 (|has| |#1| (-517)) (|has| |#1| (-968 (-525)))) (|has| |#1| (-968 (-385 (-525))))) (((-385 (-887 |#1|))) |has| |#1| (-517)) (((-887 |#1|)) |has| |#1| (-977)) (((-1091)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-713)) . T)) -((($) -3316 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) +((($) -3204 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3204 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) (((|#1|) |has| |#1| (-288 |#1|))) ((((-1159 |#1| |#2| |#3| |#4|)) . T)) ((((-525)) |has| |#1| (-821 (-525))) (((-357)) |has| |#1| (-821 (-357)))) @@ -1634,14 +1634,14 @@ (|has| |#1| (-517)) (((|#1|) . T)) ((((-798)) . T)) -(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) |has| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (-288 (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) |has| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (-288 (-2 (|:| -3390 |#1|) (|:| -2348 |#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| (-1020)))) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) (((|#1|) . T)) (((|#3|) |has| |#3| (-1020))) -(((|#2|) -3316 (|has| |#2| (-160)) (|has| |#2| (-341)))) +(((|#2|) -3204 (|has| |#2| (-160)) (|has| |#2| (-341)))) ((((-1158 |#2| |#3| |#4|)) . T)) ((((-108)) . T)) (|has| |#1| (-762)) @@ -1651,8 +1651,8 @@ (|has| |#1| (-787)) (|has| |#1| (-787)) (((|#1| (-525) (-1005)) . T)) -(-3316 (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +(-3204 (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) (((|#1| (-385 (-525)) (-1005)) . T)) (((|#1| (-713) (-1005)) . T)) (|has| |#1| (-789)) @@ -1668,28 +1668,28 @@ (((|#1|) . T)) (|has| |#1| (-1020)) ((((-525)) -12 (|has| |#1| (-341)) (|has| |#2| (-588 (-525)))) ((|#2|) |has| |#1| (-341))) -(-3316 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) +(-3204 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (((|#2|) |has| |#2| (-160))) (((|#1|) |has| |#1| (-160))) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) -((((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) +((((-2 (|:| -3390 (-1074)) (|:| -2348 |#1|))) . T)) ((((-798)) . T)) (|has| |#3| (-787)) ((((-798)) . T)) ((((-1158 |#2| |#3| |#4|) (-297 |#2| |#3| |#4|)) . T)) ((((-798)) . T)) -(((|#1| |#1|) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977)))) +(((|#1| |#1|) -3204 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977)))) (((|#1|) . T)) ((((-525)) . T)) ((((-525)) . T)) -(((|#1|) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977)))) +(((|#1|) -3204 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977)))) (((|#2|) |has| |#2| (-341))) ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-341))) (|has| |#1| (-789)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))) |has| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (-288 (-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))))) -(-3316 (|has| |#1| (-429)) (|has| |#1| (-844))) +((((-2 (|:| -3390 (-1091)) (|:| -2348 (-51)))) |has| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (-288 (-2 (|:| -3390 (-1091)) (|:| -2348 (-51)))))) +(-3204 (|has| |#1| (-429)) (|has| |#1| (-844))) (((|#2|) . T) (((-525)) |has| |#2| (-588 (-525)))) ((((-798)) . T)) ((((-798)) . T)) @@ -1724,18 +1724,18 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (((|#1|) . T)) -(-3316 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3204 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) (((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) . T) (($ $) . T)) ((((-798)) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (|has| |#1| (-341)) (|has| |#1| (-341)) (|has| (-385 |#2|) (-213)) (|has| |#1| (-844)) (((|#2|) |has| |#2| (-977))) -(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) |has| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (-288 (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) |has| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (-288 (-2 (|:| -3390 |#1|) (|:| -2348 |#2|))))) (|has| |#1| (-341)) (((|#1|) |has| |#1| (-160))) (((|#1| |#1|) . T)) @@ -1760,7 +1760,7 @@ (((|#1| (-385 (-525)) (-1005)) . T)) (((|#1| (-713) (-1005)) . T)) (((#0=(-385 |#2|) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-525)) -3316 (|has| (-385 (-525)) (-968 (-525))) (|has| |#1| (-968 (-525)))) (((-385 (-525))) . T)) +(((|#1|) . T) (((-525)) -3204 (|has| (-385 (-525)) (-968 (-525))) (|has| |#1| (-968 (-525)))) (((-385 (-525))) . T)) (((|#1| (-556 |#1| |#3|) (-556 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) @@ -1779,24 +1779,24 @@ ((((-641)) . T)) (((|#2|) |has| |#2| (-160))) (|has| |#2| (-787)) -((((-108)) |has| |#1| (-1020)) (((-798)) -3316 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020)))) +((((-108)) |has| |#1| (-1020)) (((-798)) -3204 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3511 (-1074)) (|:| -3631 (-51)))) . T)) +((((-2 (|:| -3390 (-1074)) (|:| -2348 (-51)))) . T)) ((((-798)) . 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| (-1020))) (((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) |has| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (-288 (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) |has| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (-288 (-2 (|:| -3390 |#1|) (|:| -2348 |#2|))))) ((((-357)) . T)) ((((-641)) . T)) ((((-385 (-525))) . #0=(|has| |#2| (-341))) (($) . #0#)) (((|#1|) |has| |#1| (-160))) ((((-385 (-887 |#1|))) . T)) (((|#2| |#2|) . T)) -(-3316 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) -(-3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3204 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-3204 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (((|#2|) . T)) (|has| |#2| (-789)) (((|#3|) |has| |#3| (-977))) @@ -1806,14 +1806,14 @@ (|has| |#1| (-789)) ((((-1091)) |has| |#2| (-835 (-1091)))) ((((-798)) . T)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) ((((-385 (-525))) . T) (($) . T)) (|has| |#1| (-450)) (|has| |#1| (-346)) (|has| |#1| (-346)) (|has| |#1| (-346)) (|has| |#1| (-341)) -(-3316 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-977)) (|has| |#1| (-1032))) +(-3204 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-977)) (|has| |#1| (-1032))) (|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 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) +((((-2 (|:| -3390 (-1074)) (|:| -2348 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-138)) (|has| |#1| (-136)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) |has| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (-288 (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)))) ((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) |has| (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)) (-288 (-2 (|:| -3390 |#1|) (|:| -2348 |#2|)))) ((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) (((|#2|) . T)) (((|#3|) . T)) ((((-112 |#1|)) . T)) @@ -1856,11 +1856,11 @@ ((((-501)) |has| |#1| (-567 (-501))) (((-827 (-525))) |has| |#1| (-567 (-827 (-525)))) (((-827 (-357))) |has| |#1| (-567 (-827 (-357)))) (((-357)) . #0=(|has| |#1| (-953))) (((-205)) . #0#)) (((|#1|) |has| |#1| (-341))) ((((-798)) . T)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) ((($ $) . T) (((-565 $) $) . T)) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-517))) ((($) . T) (((-1159 |#1| |#2| |#3| |#4|)) . T) (((-385 (-525))) . T)) -((($) -3316 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-517))) +((($) -3204 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) ((|#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| (-1020)))) ((((-798)) . T)) -(-3316 (|has| |#2| (-429)) (|has| |#2| (-844))) +(-3204 (|has| |#2| (-429)) (|has| |#2| (-844))) (((|#1|) . T)) (|has| |#1| (-789)) (|has| |#1| (-789)) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) ((((-501)) |has| |#1| (-567 (-501)))) (((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) (|has| |#1| (-1020)) @@ -1884,13 +1884,13 @@ (|has| |#1| (-136)) (|has| |#1| (-138)) ((((-525)) . T)) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-517))) (((#0=(-1158 |#2| |#3| |#4|)) . T) (((-385 (-525))) |has| #0# (-37 (-385 (-525)))) (($) . T)) ((((-525)) . T)) (|has| |#1| (-341)) -(-3316 (-12 (|has| (-1165 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) -(-3316 (-12 (|has| (-1165 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) +(-3204 (-12 (|has| (-1165 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) +(-3204 (-12 (|has| (-1165 |#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))) -(-3316 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) +(-3204 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) ((((-525)) . T)) (((|#1| $) |has| |#1| (-265 |#1| |#1|))) ((((-385 (-525))) . T) (($) . T) (((-385 |#1|)) . T) ((|#1|) . T)) ((((-798)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -3316 (|has| |#1| (-269)) (|has| |#1| (-341))) ((#0=(-385 (-525)) #0#) |has| |#1| (-341))) -((((-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))) . T)) +(((|#1| |#1|) . T) (($ $) -3204 (|has| |#1| (-269)) (|has| |#1| (-341))) ((#0=(-385 (-525)) #0#) |has| |#1| (-341))) +((((-2 (|:| -3390 (-1091)) (|:| -2348 (-51)))) . T)) ((($) . T)) ((((-525) |#1|) . T)) ((((-1091)) |has| (-385 |#2|) (-835 (-1091)))) -(((|#1|) . T) (($) -3316 (|has| |#1| (-269)) (|has| |#1| (-341))) (((-385 (-525))) |has| |#1| (-341))) +(((|#1|) . T) (($) -3204 (|has| |#1| (-269)) (|has| |#1| (-341))) (((-385 (-525))) |has| |#1| (-341))) ((((-501)) |has| |#2| (-567 (-501)))) ((((-632 |#2|)) . T) (((-798)) . T)) (((|#1|) . T)) @@ -1926,8 +1926,8 @@ (((|#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1020)))) ((((-805 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) -(-3316 (|has| |#4| (-735)) (|has| |#4| (-787))) -(-3316 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-3204 (|has| |#4| (-735)) (|has| |#4| (-787))) +(-3204 (|has| |#3| (-735)) (|has| |#3| (-787))) ((((-798)) . T)) ((((-798)) . T)) (((|#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1020)))) @@ -1943,17 +1943,17 @@ ((((-385 (-525))) . T) (($) . T)) ((((-385 (-525))) . T) (($) . T)) ((((-385 (-525))) . T) (($) . T)) -(-3316 (|has| |#1| (-429)) (|has| |#1| (-1131))) +(-3204 (|has| |#1| (-429)) (|has| |#1| (-1131))) ((($) . T)) ((((-385 (-525))) |has| #0=(-385 |#2|) (-968 (-385 (-525)))) (((-525)) |has| #0# (-968 (-525))) ((#0#) . T)) (((|#2|) . T) (((-525)) |has| |#2| (-588 (-525)))) (((|#1| (-713)) . T)) (|has| |#1| (-789)) (((|#1|) . T) (((-525)) |has| |#1| (-588 (-525)))) -((($) -3316 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -3316 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) -3204 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -3204 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) ((((-525)) . T)) (|has| |#1| (-37 (-385 (-525)))) -((((-2 (|:| -3511 (-1074)) (|:| -3631 (-51)))) |has| (-2 (|:| -3511 (-1074)) (|:| -3631 (-51))) (-288 (-2 (|:| -3511 (-1074)) (|:| -3631 (-51)))))) +((((-2 (|:| -3390 (-1074)) (|:| -2348 (-51)))) |has| (-2 (|:| -3390 (-1074)) (|:| -2348 (-51))) (-288 (-2 (|:| -3390 (-1074)) (|:| -2348 (-51)))))) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (|has| |#1| (-787)) (|has| |#1| (-37 (-385 (-525)))) @@ -1978,24 +1978,24 @@ (((|#1| |#2|) . T)) ((((-135)) . T)) ((((-722 |#1| (-800 |#2|))) . T)) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (|has| |#1| (-1113)) (((|#1|) . T)) -(-3316 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-669)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-977)) (|has| |#3| (-1020))) +(-3204 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-669)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-977)) (|has| |#3| (-1020))) ((((-1091) |#1|) |has| |#1| (-486 (-1091) |#1|))) (((|#2|) . T)) -((($ $) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) -((($) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($ $) -3204 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($) -3204 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-845 |#1|)) . T)) ((($) . T)) ((((-385 (-887 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) ((((-501)) |has| |#4| (-567 (-501)))) ((((-798)) . T) (((-592 |#4|)) . T)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-787)) -(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020))) (((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) |has| (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|)) (-288 (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))))) +(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020))) (((-2 (|:| -3390 (-1074)) (|:| -2348 |#1|))) |has| (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|)) (-288 (-2 (|:| -3390 (-1074)) (|:| -2348 |#1|))))) (|has| |#1| (-1020)) (|has| |#1| (-341)) (|has| |#1| (-789)) @@ -2003,16 +2003,16 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-385 (-525))) . T)) -((($) -3316 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) +((($) -3204 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3204 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) (|has| |#1| (-136)) (|has| |#1| (-138)) -(-3316 (-12 (|has| (-1089 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) -(-3316 (-12 (|has| (-1089 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) +(-3204 (-12 (|has| (-1089 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) +(-3204 (-12 (|has| (-1089 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-138)) (|has| |#1| (-136)) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) ((((-1165 |#1| |#2| |#3|)) |has| |#1| (-341))) (|has| |#1| (-787)) (((|#1| |#2|) . T)) @@ -2035,9 +2035,9 @@ ((((-798)) . T)) ((((-798)) . T)) ((((-501)) |has| |#1| (-567 (-501)))) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) ((((-1091) |#1|) |has| |#1| (-486 (-1091) |#1|)) ((|#1| |#1|) |has| |#1| (-288 |#1|))) -(((|#1|) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)))) +(((|#1|) -3204 (|has| |#1| (-160)) (|has| |#1| (-341)))) ((((-294 |#1|)) . T)) (((|#2|) |has| |#2| (-341))) (((|#2|) . T)) @@ -2053,23 +2053,23 @@ (((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (|has| |#1| (-37 (-385 (-525)))) -(((|#3|) |has| |#3| (-977)) (((-525)) -12 (|has| |#3| (-588 (-525))) (|has| |#3| (-977)))) (((|#4|) |has| |#4| (-977)) (((-525)) -12 (|has| |#4| (-588 (-525))) (|has| |#4| (-977)))) +(((|#3|) |has| |#3| (-977)) (((-525)) -12 (|has| |#3| (-588 (-525))) (|has| |#3| (-977)))) (|has| |#1| (-136)) (|has| |#1| (-138)) ((($ $) . T)) -(-3316 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020))) +(-3204 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020))) (|has| |#1| (-517)) (((|#2|) . T)) ((((-525)) . T)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) -(((|#1|) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) (((|#1|) . T)) -(-3316 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) +(-3204 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) ((((-538 |#1|)) . T)) ((($) . T)) (((|#1| (-57 |#1|) (-57 |#1|)) . T)) (((|#1|) . T)) +(((|#1|) . T)) ((($) . T)) (((|#1|) . T)) ((((-798)) . T)) @@ -2090,12 +2090,12 @@ (((|#1| |#2|) . T)) ((((-1091) |#1|) . T)) (((|#4|) . T)) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-327))) ((((-1091) (-51)) . T)) ((((-1158 |#2| |#3| |#4|) (-297 |#2| |#3| |#4|)) . T)) ((((-385 (-525))) |has| |#1| (-968 (-385 (-525)))) (((-525)) |has| |#1| (-968 (-525))) ((|#1|) . T)) ((((-798)) . T)) -(-3316 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) +(-3204 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (((#0=(-1159 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-160)) ((#0=(-385 (-525)) #0#) |has| |#1| (-517)) (($ $) |has| |#1| (-517))) (((|#1|) . T) (($) . T) (((-385 (-525))) . T)) @@ -2114,14 +2114,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) (((|#2| |#3|) . T)) -(-3316 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-3204 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) (((|#1| (-497 |#2|)) . T)) (((|#1| (-713)) . T)) (((|#1| (-497 (-1010 (-1091)))) . T)) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) (|has| |#2| (-844)) -(-3316 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3204 (|has| |#2| (-735)) (|has| |#2| (-787))) ((((-798)) . T)) ((($ $) . T) ((#0=(-1158 |#2| |#3| |#4|) #0#) . T) ((#1=(-385 (-525)) #1#) |has| #0# (-37 (-385 (-525))))) ((((-845 |#1|)) . T)) @@ -2130,13 +2130,13 @@ ((($) . T)) ((($) . T)) (|has| |#1| (-341)) -(-3316 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327)) (|has| |#1| (-517))) +(-3204 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327)) (|has| |#1| (-517))) (|has| |#1| (-341)) ((($) . T) ((#0=(-1158 |#2| |#3| |#4|)) . T) (((-385 (-525))) |has| #0# (-37 (-385 (-525))))) (((|#1| |#2|) . T)) ((((-1089 |#1| |#2| |#3|)) |has| |#1| (-341))) -(-3316 (-12 (|has| |#1| (-286)) (|has| |#1| (-844))) (|has| |#1| (-341)) (|has| |#1| (-327))) -(-3316 (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) +(-3204 (-12 (|has| |#1| (-286)) (|has| |#1| (-844))) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3204 (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) ((((-525)) |has| |#1| (-588 (-525))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-798)) . T)) @@ -2168,27 +2168,27 @@ (((|#1|) |has| |#1| (-160))) ((((-798)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1020)))) -(((|#2|) -3316 (|has| |#2| (-6 (-4257 "*"))) (|has| |#2| (-160)))) -(-3316 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) -(-3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(((|#2|) -3204 (|has| |#2| (-6 (-4257 "*"))) (|has| |#2| (-160)))) +(-3204 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-3204 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#1| (-844)) (((|#2|) |has| |#2| (-160))) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) ((((-1165 |#1| |#2| |#3|)) |has| |#1| (-341))) ((((-798)) . T)) ((((-798)) . T)) ((((-501)) . T) (((-525)) . T) (((-827 (-525))) . T) (((-357)) . T) (((-205)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) -((((-2 (|:| -3511 (-1074)) (|:| -3631 (-51)))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) +((((-2 (|:| -3390 (-1074)) (|:| -2348 (-51)))) . T)) (((|#1|) . T)) ((((-798)) . T)) (((|#1| |#2|) . T)) (((|#1| (-385 (-525))) . T)) (((|#1|) . T)) -(-3316 (|has| |#1| (-269)) (|has| |#1| (-341))) +(-3204 (|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)) ((((-798)) . T)) ((((-798)) . T)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-798)) . T)) ((((-798)) . T)) @@ -2214,7 +2214,7 @@ (((|#1|) . T)) ((((-592 (-135))) . T) (((-1074)) . T)) ((((-798)) . T)) -((((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) +((((-2 (|:| -3390 (-1074)) (|:| -2348 |#1|))) . T)) ((((-1091) |#1|) |has| |#1| (-486 (-1091) |#1|)) ((|#1| |#1|) |has| |#1| (-288 |#1|))) (|has| |#1| (-789)) ((((-798)) . T)) @@ -2226,16 +2226,16 @@ ((((-798)) . T) (((-592 |#4|)) . T)) (((|#2|) . T)) ((((-845 |#1|)) . T) (((-385 (-525))) . T) (($) . T)) -(-3316 (|has| |#4| (-160)) (|has| |#4| (-669)) (|has| |#4| (-787)) (|has| |#4| (-977))) -(-3316 (|has| |#3| (-160)) (|has| |#3| (-669)) (|has| |#3| (-787)) (|has| |#3| (-977))) +(-3204 (|has| |#4| (-160)) (|has| |#4| (-669)) (|has| |#4| (-787)) (|has| |#4| (-977))) +(-3204 (|has| |#3| (-160)) (|has| |#3| (-669)) (|has| |#3| (-787)) (|has| |#3| (-977))) ((((-1091) (-51)) . T)) -(-3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3204 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3316 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) -(-3316 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3204 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3204 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-787)) (|has| |#2| (-977))) (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#2|) . T)) @@ -2250,12 +2250,12 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (|has| |#1| (-762)) (((#0=(-845 |#1|) #0#) . T) (($ $) . T) ((#1=(-385 (-525)) #1#) . T)) ((((-385 |#2|)) . T)) (|has| |#1| (-787)) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) . T) ((#1=(-525) #1#) . T) (($ $) . T)) ((((-845 |#1|)) . T) (($) . T) (((-385 (-525))) . T)) (((|#2|) |has| |#2| (-977)) (((-525)) -12 (|has| |#2| (-588 (-525))) (|has| |#2| (-977)))) @@ -2265,25 +2265,25 @@ (|has| |#1| (-136)) (((|#2|) . T)) ((((-798)) . T)) -(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) -(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) -(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) -((((-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))) . T)) -(((#0=(-51)) . T) (((-2 (|:| -3511 (-1091)) (|:| -3631 #0#))) . T)) +(-3204 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3204 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3204 (|has| |#1| (-136)) (|has| |#1| (-346))) +((((-2 (|:| -3390 (-1091)) (|:| -2348 (-51)))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -3390 (-1091)) (|:| -2348 #0#))) . T)) (|has| |#1| (-327)) ((((-525)) . T)) ((((-798)) . T)) (((#0=(-1159 |#1| |#2| |#3| |#4|) $) |has| #0# (-265 #0# #0#))) (|has| |#1| (-341)) (((#0=(-1005) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-327))) (((#0=(-385 (-525)) #0#) . T) ((#1=(-641) #1#) . T) (($ $) . T)) ((((-294 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) |has| |#1| (-341))) (|has| |#1| (-1020)) (((|#1|) . T)) -(((|#1|) -3316 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) -(((|#1|) -3316 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) +(((|#1|) -3204 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) +(((|#1|) -3204 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) (((|#2|) . T)) ((((-385 (-525))) . T) (((-641)) . T) (($) . T)) (((|#3| |#3|) . T)) @@ -2302,7 +2302,7 @@ (((|#2|) . T)) (((|#1|) . T)) ((((-525)) . T)) -(-3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3204 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (((|#2|) . T) (((-525)) |has| |#2| (-588 (-525)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2339,7 +2339,7 @@ (|has| |#2| (-953)) ((($) . T)) (|has| |#1| (-844)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2347,24 +2347,24 @@ ((($) . T)) (|has| |#1| (-341)) ((((-845 |#1|)) . T)) -((($) -3316 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3204 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) -(-3316 (|has| |#1| (-346)) (|has| |#1| (-789))) +(-3204 (|has| |#1| (-346)) (|has| |#1| (-789))) (((|#1|) . T)) ((((-798)) . T)) ((((-1091)) -12 (|has| |#1| (-15 * (|#1| (-385 (-525)) |#1|))) (|has| |#1| (-835 (-1091))))) ((((-385 |#2|) |#3|) . T)) ((($) . T) (((-385 (-525))) . T)) ((((-713) |#1|) . T)) -(((|#2| (-220 (-3674 |#1|) (-713))) . T)) +(((|#2| (-220 (-3552 |#1|) (-713))) . T)) (((|#1| (-497 |#3|)) . T)) ((((-385 (-525))) . T)) -(-3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3204 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((((-798)) . T)) -(((#0=(-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) #0#) |has| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (-288 (-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))))) +(((#0=(-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) #0#) |has| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (-288 (-2 (|:| -3390 (-1091)) (|:| -2348 (-51)))))) (|has| |#1| (-844)) (|has| |#2| (-341)) -(-3316 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3204 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((((-157 (-357))) . T) (((-205)) . T) (((-357)) . T)) ((((-798)) . T)) (((|#1|) . T)) @@ -2381,11 +2381,11 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3316 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3204 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-37 (-385 (-525)))) (-12 (|has| |#1| (-510)) (|has| |#1| (-770))) ((((-798)) . T)) -((((-1091)) -3316 (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-835 (-1091)))) (-12 (|has| |#1| (-341)) (|has| |#2| (-835 (-1091)))))) +((((-1091)) -3204 (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-835 (-1091)))) (-12 (|has| |#1| (-341)) (|has| |#2| (-835 (-1091)))))) (|has| |#1| (-341)) ((((-1091)) -12 (|has| |#1| (-15 * (|#1| (-385 (-525)) |#1|))) (|has| |#1| (-835 (-1091))))) (|has| |#1| (-341)) @@ -2395,7 +2395,7 @@ (((|#1|) . T)) (((|#2|) |has| |#1| (-341))) (((|#2|) |has| |#1| (-341))) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#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| (-821 (-357)))) (((-525)) -12 (|has| |#1| (-341)) (|has| |#2| (-821 (-525))))) (|has| |#1| (-341)) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-341)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-341)) (|has| |#1| (-517)) (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1020)))) (((|#3|) . T)) (((|#1|) . T)) -(-3316 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3204 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) (((|#2|) . T)) (((|#2|) . T)) -(-3316 (|has| |#2| (-160)) (|has| |#2| (-669)) (|has| |#2| (-787)) (|has| |#2| (-977))) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) -((((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +(-3204 (|has| |#2| (-160)) (|has| |#2| (-669)) (|has| |#2| (-787)) (|has| |#2| (-977))) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) +((((-2 (|:| -3390 (-1074)) (|:| -2348 |#1|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) (|has| |#1| (-37 (-385 (-525)))) (((|#1| |#2|) . T)) (|has| |#1| (-37 (-385 (-525)))) -(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3204 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) ((((-1074) |#1|) . T)) -(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3204 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) -(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3204 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) ((((-538 |#1|)) . T)) ((($) . T)) @@ -2450,7 +2450,7 @@ (|has| |#1| (-517)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3316 (|has| |#1| (-136)) (|has| |#1| (-327))) +(-3204 (|has| |#1| (-136)) (|has| |#1| (-327))) (|has| |#1| (-138)) ((((-798)) . T)) ((($) . T)) @@ -2475,7 +2475,7 @@ (|has| |#1| (-733)) (|has| |#1| (-733)) ((((-501)) |has| |#1| (-567 (-501)))) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) ((((-110)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2496,7 +2496,7 @@ ((((-525)) . T)) ((((-798)) . T)) ((((-525)) . T)) -(-3316 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3204 (|has| |#2| (-735)) (|has| |#2| (-787))) ((((-157 (-357))) . T) (((-205)) . T) (((-357)) . T)) ((((-798)) . T)) ((((-798)) . T)) @@ -2508,9 +2508,9 @@ (((|#1|) . T) (($) . T) (((-385 (-525))) . T)) (|has| |#1| (-341)) (|has| |#1| (-341)) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) -(-3316 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +(-3204 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020))) (|has| |#1| (-1067)) ((((-525) |#1|) . T)) (((|#1|) . T)) @@ -2528,8 +2528,8 @@ (((|#1|) . T)) (|has| |#1| (-517)) ((((-385 |#2|)) . T) (((-385 (-525))) . T) (($) . T)) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-517))) ((((-357)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2538,7 +2538,7 @@ (|has| |#1| (-517)) (|has| |#1| (-1020)) ((((-722 |#1| (-800 |#2|))) |has| (-722 |#1| (-800 |#2|)) (-288 (-722 |#1| (-800 |#2|))))) -(-3316 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-3204 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) (((|#1|) . T)) (((|#2| |#3|) . T)) (|has| |#2| (-844)) @@ -2548,12 +2548,12 @@ (|has| |#1| (-213)) (((|#1| (-497 (-1010 (-1091)))) . T)) (|has| |#2| (-341)) -((((-2 (|:| -3511 (-1074)) (|:| -3631 (-51)))) . T)) +((((-2 (|:| -3390 (-1074)) (|:| -2348 (-51)))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) ((((-798)) . T)) ((((-798)) . T)) -(-3316 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-3204 (|has| |#3| (-735)) (|has| |#3| (-787))) ((((-798)) . T)) ((((-798)) . T)) (((|#1|) . T)) @@ -2562,8 +2562,8 @@ ((((-525)) . T)) (((|#3|) . T)) ((((-798)) . T)) -(-3316 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) -(-3316 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) +(-3204 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3204 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) (((#0=(-538 |#1|) #0#) . T) (($ $) . T) ((#1=(-385 (-525)) #1#) . T)) ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) (((|#1|) |has| |#1| (-160))) @@ -2576,7 +2576,7 @@ (((|#1|) . T)) ((((-798)) |has| |#1| (-566 (-798)))) ((((-273 |#3|)) . T)) -(((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525)))) ((|#2| |#2|) . T) (($ $) -3316 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) +(((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525)))) ((|#2| |#2|) . T) (($ $) -3204 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . 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) (($) . T)) -((($ $) -3316 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) -((($ $) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . 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T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (|has| |#2| (-844)) (|has| |#1| (-844)) -((($) -3316 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3204 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1|) . T)) -((((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) +((((-2 (|:| -3390 (-1074)) (|:| -2348 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) @@ -2611,10 +2611,10 @@ (((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) (((#0=(-385 (-525)) #0#) . T)) ((((-385 (-525))) . T)) -(-3316 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3204 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) (((|#1|) . T)) (((|#1|) . T)) -(-3316 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3204 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((((-501)) . T)) ((((-798)) . T)) ((((-1091)) |has| |#2| (-835 (-1091))) (((-1005)) . T)) @@ -2628,12 +2628,12 @@ ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) ((((-1091)) |has| |#1| (-835 (-1091)))) ((((-845 |#1|)) . T) (((-385 (-525))) . T) (($) . T)) -((($) . T) (((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) -(((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525)))) ((|#1| |#1|) . T) (($ $) -3316 (|has| |#1| (-160)) (|has| |#1| (-517)))) +((($) . T) (((-385 (-525))) -3204 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) +(((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525)))) ((|#1| |#1|) . T) (($ $) -3204 (|has| |#1| (-160)) (|has| |#1| (-517)))) ((($) . T) (((-385 (-525))) . T)) (((|#1|) . T) (((-385 (-525))) . T) (((-525)) . T) (($) . T)) (((|#2|) |has| |#2| (-977)) (((-525)) -12 (|has| |#2| (-588 (-525))) (|has| |#2| (-977)))) -((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T) (($) -3316 (|has| |#1| (-160)) (|has| |#1| (-517)))) +((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T) (($) -3204 (|has| |#1| (-160)) (|has| |#1| (-517)))) (|has| |#1| (-517)) (((|#1|) |has| |#1| (-341))) ((((-525)) . T)) @@ -2652,8 +2652,8 @@ ((((-798)) . T)) (|has| |#2| (-762)) (|has| |#2| (-762)) -((((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#2|) |has| |#1| (-341)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) . T)) +((((-385 (-525))) -3204 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#2|) |has| |#1| (-341)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-385 (-525))) -3204 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1|) . T) (((-525)) |has| |#1| (-968 (-525))) (((-385 (-525))) |has| |#1| (-968 (-385 (-525))))) ((((-525)) |has| |#1| (-821 (-525))) (((-357)) |has| |#1| (-821 (-357)))) @@ -2679,12 +2679,12 @@ (((|#2| (-713)) . T)) ((((-1091)) . T)) ((((-805 |#1|)) . 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T)) +((((-2 (|:| -3390 (-1091)) (|:| -2348 (-51)))) . T)) ((((-501)) |has| |#2| (-567 (-501))) (((-827 (-357))) |has| |#2| (-567 (-827 (-357)))) (((-827 (-525))) |has| |#2| (-567 (-827 (-525))))) ((((-798)) . T)) ((((-798)) . T)) @@ -2743,11 +2743,11 @@ ((((-385 |#2|) |#3|) . T)) (((|#1|) . T)) (|has| |#1| (-1020)) -(((|#2| (-458 (-3674 |#1|) (-713))) . T)) +(((|#2| (-458 (-3552 |#1|) (-713))) . T)) ((((-525) |#1|) . T)) (((|#2| |#2|) . T)) (((|#1| (-497 (-1091))) . T)) -(-3316 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3204 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((((-525)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -2757,9 +2757,9 @@ ((($) . T) (((-385 (-525))) . T)) ((($) . T)) ((($) . T)) -(-3316 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-3204 (|has| |#1| (-789)) (|has| |#1| (-1020))) (((|#1|) . 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T)) @@ -2858,25 +2858,25 @@ (((|#1|) |has| |#2| (-395 |#1|))) (((|#1|) |has| |#2| (-395 |#1|))) ((((-845 |#1|)) . T) (((-385 (-525))) . T) (($) . T)) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) ((((-501)) |has| |#1| (-567 (-501)))) ((((-798)) . T)) -((((-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))) |has| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (-288 (-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))))) -(-3316 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +((((-2 (|:| -3390 (-1091)) (|:| -2348 (-51)))) |has| (-2 (|:| -3390 (-1091)) (|:| -2348 (-51))) (-288 (-2 (|:| -3390 (-1091)) (|:| -2348 (-51)))))) +(-3204 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) ((((-525) |#1|) . T)) ((((-525) |#1|) . T)) ((((-525) |#1|) . 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T)) -(-3316 (|has| |#3| (-160)) (|has| |#3| (-669)) (|has| |#3| (-787)) (|has| |#3| (-977))) +(-3204 (|has| |#3| (-160)) (|has| |#3| (-669)) (|has| |#3| (-787)) (|has| |#3| (-977))) (((|#1| |#2|) . T)) (|has| |#1| (-37 (-385 (-525)))) ((((-798)) . T)) @@ -2884,15 +2884,15 @@ (((|#1|) |has| |#1| (-160)) (($) |has| |#1| (-517)) (((-385 (-525))) |has| |#1| (-517))) (((|#2|) . T) (((-525)) |has| |#2| (-588 (-525)))) (|has| |#1| (-341)) -(-3316 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (-12 (|has| |#1| (-341)) (|has| |#2| (-213)))) +(-3204 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (-12 (|has| |#1| (-341)) (|has| |#2| (-213)))) (|has| |#1| (-15 * (|#1| (-385 (-525)) |#1|))) (|has| |#1| (-341)) (((|#1|) . T)) -(((#0=(-385 (-525)) #0#) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($ $) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1| |#1|) . T)) +(((#0=(-385 (-525)) #0#) -3204 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($ $) -3204 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1| |#1|) . T)) ((((-525) |#1|) . T)) ((((-294 |#1|)) . T)) (((#0=(-641) (-1087 #0#)) . T)) -((((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1|) . T)) +((((-385 (-525))) -3204 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3204 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . T)) (|has| |#1| (-787)) ((($ $) . T) ((#0=(-800 |#1|) $) . T) ((#0# |#2|) . T)) @@ -2909,12 +2909,12 @@ (((#0=(-1159 |#1| |#2| |#3| |#4|)) |has| #0# (-288 #0#))) ((($) . T)) (((|#1|) . 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T)) -(-3316 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) -(-3316 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-126)) (|has| |#2| (-126))) (-12 (|has| |#1| (-735)) (|has| |#2| (-735)))) +(-3204 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3204 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-126)) (|has| |#2| (-126))) (-12 (|has| |#1| (-735)) (|has| |#2| (-735)))) ((((-1165 |#1| |#2| |#3|)) |has| |#1| (-341))) ((($) . T) (((-805 |#1|)) . T) (((-385 (-525))) . T)) ((((-1165 |#1| |#2| |#3|)) |has| |#1| (-341))) @@ -2951,15 +2951,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-385 |#2|)) . 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T)) (((|#2| |#2|) . T) ((#0=(-385 (-525)) #0#) . T) (($ $) . T)) ((((-525)) . T)) @@ -2988,32 +2988,32 @@ ((((-1165 |#1| |#2| |#3|)) |has| |#1| (-341))) ((((-1091)) . T) (((-798)) . T)) (|has| |#1| (-341)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3316 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3204 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) . T)) -((($) -3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3204 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-1024)) . T)) ((((-798)) . 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T)) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#1|) |has| |#1| (-160))) (((|#1|) |has| |#1| (-160))) ((((-385 (-525))) . T) (($) . T)) (((|#1| (-525)) . T)) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-341)) (|has| |#1| (-341)) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-327))) -(-3316 (|has| |#1| (-160)) (|has| |#1| (-517))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3204 (|has| |#1| (-160)) (|has| |#1| (-517))) (((|#1| (-525)) . T)) (((|#1| (-385 (-525))) . T)) (((|#1| (-713)) . T)) @@ -3028,16 +3028,16 @@ ((((-827 (-357))) . T) (((-827 (-525))) . T) (((-1091)) . T) (((-501)) . T)) (((|#1|) . T)) ((((-798)) . T)) -(-3316 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) -(-3316 (-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)))) +(-3204 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3204 (-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 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-3316 (|has| |#2| (-160)) (|has| |#2| (-669)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3204 (|has| |#2| (-160)) (|has| |#2| (-669)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((((-1091)) -12 (|has| |#2| (-835 (-1091))) (|has| |#2| (-977)))) -(-3316 (-12 (|has| |#1| (-450)) (|has| |#2| (-450))) (-12 (|has| |#1| (-669)) (|has| |#2| (-669)))) +(-3204 (-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 @@ ((((-1074) (-1091) (-525) (-205) (-798)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) -(-3316 (|has| |#1| (-327)) (|has| |#1| (-346))) +(-3204 (|has| |#1| (-327)) (|has| |#1| (-346))) (((|#1| |#2|) . T)) ((($) . T) ((|#1|) . T)) ((((-798)) . T)) @@ -3069,7 +3069,7 @@ ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2|) |has| |#2| (-1020)) (((-525)) -12 (|has| |#2| (-968 (-525))) (|has| |#2| (-1020))) (((-385 (-525))) -12 (|has| |#2| (-968 (-385 (-525)))) (|has| |#2| (-1020)))) ((((-501)) |has| |#1| (-567 (-501)))) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) ((($) . T) (((-385 (-525))) . T)) (|has| |#1| (-844)) (|has| |#1| (-844)) @@ -3078,14 +3078,14 @@ ((((-798)) . T)) (((|#2| |#2|) . T)) (((|#1| |#1|) |has| |#1| (-160))) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3316 (|has| |#1| (-21)) (|has| |#1| (-787))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3204 (|has| |#1| (-21)) (|has| |#1| (-787))) (((|#2|) . T)) -(-3316 (|has| |#1| (-21)) (|has| |#1| (-787))) +(-3204 (|has| |#1| (-21)) (|has| |#1| (-787))) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) (((|#1|) . T)) -((((-798)) -3316 (-12 (|has| |#1| (-566 (-798))) (|has| |#2| (-566 (-798)))) (-12 (|has| |#1| (-1020)) (|has| |#2| (-1020))))) +((((-798)) -3204 (-12 (|has| |#1| (-566 (-798))) (|has| |#2| (-566 (-798)))) (-12 (|has| |#1| (-1020)) (|has| |#2| (-1020))))) ((((-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)) ((($) . T) (((-385 (-525))) . T)) -(-3316 (|has| |#4| (-160)) (|has| |#4| (-669)) (|has| |#4| (-787)) (|has| |#4| (-977))) -(-3316 (|has| |#3| (-160)) (|has| |#3| (-669)) (|has| |#3| (-787)) (|has| |#3| (-977))) +(-3204 (|has| |#4| (-160)) (|has| |#4| (-669)) (|has| |#4| (-787)) (|has| |#4| (-977))) +(-3204 (|has| |#3| (-160)) (|has| |#3| (-669)) (|has| |#3| (-787)) (|has| |#3| (-977))) (|has| |#4| (-735)) -(-3316 (|has| |#4| (-735)) (|has| |#4| (-787))) +(-3204 (|has| |#4| (-735)) (|has| |#4| (-787))) (|has| |#4| (-787)) (|has| |#3| (-735)) -(-3316 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-3204 (|has| |#3| (-735)) (|has| |#3| (-787))) (|has| |#3| (-787)) ((((-525)) . T)) (((|#2|) . T)) -((((-1091)) -3316 (-12 (|has| (-1089 |#1| |#2| |#3|) (-835 (-1091))) (|has| |#1| (-341))) (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-835 (-1091)))))) +((((-1091)) -3204 (-12 (|has| (-1089 |#1| |#2| |#3|) (-835 (-1091))) (|has| |#1| (-341))) (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-835 (-1091)))))) ((((-1091)) -12 (|has| |#1| (-15 * (|#1| (-385 (-525)) |#1|))) (|has| |#1| (-835 (-1091))))) ((((-1091)) -12 (|has| |#1| (-15 * (|#1| (-713) |#1|))) (|has| |#1| (-835 (-1091))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3120,13 +3120,13 @@ (((|#1|) . T)) ((((-800 |#1|)) . T)) ((((-1089 |#1| |#2| |#3|)) |has| |#1| (-341))) -((((-1089 |#1| |#2| |#3|)) |has| |#1| (-341))) ((((-1056 |#1| |#2|)) . T)) -(((|#2|) . T) (((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) -((((-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))) . T)) +((((-1089 |#1| |#2| |#3|)) |has| |#1| (-341))) +(((|#2|) . T) (((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) +((((-2 (|:| -3390 (-1091)) (|:| -2348 (-51)))) . T)) ((($) . T)) (|has| |#1| (-953)) -(((|#2|) . T) (((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) ((((-798)) . T)) ((((-501)) |has| |#2| (-567 (-501))) (((-827 (-525))) |has| |#2| (-567 (-827 (-525)))) (((-827 (-357))) |has| |#2| (-567 (-827 (-357)))) (((-357)) . #0=(|has| |#2| (-953))) (((-205)) . #0#)) ((((-1091) (-51)) . T)) @@ -3138,15 +3138,15 @@ ((((-1089 |#1| |#2| |#3|)) . T)) ((((-1089 |#1| |#2| |#3|)) . T) (((-1082 |#1| |#2| |#3|)) . T)) ((((-798)) . T)) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) ((((-525) |#1|) . T)) ((((-1089 |#1| |#2| |#3|)) |has| |#1| (-341))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-341)) -(((|#3|) . T) ((|#2|) . T) (($) -3316 (|has| |#4| (-160)) (|has| |#4| (-787)) (|has| |#4| (-977))) ((|#4|) -3316 (|has| |#4| (-160)) (|has| |#4| (-341)) (|has| |#4| (-977)))) -(((|#2|) . T) (($) -3316 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-977))) ((|#3|) -3316 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-977)))) +(((|#3|) . T) ((|#2|) . T) (($) -3204 (|has| |#4| (-160)) (|has| |#4| (-787)) (|has| |#4| (-977))) ((|#4|) -3204 (|has| |#4| (-160)) (|has| |#4| (-341)) (|has| |#4| (-977)))) +(((|#2|) . T) (($) -3204 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-977))) ((|#3|) -3204 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-977)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-341)) @@ -3158,7 +3158,7 @@ ((((-798)) . T)) ((((-798)) . T)) (((|#1|) . T)) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) ((((-125)) . T) (((-798)) . T)) ((((-525) |#1|) . T)) (((|#1|) . T)) @@ -3166,30 +3166,30 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-341)) (|has| |#2| (-265 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-844))) -(-3316 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-844))) +(-3204 (|has| |#1| (-789)) (|has| |#1| (-1020))) ((((-798)) . T)) ((((-798)) . T)) ((((-798)) . T)) (((|#1| (-497 |#2|)) . T)) -((((-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))) . T)) +((((-2 (|:| -3390 (-1091)) (|:| -2348 (-51)))) . T)) (((|#1| (-525)) . T)) (((|#1| (-385 (-525))) . T)) (((|#1| (-713)) . T)) ((((-112 |#1|)) . T) (($) . T) (((-385 (-525))) . T)) -(-3316 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) -(-3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3204 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-3204 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((($) . T)) (((|#2| (-497 (-800 |#1|))) . T)) ((((-525) |#1|) . T)) (((|#2|) . T)) (((|#2| (-713)) . T)) -((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3204 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#1|) . T)) (((|#1| |#2|) . T)) ((((-1074) |#1|) . T)) ((((-385 |#2|)) . T)) -((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3390 |#1|) (|:| -2348 |#2|))) . T)) (|has| |#1| (-517)) (|has| |#1| (-517)) ((($) . T) ((|#2|) . T)) @@ -3197,12 +3197,12 @@ (((|#1| |#2|) . T)) (((|#2| $) |has| |#2| (-265 |#2| |#2|))) (((|#1| (-592 |#1|)) |has| |#1| (-787))) -(-3316 (|has| |#1| (-213)) (|has| |#1| (-327))) -(-3316 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3204 (|has| |#1| (-213)) (|has| |#1| (-327))) +(-3204 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-1020)) (((|#1|) . T)) ((((-385 (-525))) . T) (($) . T)) -((((-931 |#1|)) . T) ((|#1|) . T) (((-525)) -3316 (|has| (-931 |#1|) (-968 (-525))) (|has| |#1| (-968 (-525)))) (((-385 (-525))) -3316 (|has| (-931 |#1|) (-968 (-385 (-525)))) (|has| |#1| (-968 (-385 (-525)))))) +((((-931 |#1|)) . T) ((|#1|) . T) (((-525)) -3204 (|has| (-931 |#1|) (-968 (-525))) (|has| |#1| (-968 (-525)))) (((-385 (-525))) -3204 (|has| (-931 |#1|) (-968 (-385 (-525)))) (|has| |#1| (-968 (-385 (-525)))))) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) @@ -3213,10 +3213,10 @@ (((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . 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138182) ((-230 . -735) 138161) ((-229 . -733) 138140) ((-229 . -736) 138091) ((-229 . -735) 138070) ((-49 . -984) T) ((-230 . -669) 137981) ((-229 . -669) 137892) ((-1122 . -1020) T) ((-616 . -23) T) ((-538 . -984) T) ((-489 . -984) T) ((-357 . -983) 137857) ((-300 . -107) 137832) ((-71 . -361) T) ((-71 . -373) T) ((-955 . -37) 137769) ((-636 . -378) 137751) ((-94 . -97) T) ((-654 . -1020) T) ((-935 . -136) 137723) ((-935 . -138) 137695) ((-357 . -107) 137651) ((-297 . -1131) 137630) ((-451 . -934) 137596) ((-332 . -37) 137561) ((-39 . -348) 137533) ((-808 . -566) 137405) ((-123 . -121) 137389) ((-117 . -121) 137373) ((-776 . -983) 137343) ((-775 . -21) 137295) ((-769 . -983) 137279) ((-775 . -25) 137231) ((-297 . -517) 137182) ((-525 . -770) T) ((-220 . -1127) T) ((-776 . -107) 137147) ((-769 . -107) 137126) ((-1157 . -566) 137108) ((-1136 . -566) 137090) ((-1136 . -567) 136763) ((-1087 . -844) 136742) ((-1043 . -844) 136721) ((-47 . -37) 136686) ((-1193 . -1032) T) ((-556 . -566) 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((-1159 . -97) T) ((-1158 . -46) 134386) ((-1137 . -46) 134363) ((-1122 . -160) 134314) ((-1003 . -1131) 134265) ((-254 . -1020) T) ((-83 . -418) T) ((-83 . -373) T) ((-1088 . -286) 134244) ((-1082 . -286) 134223) ((-49 . -1020) T) ((-1003 . -517) 134174) ((-654 . -160) T) ((-550 . -46) 134151) ((-205 . -594) 134116) ((-538 . -1020) T) ((-489 . -1020) T) ((-337 . -1131) T) ((-331 . -1131) T) ((-323 . -1131) T) ((-462 . -762) T) ((-462 . -855) T) ((-297 . -1032) T) ((-103 . -1131) T) ((-317 . -789) T) ((-198 . -855) T) ((-198 . -762) T) ((-657 . -983) 134086) ((-337 . -517) T) ((-331 . -517) T) ((-323 . -517) T) ((-103 . -517) T) ((-604 . -660) 134056) ((-1082 . -953) NIL) ((-297 . -23) T) ((-65 . -1127) T) ((-932 . -566) 133988) ((-636 . -211) 133970) ((-657 . -107) 133935) ((-592 . -33) T) ((-225 . -464) 133919) ((-1022 . -1018) 133903) ((-159 . -1020) T) ((-887 . -844) 133882) ((-457 . -844) 133861) ((-1195 . -21) T) ((-1195 . -25) T) ((-1193 . -126) T) ((-1191 . -126) T) ((-1009 . -660) 133710) ((-988 . -594) 133697) ((-887 . -594) 133622) ((-724 . -660) 133451) ((-501 . -566) 133433) ((-501 . -567) 133414) ((-722 . -660) 133263) ((-1184 . -97) T) ((-1000 . -97) T) ((-359 . -25) T) ((-359 . -21) T) ((-457 . -594) 133188) ((-438 . -660) 133159) ((-431 . -660) 133008) ((-920 . -97) T) ((-680 . -97) T) ((-1199 . -1067) T) ((-497 . -25) T) ((-1137 . -1127) 132987) ((-1169 . -566) 132953) ((-1137 . -821) NIL) ((-1137 . -819) 132905) ((-132 . -97) T) ((-43 . -126) T) ((-1101 . -567) NIL) ((-1101 . -566) 132887) ((-1058 . -1041) 132832) ((-321 . -984) T) ((-610 . -566) 132814) ((-268 . -1032) T) ((-333 . -566) 132796) ((-330 . -566) 132778) ((-322 . -566) 132760) ((-243 . -567) 132508) ((-243 . -566) 132490) ((-227 . -566) 132472) ((-227 . -567) 132333) ((-974 . -1121) 132262) ((-836 . -288) 132200) ((-1158 . -968) 132135) ((-1137 . -968) 132101) ((-1122 . -486) 132068) ((-1057 . -566) 132050) ((-761 . -796) T) ((-761 . -669) T) ((-556 . -267) 132027) ((-538 . -660) 131992) ((-455 . -567) NIL) ((-455 . -566) 131974) ((-489 . -660) 131919) ((-294 . -97) T) ((-291 . -97) T) ((-268 . -23) T) ((-143 . -126) T) ((-364 . -669) T) ((-807 . -983) 131871) ((-845 . -566) 131853) ((-845 . -567) 131835) ((-807 . -107) 131773) ((-130 . -97) T) ((-110 . -97) T) ((-655 . -1149) 131757) ((-657 . -977) T) ((-636 . -327) NIL) ((-490 . -566) 131689) ((-357 . -737) T) ((-203 . -1020) T) ((-357 . -734) T) ((-205 . -736) T) ((-205 . -733) T) ((-57 . -567) 131650) ((-57 . -566) 131562) ((-205 . -669) T) ((-488 . -567) 131523) ((-488 . -566) 131435) ((-470 . -566) 131367) ((-469 . -567) 131328) ((-469 . -566) 131240) ((-1003 . -341) 131191) ((-39 . -389) 131168) ((-75 . -1127) T) ((-806 . -844) NIL) ((-337 . -307) 131152) ((-337 . -341) T) ((-331 . -307) 131136) ((-331 . -341) T) ((-323 . -307) 131120) ((-323 . -341) T) ((-294 . -263) 131099) ((-103 . -341) T) ((-68 . -1127) T) ((-1137 . -316) 131051) ((-806 . -594) 130996) ((-1137 . -355) 130948) ((-898 . -126) 130803) ((-757 . -126) 130674) ((-892 . -597) 130658) ((-1009 . -160) 130569) ((-892 . -351) 130553) ((-988 . -736) T) ((-988 . -733) T) ((-724 . -160) 130444) ((-722 . -160) 130355) ((-758 . -46) 130317) ((-988 . -669) T) ((-305 . -464) 130301) ((-887 . -669) T) ((-431 . -160) 130212) ((-225 . -265) 130189) ((-457 . -669) T) ((-1184 . -288) 130127) ((-1165 . -835) 130040) ((-1158 . -835) 129946) ((-1157 . -983) 129781) ((-1137 . -835) 129614) ((-1136 . -983) 129422) ((-1122 . -269) 129401) ((-1062 . -142) 129385) ((-998 . -97) T) ((-862 . -889) T) ((-73 . -1127) T) ((-680 . -288) 129323) ((-157 . -844) 129276) ((-610 . -360) 129248) ((-30 . -889) T) ((-1 . -566) 129230) ((-1038 . -97) T) ((-1003 . -23) T) ((-49 . -570) 129214) ((-1003 . -1032) T) ((-935 . -387) 129186) ((-550 . -835) 129099) ((-416 . -97) T) ((-132 . -288) NIL) ((-807 . -977) T) ((-775 . -789) 129078) ((-79 . -1127) T) ((-654 . -269) T) ((-39 . -984) T) ((-538 . -160) T) ((-489 . -160) T) ((-483 . -566) 129060) ((-157 . -594) 128970) ((-479 . -566) 128952) ((-329 . -138) 128934) ((-329 . -136) T) ((-337 . -1032) T) ((-331 . -1032) T) ((-323 . -1032) T) ((-936 . -286) T) ((-849 . -286) T) ((-807 . -223) T) ((-103 . -1032) T) ((-807 . -213) 128913) ((-1157 . -107) 128734) ((-1136 . -107) 128523) ((-225 . -1161) 128507) ((-525 . -787) T) ((-337 . -23) T) ((-332 . -327) T) ((-294 . -288) 128494) ((-291 . -288) 128435) ((-331 . -23) T) ((-297 . -126) T) ((-323 . -23) T) ((-936 . -953) T) ((-103 . -23) T) ((-225 . -558) 128412) ((-1159 . -37) 128304) ((-1146 . -844) 128283) ((-108 . -1020) T) ((-966 . -97) T) ((-1146 . -594) 128208) ((-806 . -736) NIL) ((-794 . -594) 128182) ((-806 . -733) NIL) ((-758 . -821) NIL) ((-806 . -669) T) ((-1009 . -486) 128055) ((-724 . -486) 128002) ((-722 . -486) 127954) ((-532 . -594) 127941) ((-758 . -968) 127771) ((-431 . -486) 127714) ((-366 . -367) T) ((-58 . -1127) T) ((-571 . -789) 127693) ((-473 . -607) T) ((-1062 . -909) 127662) ((-935 . -429) T) ((-641 . -787) T) ((-482 . -734) T) ((-451 . -983) 127497) ((-321 . -1020) T) ((-291 . -1067) NIL) ((-268 . -126) T) ((-372 . -1020) T) ((-636 . -348) 127464) ((-805 . -984) T) ((-203 . -570) 127441) ((-305 . -265) 127418) ((-451 . -107) 127239) ((-1157 . -977) T) ((-1136 . -977) T) ((-758 . -355) 127223) ((-157 . -669) T) ((-600 . -97) T) ((-1157 . -223) 127202) ((-1157 . -213) 127154) ((-1136 . -213) 127059) ((-1136 . -223) 127038) ((-935 . -380) NIL) ((-616 . -588) 126986) ((-294 . -37) 126896) ((-291 . -37) 126825) ((-67 . -566) 126807) ((-297 . -466) 126773) ((-1101 . -267) 126752) ((-1033 . -1032) 126663) ((-81 . -1127) T) ((-59 . -566) 126645) ((-455 . -267) 126624) ((-1186 . -968) 126601) ((-1080 . -1020) T) ((-1033 . -23) 126472) ((-758 . -835) 126408) ((-1146 . -669) T) ((-1022 . -1127) T) ((-1009 . -269) 126339) ((-828 . -97) T) ((-724 . -269) 126250) ((-305 . -19) 126234) ((-57 . -267) 126211) ((-722 . -269) 126142) ((-794 . -669) T) ((-113 . -787) NIL) ((-488 . -267) 126119) ((-305 . -558) 126096) ((-469 . -267) 126073) ((-431 . -269) 126004) ((-966 . -288) 125855) ((-532 . -669) T) ((-608 . -566) 125837) ((-225 . -567) 125798) ((-225 . -566) 125710) ((-1063 . -33) T) ((-878 . -1127) T) ((-321 . -660) 125655) ((-616 . -25) T) ((-616 . -21) T) ((-451 . -977) T) ((-584 . -395) 125620) ((-560 . -395) 125585) ((-1038 . -1067) T) ((-538 . -269) T) ((-489 . -269) T) ((-1158 . -286) 125564) ((-451 . -213) 125516) ((-451 . -223) 125495) ((-1137 . -286) 125474) ((-1003 . -126) T) ((-807 . -737) 125453) ((-135 . -97) T) ((-39 . -1020) T) ((-807 . -734) 125432) ((-592 . -942) 125416) ((-537 . -984) T) ((-525 . -984) T) ((-468 . -984) T) ((-385 . -429) T) ((-337 . -126) T) ((-294 . -378) 125400) ((-291 . -378) 125361) ((-331 . -126) T) ((-323 . -126) T) ((-1137 . -953) NIL) ((-1096 . -1020) T) ((-1015 . -566) 125328) ((-103 . -126) T) ((-1038 . -37) 125315) ((-856 . -1020) T) ((-713 . -1020) T) ((-617 . -1020) T) ((-643 . -138) T) ((-112 . -138) T) ((-1193 . -21) T) ((-1193 . -25) T) ((-1191 . -21) T) ((-1191 . -25) T) ((-610 . -983) 125299) ((-497 . -789) T) ((-473 . -789) T) ((-333 . -983) 125251) ((-330 . -983) 125203) ((-322 . -983) 125155) ((-230 . -1127) T) ((-229 . -1127) T) ((-243 . -983) 124998) ((-227 . -983) 124841) ((-610 . -107) 124820) ((-333 . -107) 124758) ((-330 . -107) 124696) ((-322 . -107) 124634) ((-243 . -107) 124463) ((-227 . -107) 124292) ((-759 . -1131) 124271) ((-573 . -389) 124255) ((-43 . -21) T) ((-43 . -25) T) ((-757 . -588) 124163) ((-759 . -517) 124142) ((-230 . -968) 123971) ((-229 . -968) 123800) ((-122 . -115) 123784) ((-845 . -983) 123749) ((-641 . -984) T) ((-655 . -97) T) ((-321 . -160) T) ((-143 . -21) T) ((-143 . -25) T) ((-86 . -566) 123731) ((-845 . -107) 123687) ((-39 . -660) 123632) ((-805 . -1020) T) ((-305 . -567) 123593) ((-305 . -566) 123505) ((-1136 . -734) 123458) ((-1136 . -737) 123411) ((-230 . -355) 123381) ((-229 . -355) 123351) ((-600 . -37) 123321) ((-561 . -33) T) ((-458 . -1032) 123232) ((-452 . -33) T) 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NIL) ((-357 . -594) 121888) ((-805 . -660) 121875) ((-974 . -142) 121840) ((-39 . -160) T) ((-636 . -389) 121822) ((-655 . -288) 121809) ((-776 . -594) 121769) ((-769 . -594) 121743) ((-297 . -25) T) ((-297 . -21) T) ((-604 . -265) 121722) ((-537 . -1020) T) ((-525 . -1020) T) ((-468 . -1020) T) ((-225 . -267) 121699) ((-291 . -211) 121660) ((-1087 . -821) NIL) ((-1043 . -821) 121519) ((-125 . -789) T) ((-1087 . -968) 121401) ((-1043 . -968) 121286) ((-169 . -566) 121268) ((-793 . -968) 121166) ((-724 . -265) 121093) ((-759 . -1032) T) ((-965 . -669) T) ((-556 . -597) 121077) ((-974 . -909) 121006) ((-931 . -97) T) ((-759 . -23) T) ((-655 . -1067) 120984) ((-636 . -984) T) ((-556 . -351) 120968) ((-329 . -429) T) ((-321 . -269) T) ((-1174 . -1020) T) ((-377 . -97) T) ((-268 . -21) T) ((-268 . -25) T) ((-339 . -669) T) ((-653 . -1020) T) ((-641 . -1020) T) ((-339 . -450) T) ((-1122 . -566) 120950) ((-1087 . -355) 120934) ((-1043 . -355) 120918) ((-955 . -389) 120880) ((-132 . -209) 120862) ((-357 . -736) T) ((-357 . -733) T) ((-805 . -160) T) ((-357 . -669) T) ((-654 . -566) 120844) ((-655 . -37) 120673) ((-1173 . -1171) 120657) ((-329 . -380) T) ((-1173 . -1020) 120607) ((-537 . -660) 120594) ((-525 . -660) 120581) ((-468 . -660) 120546) ((-294 . -578) 120525) ((-776 . -669) T) ((-769 . -669) T) ((-592 . -1127) T) ((-1003 . -588) 120473) ((-1087 . -835) 120416) ((-1043 . -835) 120400) ((-608 . -983) 120384) ((-103 . -588) 120366) ((-458 . -126) 120237) ((-1093 . -1032) T) ((-887 . -46) 120206) ((-573 . -1020) T) ((-608 . -107) 120185) ((-305 . -267) 120162) ((-457 . -46) 120119) ((-1093 . -23) T) ((-113 . -1020) T) ((-98 . -97) 120097) ((-1183 . -1032) T) ((-981 . -126) T) ((-955 . -984) T) ((-761 . -968) 120081) ((-935 . -667) 120053) ((-1183 . -23) T) ((-641 . -660) 120018) ((-542 . -566) 120000) ((-364 . -968) 119984) ((-332 . -984) T) ((-363 . -126) T) ((-302 . -968) 119968) ((-205 . -821) 119950) ((-936 . -855) T) ((-89 . -33) T) ((-936 . -762) T) ((-849 . -855) T) ((-462 . -1131) T) ((-1108 . -566) 119932) ((-1025 . -1020) T) ((-198 . -1131) T) ((-931 . -288) 119897) ((-205 . -968) 119857) ((-39 . -269) T) ((-1003 . -21) T) ((-1003 . -25) T) ((-1038 . -770) T) ((-462 . -517) T) ((-337 . -25) T) ((-198 . -517) T) ((-337 . -21) T) ((-331 . -25) T) ((-331 . -21) T) ((-657 . -594) 119817) ((-323 . -25) T) ((-323 . -21) T) ((-103 . -25) T) ((-103 . -21) T) ((-47 . -984) T) ((-537 . -160) T) ((-525 . -160) T) ((-468 . -160) T) ((-604 . -566) 119799) ((-680 . -679) 119783) ((-314 . -566) 119765) ((-66 . -361) T) ((-66 . -373) T) ((-1022 . -102) 119749) ((-988 . -821) 119731) ((-887 . -821) 119656) ((-599 . -1032) T) ((-573 . -660) 119643) ((-457 . -821) NIL) ((-1062 . -97) T) ((-988 . -968) 119625) ((-92 . -566) 119607) ((-454 . -138) T) ((-887 . -968) 119489) ((-113 . -660) 119434) ((-599 . -23) T) ((-457 . -968) 119312) ((-1009 . -567) NIL) ((-1009 . -566) 119294) ((-724 . -567) NIL) ((-724 . -566) 119255) ((-722 . -567) 118890) ((-722 . -566) 118804) ((-1033 . -588) 118712) ((-438 . -566) 118694) ((-431 . -566) 118676) ((-431 . -567) 118537) ((-966 . -209) 118483) ((-122 . -33) T) ((-759 . -126) T) ((-807 . -844) 118462) ((-595 . -566) 118444) ((-333 . -1190) 118428) ((-330 . -1190) 118412) ((-322 . -1190) 118396) ((-123 . -486) 118329) ((-117 . -486) 118262) ((-483 . -734) T) ((-483 . -737) T) ((-482 . -736) T) ((-98 . -288) 118200) ((-202 . -97) 118178) ((-636 . -1020) T) ((-641 . -160) T) ((-807 . -594) 118130) ((-63 . -362) T) ((-254 . -566) 118112) ((-63 . -373) T) ((-887 . -355) 118096) ((-805 . -269) T) ((-49 . -566) 118078) ((-931 . -37) 118026) ((-538 . -566) 118008) ((-457 . -355) 117992) ((-538 . -567) 117974) ((-489 . -566) 117956) ((-845 . -1190) 117943) ((-806 . -1127) T) ((-643 . -429) T) ((-468 . -486) 117909) ((-462 . -341) T) ((-333 . -346) 117888) ((-330 . -346) 117867) ((-322 . -346) 117846) ((-198 . -341) T) ((-657 . -669) T) ((-112 . -429) T) ((-1194 . -1185) 117830) ((-806 . -819) 117807) ((-806 . -821) NIL) ((-898 . -789) 117706) ((-757 . -789) 117657) ((-600 . -602) 117641) ((-1114 . -33) T) ((-159 . -566) 117623) ((-1033 . -21) 117534) ((-1033 . -25) 117386) ((-806 . -968) 117363) ((-887 . -835) 117344) ((-1146 . -46) 117321) ((-845 . -346) T) ((-57 . -597) 117305) ((-488 . -597) 117289) ((-457 . -835) 117266) ((-69 . -418) T) ((-69 . -373) T) ((-469 . -597) 117250) ((-57 . -351) 117234) ((-573 . -160) T) ((-488 . -351) 117218) ((-469 . -351) 117202) ((-769 . -651) 117186) ((-1087 . -286) 117165) ((-1093 . -126) T) ((-113 . -160) T) ((-1062 . -288) 117103) ((-157 . -1127) T) ((-584 . -687) 117087) ((-560 . -687) 117071) ((-1183 . -126) T) ((-1158 . -855) 117050) ((-1137 . -855) 117029) ((-1137 . -762) NIL) ((-636 . -660) 116979) ((-1136 . -844) 116932) ((-955 . -1020) T) ((-806 . -355) 116909) ((-806 . -316) 116886) ((-840 . -1032) T) ((-157 . -819) 116870) ((-157 . -821) 116795) ((-462 . -1032) T) ((-332 . -1020) T) ((-198 . -1032) T) ((-74 . -418) T) ((-74 . -373) T) 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T) ((-1122 . -107) 115280) ((-451 . -594) 115177) ((-332 . -660) 115122) ((-157 . -835) 115081) ((-641 . -269) T) ((-636 . -160) T) ((-654 . -107) 115037) ((-1199 . -984) T) ((-1146 . -355) 115021) ((-396 . -1131) 114999) ((-291 . -787) NIL) ((-396 . -517) T) ((-205 . -286) T) ((-1136 . -733) 114952) ((-1136 . -736) 114905) ((-1157 . -669) T) ((-1136 . -669) T) ((-47 . -660) 114870) ((-205 . -953) T) ((-329 . -1180) 114847) ((-1159 . -389) 114813) ((-661 . -669) T) ((-1146 . -835) 114756) ((-108 . -566) 114738) ((-108 . -567) 114720) ((-661 . -450) T) ((-458 . -21) 114631) ((-123 . -464) 114615) ((-117 . -464) 114599) ((-458 . -25) 114451) ((-573 . -269) T) ((-542 . -983) 114426) ((-415 . -1020) T) ((-988 . -286) T) ((-113 . -269) T) ((-1024 . -97) T) ((-935 . -97) T) ((-542 . -107) 114394) ((-1058 . -288) 114332) ((-1122 . -977) T) ((-988 . -953) T) ((-64 . -1127) T) ((-981 . -25) T) ((-981 . -21) T) ((-654 . -977) T) ((-363 . -21) T) ((-363 . -25) T) ((-636 . -486) NIL) ((-955 . -160) T) ((-654 . -223) T) ((-988 . -510) T) ((-475 . -97) T) ((-332 . -160) T) ((-321 . -566) 114314) ((-372 . -566) 114296) ((-451 . -669) T) ((-1038 . -787) T) ((-827 . -968) 114264) ((-103 . -789) T) ((-604 . -983) 114248) ((-462 . -126) T) ((-1159 . -984) T) ((-198 . -126) T) ((-1072 . -97) 114226) ((-94 . -1020) T) ((-225 . -612) 114210) ((-225 . -597) 114194) ((-604 . -107) 114173) ((-294 . -389) 114157) ((-225 . -351) 114141) ((-1075 . -215) 114088) ((-931 . -211) 114072) ((-72 . -1127) T) ((-47 . -160) T) ((-643 . -365) T) ((-643 . -134) T) ((-1194 . -97) T) ((-1009 . -983) 113915) ((-243 . -844) 113894) ((-227 . -844) 113873) ((-724 . -983) 113696) ((-722 . -983) 113539) ((-561 . -1127) T) ((-1080 . -566) 113521) ((-1009 . -107) 113350) ((-974 . -97) T) ((-452 . -1127) T) ((-438 . -983) 113321) ((-431 . -983) 113164) ((-610 . -594) 113148) ((-806 . -286) T) ((-724 . -107) 112957) ((-722 . -107) 112786) ((-333 . -594) 112738) ((-330 . -594) 112690) ((-322 . -594) 112642) 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-566) 111506) ((-1101 . -33) T) ((-856 . -566) 111488) ((-1033 . -789) 111439) ((-713 . -566) 111421) ((-617 . -566) 111403) ((-1072 . -288) 111341) ((-455 . -33) T) ((-1013 . -1127) T) ((-454 . -429) T) ((-1009 . -977) T) ((-1057 . -33) T) ((-724 . -977) T) ((-722 . -977) T) ((-593 . -215) 111325) ((-581 . -215) 111271) ((-1146 . -286) 111250) ((-1009 . -304) 111211) ((-431 . -977) T) ((-1093 . -21) T) ((-1009 . -213) 111190) ((-724 . -304) 111167) ((-724 . -213) T) ((-722 . -304) 111139) ((-305 . -597) 111123) ((-674 . -1131) 111102) ((-1093 . -25) T) ((-57 . -33) T) ((-490 . -33) T) ((-488 . -33) T) ((-431 . -304) 111081) ((-305 . -351) 111065) ((-470 . -33) T) ((-469 . -33) T) ((-935 . -1067) NIL) ((-584 . -97) T) ((-560 . -97) T) ((-674 . -517) 110996) ((-333 . -669) T) ((-330 . -669) T) ((-322 . -669) T) ((-243 . -669) T) ((-227 . -669) T) ((-974 . -288) 110904) ((-836 . -1020) 110882) ((-49 . -977) T) ((-1183 . -21) T) ((-1183 . -25) T) ((-1089 . -517) 110861) ((-1088 . -1131) 110840) ((-538 . -977) T) ((-489 . -977) T) ((-1082 . -1131) 110819) ((-339 . -968) 110803) ((-300 . -968) 110787) ((-955 . -269) T) ((-357 . -821) 110769) ((-1088 . -517) 110720) ((-1082 . -517) 110671) ((-935 . -37) 110616) ((-741 . -1032) T) ((-845 . -669) T) ((-538 . -223) T) ((-538 . -213) T) ((-489 . -213) T) ((-489 . -223) T) ((-1044 . -517) 110595) ((-332 . -269) T) ((-593 . -637) 110579) ((-357 . -968) 110539) ((-1038 . -984) T) ((-98 . -121) 110523) ((-741 . -23) T) ((-1173 . -265) 110500) ((-385 . -288) 110465) ((-1193 . -1188) 110441) ((-1191 . -1188) 110420) ((-1159 . -1020) T) ((-805 . -566) 110402) ((-776 . -968) 110371) ((-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 . -934) 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) T) ((-565 . -789) T) ((-600 . -389) 110355) ((-106 . -789) T) ((-599 . -21) T) ((-599 . -25) T) ((-1194 . -37) 110325) ((-113 . -265) 110276) ((-1173 . -19) 110260) ((-1173 . -558) 110237) ((-1184 . -1020) T) ((-1000 . -1020) T) ((-920 . -1020) T) ((-897 . -126) T) ((-680 . -1020) T) ((-678 . -126) T) ((-658 . -126) T) ((-483 . -735) T) ((-385 . -1067) 110215) ((-430 . -126) T) ((-483 . -736) T) ((-203 . -977) T) ((-273 . -97) 109998) ((-132 . -1020) T) ((-641 . -934) T) ((-89 . -1127) T) ((-123 . -566) 109930) ((-117 . -566) 109862) ((-1199 . -160) T) ((-1088 . -341) 109841) ((-1082 . -341) 109820) ((-294 . -1020) T) ((-396 . -126) T) ((-291 . -1020) T) ((-385 . -37) 109772) ((-1051 . -97) T) ((-1159 . -660) 109664) ((-600 . -984) T) ((-297 . -136) 109643) ((-297 . -138) 109622) ((-130 . -1020) T) ((-110 . -1020) T) ((-797 . -97) T) ((-537 . -566) 109604) ((-525 . -567) 109503) ((-525 . -566) 109485) ((-468 . -566) 109467) ((-468 . -567) 109412) ((-460 . -23) T) ((-458 . -789) 109363) 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108659) ((-1173 . -567) 108620) ((-1159 . -160) T) ((-225 . -33) T) ((-861 . -907) T) ((-1114 . -1127) T) ((-608 . -733) 108599) ((-608 . -736) 108578) ((-376 . -373) T) ((-494 . -97) 108556) ((-966 . -1020) T) ((-202 . -927) 108540) ((-477 . -97) T) ((-573 . -566) 108522) ((-44 . -789) NIL) ((-573 . -567) 108499) ((-966 . -563) 108474) ((-836 . -486) 108407) ((-321 . -977) T) ((-113 . -567) NIL) ((-113 . -566) 108389) ((-807 . -1127) T) ((-616 . -395) 108373) ((-616 . -1041) 108318) ((-473 . -142) 108300) ((-321 . -213) T) ((-321 . -223) T) ((-39 . -983) 108245) ((-807 . -819) 108229) ((-807 . -821) 108154) ((-655 . -984) T) ((-636 . -934) NIL) ((-3 . |UnionCategory|) T) ((-1157 . -46) 108124) ((-1136 . -46) 108101) ((-1057 . -942) 108072) ((-205 . -855) T) ((-39 . -107) 108001) ((-807 . -968) 107868) ((-1038 . -660) 107855) ((-1025 . -566) 107837) ((-1003 . -138) 107816) ((-1003 . -136) 107767) ((-936 . -341) T) ((-297 . -1116) 107733) ((-357 . -286) T) ((-297 . -1113) 107699) ((-294 . -160) 107678) ((-291 . -160) T) ((-935 . -211) 107655) ((-849 . -341) T) ((-538 . -1190) 107642) ((-489 . -1190) 107619) ((-337 . -138) 107598) ((-337 . -136) 107549) ((-331 . -138) 107528) ((-331 . -136) 107479) ((-561 . -1104) 107455) ((-323 . -138) 107434) ((-323 . -136) 107385) ((-297 . -34) 107351) ((-452 . -1104) 107330) ((0 . |EnumerationCategory|) T) ((-297 . -91) 107296) ((-357 . -953) T) ((-103 . -138) T) ((-103 . -136) NIL) ((-44 . -215) 107246) ((-600 . -1020) T) ((-561 . -102) 107193) ((-460 . -126) T) ((-452 . -102) 107143) ((-220 . -1032) 107054) ((-807 . -355) 107038) ((-807 . -316) 107022) ((-220 . -23) 106893) ((-988 . -855) T) ((-988 . -762) T) ((-538 . -346) T) ((-489 . -346) T) ((-329 . -1067) T) ((-305 . -33) T) ((-43 . -395) 106877) ((-808 . -1127) T) ((-368 . -687) 106861) ((-1184 . -486) 106794) ((-674 . -126) T) ((-1165 . -517) 106773) ((-1158 . -1131) 106752) ((-1158 . -517) 106703) ((-680 . -486) 106636) ((-1137 . -1131) 106615) ((-1137 . -517) 106566) ((-828 . -1020) T) ((-135 . -783) T) ((-1136 . -1127) 106545) ((-1136 . -821) 106418) ((-1136 . -819) 106388) ((-494 . -288) 106326) ((-1089 . -126) T) ((-132 . -486) NIL) ((-1088 . -126) T) ((-1082 . -126) T) ((-1044 . -126) T) ((-955 . -934) T) ((-329 . -37) 106291) ((-936 . -1032) T) ((-849 . -1032) T) ((-80 . -566) 106273) ((-39 . -977) T) ((-805 . -983) 106260) ((-936 . -23) T) ((-807 . -835) 106219) ((-643 . -97) T) ((-935 . -327) NIL) ((-556 . -1127) T) ((-904 . -23) T) ((-849 . -23) T) ((-805 . -107) 106204) ((-405 . -1032) T) ((-451 . -46) 106174) ((-128 . -97) T) ((-39 . -213) 106146) ((-39 . -223) T) ((-112 . -97) T) ((-551 . -517) 106125) ((-550 . -517) 106104) ((-636 . -566) 106086) ((-636 . -567) 105994) ((-294 . -486) 105960) ((-291 . -486) 105852) ((-1157 . -968) 105836) ((-1136 . -968) 105625) ((-931 . -389) 105609) ((-405 . -23) T) ((-1038 . -160) T) ((-1159 . -269) T) ((-600 . -660) 105579) ((-135 . -1020) T) ((-47 . -934) T) ((-385 . -211) 105563) ((-274 . -215) 105513) ((-806 . -855) T) ((-806 . -762) NIL) ((-800 . -789) T) ((-1136 . -316) 105483) ((-1136 . -355) 105453) ((-202 . -1039) 105437) ((-1173 . -267) 105414) ((-1122 . -594) 105339) ((-897 . -21) T) ((-897 . -25) T) ((-678 . -21) T) ((-678 . -25) T) ((-658 . -21) T) ((-658 . -25) T) ((-654 . -594) 105304) ((-430 . -21) T) ((-430 . -25) T) ((-317 . -97) T) ((-161 . -97) T) ((-931 . -984) T) ((-805 . -977) T) ((-716 . -97) T) ((-1158 . -341) 105283) ((-1157 . -835) 105189) ((-1137 . -341) 105168) ((-1136 . -835) 105019) ((-955 . -566) 105001) ((-385 . -770) 104954) ((-1089 . -466) 104920) ((-157 . -855) 104851) ((-1088 . -466) 104817) ((-1082 . -466) 104783) ((-655 . -1020) T) ((-1044 . -466) 104749) ((-537 . -983) 104736) ((-525 . -983) 104723) ((-468 . -983) 104688) ((-294 . -269) 104667) ((-291 . -269) T) ((-332 . -566) 104649) ((-396 . -25) T) ((-396 . -21) T) ((-94 . -265) 104628) ((-537 . -107) 104613) ((-525 . -107) 104598) ((-468 . -107) 104554) ((-1091 . -821) 104521) ((-836 . -464) 104505) ((-47 . -566) 104487) ((-47 . -567) 104432) ((-220 . -126) 104303) ((-1146 . -855) 104282) ((-758 . -1131) 104261) ((-966 . -486) 104105) ((-366 . -566) 104087) ((-758 . -517) 104018) ((-542 . -594) 103993) ((-243 . -46) 103965) ((-227 . -46) 103922) ((-497 . -481) 103899) ((-932 . -1127) T) ((-641 . -983) 103864) ((-1165 . -1032) T) ((-1158 . -1032) T) ((-1137 . -1032) T) ((-935 . -348) 103836) ((-108 . -346) T) ((-451 . -835) 103742) ((-1165 . -23) T) ((-1158 . -23) T) ((-839 . -566) 103724) ((-89 . -102) 103708) ((-1122 . -669) T) ((-840 . -789) 103659) ((-643 . -1067) T) ((-641 . -107) 103615) ((-1137 . -23) T) ((-551 . -1032) T) ((-550 . -1032) T) ((-655 . -660) 103444) ((-654 . -669) T) ((-1038 . -269) T) ((-936 . -126) T) ((-462 . -789) T) ((-904 . -126) T) ((-849 . -126) T) ((-741 . -25) T) ((-198 . -789) T) ((-741 . -21) T) ((-537 . -977) T) ((-525 . -977) T) ((-468 . -977) T) ((-551 . -23) T) ((-321 . -1190) 103421) ((-297 . -429) 103400) ((-317 . -288) 103387) 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102127) ((-57 . -1127) T) ((-490 . -1127) T) ((-488 . -1127) T) ((-470 . -1127) T) ((-469 . -1127) T) ((-415 . -566) 102109) ((-412 . -566) 102091) ((-3 . -97) T) ((-958 . -1121) 102060) ((-775 . -97) T) ((-632 . -55) 102018) ((-641 . -977) T) ((-49 . -594) 101992) ((-268 . -429) T) ((-453 . -1121) 101961) ((0 . -97) T) ((-538 . -594) 101926) ((-489 . -594) 101871) ((-48 . -97) T) ((-845 . -968) 101858) ((-641 . -223) T) ((-1003 . -387) 101837) ((-674 . -588) 101785) ((-931 . -1020) T) ((-655 . -160) 101676) ((-462 . -925) 101658) ((-243 . -355) 101642) ((-227 . -355) 101626) ((-377 . -1020) T) ((-317 . -37) 101610) ((-957 . -97) 101588) ((-198 . -925) 101570) ((-161 . -37) 101502) ((-1157 . -286) 101481) ((-1136 . -286) 101460) ((-604 . -669) T) ((-94 . -566) 101442) ((-1082 . -588) 101394) ((-460 . -25) T) ((-460 . -21) T) ((-1136 . -953) 101347) ((-573 . -977) T) ((-357 . -382) T) ((-368 . -97) T) ((-243 . -835) 101293) ((-227 . -835) 101270) ((-113 . -977) T) ((-758 . -1032) T) 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99483) ((-297 . -906) 99445) ((-100 . -97) T) ((-47 . -983) 99410) ((-1195 . -97) T) ((-359 . -97) T) ((-47 . -107) 99366) ((-936 . -588) 99348) ((-1159 . -566) 99330) ((-497 . -97) T) ((-473 . -97) T) ((-1051 . -1052) 99314) ((-143 . -1180) 99298) ((-225 . -1127) T) ((-1087 . -1131) 99277) ((-1043 . -1131) 99256) ((-220 . -21) 99167) ((-220 . -25) 99019) ((-123 . -115) 99003) ((-117 . -115) 98987) ((-43 . -687) 98971) ((-1087 . -517) 98882) ((-1043 . -517) 98813) ((-966 . -265) 98788) ((-758 . -126) T) ((-113 . -737) NIL) ((-113 . -734) NIL) ((-333 . -286) T) ((-330 . -286) T) ((-322 . -286) T) ((-1015 . -1127) T) ((-230 . -1032) 98699) ((-229 . -1032) 98610) ((-955 . -977) T) ((-935 . -984) T) ((-321 . -594) 98555) ((-571 . -37) 98539) ((-1184 . -566) 98501) ((-1184 . -567) 98462) ((-1000 . -566) 98444) ((-955 . -223) T) ((-332 . -977) T) ((-757 . -1180) 98414) ((-230 . -23) T) ((-229 . -23) T) ((-920 . -566) 98396) ((-680 . -567) 98357) ((-680 . -566) 98339) ((-741 . -789) 98318) 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. -1020) T) ((-332 . -594) 90266) ((-1087 . -588) 90214) ((-1043 . -588) 90162) ((-363 . -481) 90141) ((-775 . -787) 90120) ((-357 . -1131) T) ((-636 . -669) T) ((-317 . -984) T) ((-1137 . -925) 90072) ((-161 . -984) T) ((-98 . -566) 90004) ((-1089 . -136) 89983) ((-1089 . -138) 89962) ((-357 . -517) T) ((-1088 . -138) 89941) ((-1088 . -136) 89920) ((-1082 . -136) 89827) ((-385 . -269) T) ((-1082 . -138) 89734) ((-1044 . -138) 89713) ((-1044 . -136) 89692) ((-297 . -37) 89533) ((-157 . -126) T) ((-291 . -737) NIL) ((-291 . -734) NIL) ((-600 . -977) T) ((-47 . -594) 89498) ((-926 . -21) T) ((-123 . -942) 89482) ((-117 . -942) 89466) ((-926 . -25) T) ((-836 . -115) 89450) ((-1074 . -97) T) ((-758 . -789) 89429) ((-1146 . -126) T) ((-1087 . -25) T) ((-1087 . -21) T) ((-794 . -126) T) ((-1043 . -25) T) ((-1043 . -21) T) ((-793 . -25) T) ((-793 . -21) T) ((-724 . -286) 89408) ((-593 . -97) 89386) ((-581 . -97) T) ((-1075 . -288) 89181) ((-532 . -126) T) ((-571 . -787) 89160) ((-1072 . -464) 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-25) T) ((-300 . -23) T) ((-878 . -789) 86982) ((-655 . -304) 86959) ((-457 . -588) 86907) ((-39 . -968) 86797) ((-643 . -660) 86784) ((-655 . -213) T) ((-317 . -1020) T) ((-161 . -1020) T) ((-309 . -789) T) ((-396 . -429) 86734) ((-357 . -23) T) ((-337 . -37) 86699) ((-331 . -37) 86664) ((-323 . -37) 86629) ((-78 . -418) T) ((-78 . -373) T) ((-205 . -25) T) ((-205 . -21) T) ((-776 . -1032) T) ((-103 . -37) 86579) ((-769 . -1032) T) ((-716 . -1020) T) ((-112 . -660) 86566) ((-617 . -968) 86550) ((-565 . -97) T) ((-776 . -23) T) ((-769 . -23) T) ((-1072 . -265) 86527) ((-1033 . -288) 86465) ((-1022 . -215) 86449) ((-62 . -374) T) ((-62 . -373) T) ((-106 . -97) T) ((-39 . -355) 86426) ((-599 . -791) 86410) ((-988 . -21) T) ((-988 . -25) T) ((-757 . -211) 86380) ((-887 . -25) T) ((-887 . -21) T) ((-571 . -984) T) ((-457 . -25) T) ((-457 . -21) T) ((-958 . -288) 86318) ((-824 . -566) 86300) ((-820 . -566) 86282) ((-230 . -789) 86233) ((-229 . -789) 86184) ((-494 . -486) 86117) ((-806 . 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. -23) T) ((-300 . -126) T) ((-3 . -1020) T) ((-935 . -567) 84901) ((-931 . -223) 84880) ((-931 . -213) 84859) ((-1199 . -669) T) ((-1165 . -136) 84838) ((-775 . -1020) T) ((-1165 . -138) 84817) ((-1158 . -138) 84796) ((-1158 . -136) 84775) ((-1157 . -1131) 84754) ((-1137 . -136) 84661) ((-1137 . -138) 84568) ((-1136 . -1131) 84547) ((-357 . -126) T) ((-525 . -821) 84529) ((0 . -1020) T) ((-161 . -160) T) ((-157 . -21) T) ((-157 . -25) T) ((-48 . -1020) T) ((-1159 . -594) 84434) ((-1157 . -517) 84385) ((-657 . -1032) T) ((-1136 . -517) 84336) ((-525 . -968) 84318) ((-550 . -138) 84297) ((-550 . -136) 84276) ((-468 . -968) 84219) ((-85 . -362) T) ((-85 . -373) T) ((-807 . -341) T) ((-776 . -126) T) ((-769 . -126) T) ((-657 . -23) T) ((-475 . -566) 84201) ((-1195 . -984) T) ((-357 . -986) T) ((-957 . -1020) 84179) ((-836 . -33) T) ((-458 . -288) 84117) ((-1072 . -567) 84078) ((-1072 . -566) 84010) ((-1087 . -789) 83989) ((-44 . -97) T) ((-1043 . -789) 83968) ((-759 . -97) T) ((-1146 . 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78940) ((-1146 . -789) 78919) ((-757 . -389) 78888) ((-98 . -115) 78872) ((-125 . -1020) T) ((-51 . -1020) T) ((-861 . -566) 78854) ((-806 . -925) 78831) ((-765 . -97) T) ((-1194 . -107) 78810) ((-599 . -37) 78780) ((-532 . -789) T) ((-333 . -1032) T) ((-330 . -1032) T) ((-322 . -1032) T) ((-243 . -1032) T) ((-227 . -1032) T) ((-573 . -286) 78759) ((-1066 . -288) 78563) ((-610 . -23) T) ((-458 . -211) 78533) ((-143 . -984) T) ((-333 . -23) T) ((-330 . -23) T) ((-322 . -23) T) ((-113 . -286) T) ((-243 . -23) T) ((-227 . -23) T) ((-935 . -977) T) ((-655 . -844) 78512) ((-935 . -213) 78484) ((-935 . -223) T) ((-113 . -953) NIL) ((-845 . -1032) T) ((-1158 . -429) 78463) ((-1137 . -429) 78442) ((-494 . -566) 78374) ((-655 . -594) 78299) ((-385 . -983) 78251) ((-477 . -566) 78233) ((-845 . -23) T) ((-462 . -288) NIL) ((-451 . -126) T) ((-198 . -288) NIL) ((-385 . -107) 78171) ((-757 . -984) 78102) ((-680 . -1018) 78086) ((-1157 . -466) 78052) ((-1136 . -466) 78018) ((-454 . -269) T) ((-132 . 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-660) 76304) ((-47 . -286) T) ((-1191 . -660) 76274) ((-898 . -1020) T) ((-757 . -1020) 76065) ((-290 . -97) T) ((-836 . -1127) T) ((-47 . -953) T) ((-1136 . -588) 75973) ((-632 . -97) 75951) ((-43 . -660) 75935) ((-511 . -97) T) ((-65 . -361) T) ((-65 . -373) T) ((-608 . -23) T) ((-616 . -704) T) ((-1125 . -1020) 75913) ((-329 . -983) 75858) ((-620 . -1020) 75836) ((-988 . -138) T) ((-887 . -138) 75815) ((-887 . -136) 75794) ((-741 . -97) T) ((-143 . -660) 75778) ((-457 . -138) 75757) ((-457 . -136) 75736) ((-329 . -107) 75665) ((-1003 . -984) T) ((-300 . -789) 75644) ((-1165 . -906) 75613) ((-576 . -1020) T) ((-1158 . -906) 75575) ((-483 . -126) T) ((-479 . -126) T) ((-274 . -209) 75525) ((-337 . -984) T) ((-331 . -984) T) ((-323 . -984) T) ((-273 . -977) 75468) ((-1137 . -906) 75437) ((-357 . -789) T) ((-103 . -984) T) ((-931 . -669) T) ((-805 . -855) T) ((-782 . -737) 75416) ((-782 . -734) 75395) ((-396 . -288) 75334) ((-445 . -97) T) ((-550 . -906) 75303) ((-297 . -1020) T) ((-385 . -737) 75282) ((-385 . -734) 75261) ((-473 . -464) 75243) ((-1159 . -968) 75209) ((-1157 . -21) T) ((-1157 . -25) T) ((-1136 . -21) T) ((-1136 . -25) T) ((-757 . -660) 75151) ((-641 . -382) T) ((-1184 . -1127) T) ((-1033 . -389) 75120) ((-935 . -346) NIL) ((-98 . -33) T) ((-680 . -1127) T) ((-43 . -704) T) ((-548 . -97) T) ((-75 . -374) T) ((-75 . -373) T) ((-599 . -602) 75104) ((-132 . -1127) T) ((-806 . -138) T) ((-806 . -136) NIL) ((-329 . -977) T) ((-68 . -361) T) ((-68 . -373) T) ((-1081 . -97) T) ((-616 . -486) 75037) ((-632 . -288) 74975) ((-897 . -37) 74872) ((-678 . -37) 74842) ((-511 . -288) 74646) ((-294 . -1127) T) ((-329 . -213) T) ((-329 . -223) T) ((-291 . -1127) T) ((-268 . -1020) T) ((-1095 . -566) 74628) ((-654 . -1131) T) ((-1072 . -597) 74612) ((-1122 . -517) 74591) ((-654 . -517) T) ((-294 . -819) 74575) ((-294 . -821) 74500) ((-291 . -819) 74461) ((-291 . -821) NIL) ((-741 . -288) 74426) ((-297 . -660) 74267) ((-302 . -301) 74244) ((-460 . -97) T) ((-451 . -25) 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T) ((-268 . -660) 73203) ((-1075 . -563) 73179) ((-548 . -288) NIL) ((-459 . -1020) 73157) ((-368 . -566) 73139) ((-482 . -789) T) ((-1066 . -209) 73089) ((-1165 . -1164) 73073) ((-1165 . -1151) 73050) ((-1158 . -1156) 73011) ((-1158 . -1151) 72981) ((-1158 . -1154) 72965) ((-1137 . -1135) 72926) ((-1137 . -1151) 72903) ((-571 . -566) 72885) ((-1137 . -1133) 72869) ((-641 . -855) T) ((-1089 . -263) 72835) ((-1088 . -263) 72801) ((-1082 . -263) 72767) ((-1003 . -1020) T) ((-987 . -1020) T) ((-47 . -281) T) ((-294 . -835) 72734) ((-291 . -835) NIL) ((-987 . -993) 72713) ((-1038 . -821) 72695) ((-741 . -37) 72679) ((-243 . -588) 72627) ((-227 . -588) 72575) ((-643 . -983) 72562) ((-550 . -1151) 72539) ((-1044 . -263) 72505) ((-297 . -160) 72436) ((-337 . -1020) T) ((-331 . -1020) T) ((-323 . -1020) T) ((-473 . -19) 72418) ((-1038 . -968) 72400) ((-1022 . -142) 72384) ((-103 . -1020) T) ((-112 . -983) 72371) ((-654 . -341) T) ((-473 . -558) 72346) ((-643 . -107) 72331) ((-414 . -97) T) 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. -46) 68746) ((-337 . -160) T) ((-331 . -160) T) ((-490 . -55) 68720) ((-470 . -55) 68670) ((-329 . -1190) 68647) ((-205 . -429) T) ((-297 . -269) 68598) ((-323 . -160) T) ((-161 . -223) T) ((-1136 . -789) 68497) ((-103 . -160) T) ((-807 . -925) 68481) ((-604 . -1032) T) ((-538 . -341) T) ((-538 . -307) 68468) ((-489 . -307) 68445) ((-489 . -341) T) ((-294 . -286) 68424) ((-291 . -286) T) ((-556 . -789) 68403) ((-1033 . -660) 68345) ((-491 . -261) 68329) ((-604 . -23) T) ((-396 . -211) 68313) ((-291 . -953) NIL) ((-314 . -23) T) ((-98 . -942) 68297) ((-44 . -35) 68276) ((-565 . -1020) T) ((-329 . -346) T) ((-468 . -27) T) ((-220 . -288) 68214) ((-1009 . -1032) T) ((-1194 . -594) 68188) ((-724 . -1032) T) ((-722 . -1032) T) ((-431 . -1032) T) ((-988 . -429) T) ((-887 . -429) 68139) ((-106 . -1020) T) ((-1009 . -23) T) ((-759 . -984) T) ((-724 . -23) T) ((-722 . -23) T) ((-457 . -429) 68090) ((-1075 . -486) 67873) ((-359 . -360) 67852) ((-1093 . -389) 67836) ((-438 . -23) T) ((-431 . 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59268) ((-1140 . -97) 59246) ((-1075 . -567) NIL) ((-1075 . -566) 59228) ((-1157 . -1113) 59194) ((-1157 . -1116) 59160) ((-1137 . -211) 59112) ((-1136 . -1113) 59078) ((-1136 . -1116) 59044) ((-1058 . -355) 59028) ((-1038 . -762) T) ((-1038 . -855) T) ((-1033 . -558) 59005) ((-1003 . -567) 58989) ((-459 . -566) 58921) ((-757 . -267) 58898) ((-561 . -142) 58845) ((-396 . -984) T) ((-462 . -660) 58795) ((-458 . -464) 58779) ((-305 . -789) 58758) ((-317 . -594) 58732) ((-49 . -21) T) ((-49 . -25) T) ((-198 . -660) 58682) ((-157 . -667) 58653) ((-161 . -594) 58585) ((-538 . -21) T) ((-538 . -25) T) ((-489 . -25) T) ((-489 . -21) T) ((-452 . -142) 58535) ((-1003 . -566) 58517) ((-987 . -566) 58499) ((-926 . -97) T) ((-798 . -97) T) ((-741 . -389) 58463) ((-39 . -126) T) ((-641 . -341) T) ((-194 . -830) T) ((-643 . -736) T) ((-643 . -733) T) ((-537 . -1032) T) ((-525 . -1032) T) ((-468 . -1032) T) ((-643 . -669) T) ((-337 . -566) 58445) ((-331 . -566) 58427) ((-323 . -566) 58409) ((-64 . 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32381) ((-1022 . -486) 32314) ((-897 . -107) 32183) ((-845 . -97) T) ((-678 . -107) 32148) ((-57 . -97) 32098) ((-491 . -567) 32059) ((-491 . -566) 31971) ((-490 . -97) 31949) ((-488 . -97) 31899) ((-470 . -97) 31877) ((-469 . -97) 31827) ((-430 . -107) 31790) ((-230 . -160) 31769) ((-229 . -160) 31748) ((-396 . -983) 31722) ((-1122 . -906) 31684) ((-931 . -1032) T) ((-878 . -486) 31617) ((-462 . -737) T) ((-451 . -37) 31458) ((-396 . -107) 31425) ((-462 . -734) T) ((-932 . -288) 31363) ((-198 . -737) T) ((-198 . -734) T) ((-931 . -23) T) ((-655 . -126) T) ((-1136 . -378) 31333) ((-294 . -25) 31186) ((-157 . -389) 31170) ((-294 . -21) 31042) ((-291 . -25) T) ((-291 . -21) T) ((-800 . -346) T) ((-106 . -33) T) ((-458 . -594) 30892) ((-806 . -984) T) ((-548 . -267) 30867) ((-537 . -138) T) ((-525 . -138) T) ((-468 . -138) T) ((-1087 . -660) 30696) ((-1043 . -660) 30545) ((-1038 . -588) 30527) ((-793 . -660) 30497) ((-616 . -1127) T) ((-1 . -97) T) ((-220 . -566) 30229) ((-1146 . -389) 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14834) ((-561 . -486) 14617) ((-760 . -968) 14601) ((-452 . -486) 14393) ((-897 . -669) T) ((-678 . -669) T) ((-658 . -669) T) ((-329 . -1032) T) ((-1094 . -566) 14375) ((-203 . -97) T) ((-458 . -355) 14345) ((-487 . -1020) T) ((-482 . -1020) T) ((-480 . -1020) T) ((-741 . -594) 14319) ((-955 . -429) T) ((-892 . -486) 14252) ((-329 . -23) T) ((-584 . -126) T) ((-560 . -126) T) ((-332 . -429) T) ((-220 . -346) 14231) ((-357 . -160) T) ((-1157 . -984) T) ((-1136 . -984) T) ((-205 . -934) T) ((-641 . -365) T) ((-396 . -669) T) ((-643 . -1131) T) ((-1058 . -588) 14179) ((-537 . -804) 14163) ((-1075 . -1104) 14139) ((-643 . -517) T) ((-122 . -1020) 14117) ((-1186 . -983) 14101) ((-657 . -1020) T) ((-458 . -835) 14034) ((-604 . -37) 14004) ((-332 . -380) T) ((-294 . -138) 13983) ((-294 . -136) 13962) ((-112 . -517) T) ((-291 . -138) 13918) ((-291 . -136) 13874) ((-47 . -429) T) ((-150 . -1020) T) ((-146 . -1020) T) ((-1075 . -102) 13821) ((-724 . -1067) 13799) ((-632 . -33) T) ((-1186 . 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-669) T) ((-556 . -267) 132027) ((-538 . -660) 131992) ((-455 . -567) NIL) ((-455 . -566) 131974) ((-489 . -660) 131919) ((-294 . -97) T) ((-291 . -97) T) ((-268 . -23) T) ((-143 . -126) T) ((-364 . -669) T) ((-807 . -983) 131871) ((-845 . -566) 131853) ((-845 . -567) 131835) ((-807 . -107) 131773) ((-130 . -97) T) ((-110 . -97) T) ((-655 . -1149) 131757) ((-657 . -977) T) ((-636 . -327) NIL) ((-490 . -566) 131689) ((-357 . -737) T) ((-203 . -1020) T) ((-357 . -734) T) ((-205 . -736) T) ((-205 . -733) T) ((-57 . -567) 131650) ((-57 . -566) 131562) ((-205 . -669) T) ((-488 . -567) 131523) ((-488 . -566) 131435) ((-470 . -566) 131367) ((-469 . -567) 131328) ((-469 . -566) 131240) ((-1003 . -341) 131191) ((-39 . -389) 131168) ((-75 . -1127) T) ((-806 . -844) NIL) ((-337 . -307) 131152) ((-337 . -341) T) ((-331 . -307) 131136) ((-331 . -341) T) ((-323 . -307) 131120) ((-323 . -341) T) ((-294 . -263) 131099) ((-103 . -341) T) ((-68 . -1127) T) ((-1137 . -316) 131051) ((-806 . -594) 130996) ((-1137 . -355) 130948) ((-898 . -126) 130803) ((-757 . -126) 130674) ((-892 . -597) 130658) ((-1009 . -160) 130569) ((-892 . -351) 130553) ((-988 . -736) T) ((-988 . -733) T) ((-724 . -160) 130444) ((-722 . -160) 130355) ((-758 . -46) 130317) ((-988 . -669) T) ((-305 . -464) 130301) ((-887 . -669) T) ((-431 . -160) 130212) ((-225 . -265) 130189) ((-457 . -669) T) ((-1184 . -288) 130127) ((-1165 . -835) 130040) ((-1158 . -835) 129946) ((-1157 . -983) 129781) ((-1137 . -835) 129614) ((-1136 . -983) 129422) ((-1122 . -269) 129401) ((-1062 . -142) 129385) ((-998 . -97) T) ((-862 . -889) T) ((-73 . -1127) T) ((-680 . -288) 129323) ((-157 . -844) 129276) ((-610 . -360) 129248) ((-30 . -889) T) ((-1 . -566) 129230) ((-1038 . -97) T) ((-1003 . -23) T) ((-49 . -570) 129214) ((-1003 . -1032) T) ((-935 . -387) 129186) ((-550 . -835) 129099) ((-416 . -97) T) ((-132 . -288) NIL) ((-807 . -977) T) ((-775 . -789) 129078) ((-79 . -1127) T) ((-654 . -269) T) ((-39 . -984) T) ((-538 . -160) T) ((-489 . -160) T) ((-483 . -566) 129060) ((-157 . -594) 128970) ((-479 . -566) 128952) ((-329 . -138) 128934) ((-329 . -136) T) ((-337 . -1032) T) ((-331 . -1032) T) ((-323 . -1032) T) ((-936 . -286) T) ((-849 . -286) T) ((-807 . -223) T) ((-103 . -1032) T) ((-807 . -213) 128913) ((-1157 . -107) 128734) ((-1136 . -107) 128523) ((-225 . -1161) 128507) ((-525 . -787) T) ((-337 . -23) T) ((-332 . -327) T) ((-294 . -288) 128494) ((-291 . -288) 128435) ((-331 . -23) T) ((-297 . -126) T) ((-323 . -23) T) ((-936 . -953) T) ((-103 . -23) T) ((-225 . -558) 128412) ((-1159 . -37) 128304) ((-1146 . -844) 128283) ((-108 . -1020) T) ((-966 . -97) T) ((-1146 . -594) 128208) ((-806 . -736) NIL) ((-794 . -594) 128182) ((-806 . -733) NIL) ((-758 . -821) NIL) ((-806 . -669) T) ((-1009 . -486) 128055) ((-724 . -486) 128002) ((-722 . -486) 127954) ((-532 . -594) 127941) ((-758 . -968) 127771) ((-431 . -486) 127714) ((-366 . -367) T) ((-58 . -1127) T) ((-571 . -789) 127693) ((-473 . -607) T) ((-1062 . -909) 127662) ((-935 . -429) T) ((-641 . -787) T) ((-482 . -734) T) ((-451 . -983) 127497) ((-321 . -1020) T) ((-291 . -1067) NIL) ((-268 . -126) T) ((-372 . -1020) T) ((-636 . -348) 127464) ((-805 . -984) T) ((-203 . -570) 127441) ((-305 . -265) 127418) ((-451 . -107) 127239) ((-1157 . -977) T) ((-1136 . -977) T) ((-758 . -355) 127223) ((-157 . -669) T) ((-600 . -97) T) ((-1157 . -223) 127202) ((-1157 . -213) 127154) ((-1136 . -213) 127059) ((-1136 . -223) 127038) ((-935 . -380) NIL) ((-616 . -588) 126986) ((-294 . -37) 126896) ((-291 . -37) 126825) ((-67 . -566) 126807) ((-297 . -466) 126773) ((-1101 . -267) 126752) ((-1033 . -1032) 126663) ((-81 . -1127) T) ((-59 . -566) 126645) ((-455 . -267) 126624) ((-1186 . -968) 126601) ((-1080 . -1020) T) ((-1033 . -23) 126472) ((-758 . -835) 126408) ((-1146 . -669) T) ((-1022 . -1127) T) ((-1009 . -269) 126339) ((-828 . -97) T) ((-724 . -269) 126250) ((-305 . -19) 126234) ((-57 . -267) 126211) ((-722 . -269) 126142) ((-794 . -669) T) ((-113 . -787) NIL) 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T) ((-1193 . -21) T) ((-1193 . -25) T) ((-1191 . -21) T) ((-1191 . -25) T) ((-610 . -983) 125299) ((-497 . -789) T) ((-473 . -789) T) ((-333 . -983) 125251) ((-330 . -983) 125203) ((-322 . -983) 125155) ((-230 . -1127) T) ((-229 . -1127) T) ((-243 . -983) 124998) ((-227 . -983) 124841) ((-610 . -107) 124820) ((-333 . -107) 124758) ((-330 . -107) 124696) ((-322 . -107) 124634) ((-243 . -107) 124463) ((-227 . -107) 124292) ((-759 . -1131) 124271) ((-573 . -389) 124255) ((-43 . -21) T) ((-43 . -25) T) ((-757 . -588) 124163) ((-759 . -517) 124142) ((-230 . -968) 123971) ((-229 . -968) 123800) ((-122 . -115) 123784) ((-845 . -983) 123749) ((-641 . -984) T) ((-655 . -97) T) ((-321 . -160) T) ((-143 . -21) T) ((-143 . -25) T) ((-86 . -566) 123731) ((-845 . -107) 123687) ((-39 . -660) 123632) ((-805 . -1020) T) ((-305 . -567) 123593) ((-305 . -566) 123505) ((-1136 . -734) 123458) ((-1136 . -737) 123411) ((-230 . -355) 123381) ((-229 . -355) 123351) ((-600 . -37) 123321) ((-561 . -33) T) ((-458 . -1032) 123232) ((-452 . -33) T) ((-1033 . -126) 123103) ((-898 . -25) 122914) ((-809 . -566) 122896) ((-898 . -21) 122851) ((-757 . -21) 122762) ((-757 . -25) 122614) ((-573 . -984) T) ((-1093 . -517) 122593) ((-1087 . -46) 122570) ((-333 . -977) T) ((-330 . -977) T) ((-458 . -23) 122441) ((-322 . -977) T) ((-227 . -977) T) ((-243 . -977) T) ((-1043 . -46) 122413) ((-113 . -984) T) ((-965 . -594) 122387) ((-892 . -33) T) ((-333 . -213) 122366) ((-333 . -223) T) ((-330 . -213) 122345) ((-330 . -223) T) ((-227 . -304) 122302) ((-322 . -213) 122281) ((-322 . -223) T) ((-243 . -304) 122253) ((-243 . -213) 122232) ((-1072 . -142) 122216) ((-230 . -835) 122149) ((-229 . -835) 122082) ((-1005 . -789) T) ((-1140 . -1127) T) ((-392 . -1032) T) ((-981 . -23) T) ((-845 . -977) T) ((-300 . -594) 122064) ((-955 . -787) T) ((-1122 . -934) 122030) ((-1088 . -855) 122009) ((-1082 . -855) 121988) ((-845 . -223) T) ((-759 . -341) 121967) ((-363 . -23) T) ((-123 . -1020) 121945) ((-117 . -1020) 121923) 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-355) 120918) ((-955 . -389) 120880) ((-132 . -209) 120862) ((-357 . -736) T) ((-357 . -733) T) ((-805 . -160) T) ((-357 . -669) T) ((-654 . -566) 120844) ((-655 . -37) 120673) ((-1173 . -1171) 120657) ((-329 . -380) T) ((-1173 . -1020) 120607) ((-537 . -660) 120594) ((-525 . -660) 120581) ((-468 . -660) 120546) ((-294 . -578) 120525) ((-776 . -669) T) ((-769 . -669) T) ((-592 . -1127) T) ((-1003 . -588) 120473) ((-1087 . -835) 120416) ((-1043 . -835) 120400) ((-608 . -983) 120384) ((-103 . -588) 120366) ((-458 . -126) 120237) ((-1093 . -1032) T) ((-887 . -46) 120206) ((-573 . -1020) T) ((-608 . -107) 120185) ((-305 . -267) 120162) ((-457 . -46) 120119) ((-1093 . -23) T) ((-113 . -1020) T) ((-98 . -97) 120097) ((-1183 . -1032) T) ((-981 . -126) T) ((-955 . -984) T) ((-761 . -968) 120081) ((-935 . -667) 120053) ((-1183 . -23) T) ((-641 . -660) 120018) ((-542 . -566) 120000) ((-364 . -968) 119984) ((-332 . -984) T) ((-363 . -126) T) ((-302 . -968) 119968) ((-205 . -821) 119950) ((-936 . -855) T) ((-89 . -33) T) ((-936 . -762) T) ((-849 . -855) T) ((-462 . -1131) T) ((-1108 . -566) 119932) ((-1025 . -1020) T) ((-198 . -1131) T) ((-931 . -288) 119897) ((-205 . -968) 119857) ((-39 . -269) T) ((-1003 . -21) T) ((-1003 . -25) T) ((-1038 . -770) T) ((-462 . -517) T) ((-337 . -25) T) ((-198 . -517) T) ((-337 . -21) T) ((-331 . -25) T) ((-331 . -21) T) ((-657 . -594) 119817) ((-323 . -25) T) ((-323 . -21) T) ((-103 . -25) T) ((-103 . -21) T) ((-47 . -984) T) ((-537 . -160) T) ((-525 . -160) T) ((-468 . -160) T) ((-604 . -566) 119799) ((-680 . -679) 119783) ((-314 . -566) 119765) ((-66 . -361) T) ((-66 . -373) T) ((-1022 . -102) 119749) ((-988 . -821) 119731) ((-887 . -821) 119656) ((-599 . -1032) T) ((-573 . -660) 119643) ((-457 . -821) NIL) ((-1062 . -97) T) ((-988 . -968) 119625) ((-92 . -566) 119607) ((-454 . -138) T) ((-887 . -968) 119489) ((-113 . -660) 119434) ((-599 . -23) T) ((-457 . -968) 119312) ((-1009 . -567) NIL) ((-1009 . -566) 119294) ((-724 . -567) NIL) ((-724 . -566) 119255) ((-722 . -567) 118890) ((-722 . -566) 118804) ((-1033 . -588) 118712) ((-438 . -566) 118694) ((-431 . -566) 118676) ((-431 . -567) 118537) ((-966 . -209) 118483) ((-122 . -33) T) ((-759 . -126) T) ((-807 . -844) 118462) ((-595 . -566) 118444) ((-333 . -1190) 118428) ((-330 . -1190) 118412) ((-322 . -1190) 118396) ((-123 . -486) 118329) ((-117 . -486) 118262) ((-483 . -734) T) ((-483 . -737) T) ((-482 . -736) T) ((-98 . -288) 118200) ((-202 . -97) 118178) ((-636 . -1020) T) ((-641 . -160) T) ((-807 . -594) 118130) ((-63 . -362) T) ((-254 . -566) 118112) ((-63 . -373) T) ((-887 . -355) 118096) ((-805 . -269) T) ((-49 . -566) 118078) ((-931 . -37) 118026) ((-538 . -566) 118008) ((-457 . -355) 117992) ((-538 . -567) 117974) ((-489 . -566) 117956) ((-845 . -1190) 117943) ((-806 . -1127) T) ((-643 . -429) T) ((-468 . -486) 117909) ((-462 . -341) T) ((-333 . -346) 117888) ((-330 . -346) 117867) ((-322 . -346) 117846) ((-198 . -341) T) ((-657 . -669) T) ((-112 . -429) T) ((-1194 . -1185) 117830) ((-806 . -819) 117807) ((-806 . -821) NIL) ((-898 . -789) 117706) ((-757 . -789) 117657) ((-600 . -602) 117641) ((-1114 . -33) T) ((-159 . -566) 117623) ((-1033 . -21) 117534) ((-1033 . -25) 117386) ((-806 . -968) 117363) ((-887 . -835) 117344) ((-1146 . -46) 117321) ((-845 . -346) T) ((-57 . -597) 117305) ((-488 . -597) 117289) ((-457 . -835) 117266) ((-69 . -418) T) ((-69 . -373) T) ((-469 . -597) 117250) ((-57 . -351) 117234) ((-573 . -160) T) ((-488 . -351) 117218) ((-469 . -351) 117202) ((-769 . -651) 117186) ((-1087 . -286) 117165) ((-1093 . -126) T) ((-113 . -160) T) ((-1062 . -288) 117103) ((-157 . -1127) T) ((-584 . -687) 117087) ((-560 . -687) 117071) ((-1183 . -126) T) ((-1158 . -855) 117050) ((-1137 . -855) 117029) ((-1137 . -762) NIL) ((-636 . -660) 116979) ((-1136 . -844) 116932) ((-955 . -1020) T) ((-806 . -355) 116909) ((-806 . -316) 116886) ((-840 . -1032) T) ((-157 . -819) 116870) ((-157 . -821) 116795) ((-462 . -1032) T) ((-332 . -1020) T) ((-198 . -1032) T) ((-74 . -418) T) ((-74 . -373) T) ((-157 . -968) 116693) ((-297 . -789) T) ((-1173 . -486) 116626) ((-1157 . -594) 116523) ((-1136 . -594) 116393) ((-807 . -736) 116372) ((-807 . -733) 116351) ((-807 . -669) T) ((-462 . -23) T) ((-203 . -566) 116333) ((-161 . -429) T) ((-202 . -288) 116271) ((-84 . -418) T) ((-84 . -373) T) ((-198 . -23) T) ((-1195 . -1188) 116250) ((-537 . -269) T) ((-525 . -269) T) ((-621 . -968) 116234) ((-468 . -269) T) ((-130 . -447) 116189) ((-47 . -1020) T) ((-655 . -211) 116173) ((-806 . -835) NIL) ((-1146 . -821) NIL) ((-824 . -97) T) ((-820 . -97) T) ((-366 . -1020) T) ((-157 . -355) 116157) ((-157 . -316) 116141) ((-1146 . -968) 116023) ((-794 . -968) 115921) ((-1058 . -97) T) ((-599 . -126) T) ((-113 . -486) 115829) ((-608 . -734) 115808) ((-608 . -737) 115787) ((-532 . -968) 115769) ((-273 . -1180) 115739) ((-801 . -97) T) ((-897 . -517) 115718) ((-1122 . -983) 115601) ((-458 . -588) 115509) ((-839 . -1020) T) ((-955 . -660) 115446) 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-21) T) ((-363 . -25) T) ((-636 . -486) NIL) ((-955 . -160) T) ((-654 . -223) T) ((-988 . -510) T) ((-475 . -97) T) ((-332 . -160) T) ((-321 . -566) 114314) ((-372 . -566) 114296) ((-451 . -669) T) ((-1038 . -787) T) ((-827 . -968) 114264) ((-103 . -789) T) ((-604 . -983) 114248) ((-462 . -126) T) ((-1159 . -984) T) ((-198 . -126) T) ((-1072 . -97) 114226) ((-94 . -1020) T) ((-225 . -612) 114210) ((-225 . -597) 114194) ((-604 . -107) 114173) ((-294 . -389) 114157) ((-225 . -351) 114141) ((-1075 . -215) 114088) ((-931 . -211) 114072) ((-72 . -1127) T) ((-47 . -160) T) ((-643 . -365) T) ((-643 . -134) T) ((-1194 . -97) T) ((-1009 . -983) 113915) ((-243 . -844) 113894) ((-227 . -844) 113873) ((-724 . -983) 113696) ((-722 . -983) 113539) ((-561 . -1127) T) ((-1080 . -566) 113521) ((-1009 . -107) 113350) ((-974 . -97) T) ((-452 . -1127) T) ((-438 . -983) 113321) ((-431 . -983) 113164) ((-610 . -594) 113148) ((-806 . -286) T) ((-724 . -107) 112957) ((-722 . -107) 112786) ((-333 . -594) 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. -486) 111540) ((-1114 . -942) 111524) ((-1096 . -566) 111506) ((-1101 . -33) T) ((-856 . -566) 111488) ((-1033 . -789) 111439) ((-713 . -566) 111421) ((-617 . -566) 111403) ((-1072 . -288) 111341) ((-455 . -33) T) ((-1013 . -1127) T) ((-454 . -429) T) ((-1009 . -977) T) ((-1057 . -33) T) ((-724 . -977) T) ((-722 . -977) T) ((-593 . -215) 111325) ((-581 . -215) 111271) ((-1146 . -286) 111250) ((-1009 . -304) 111211) ((-431 . -977) T) ((-1093 . -21) T) ((-1009 . -213) 111190) ((-724 . -304) 111167) ((-724 . -213) T) ((-722 . -304) 111139) ((-305 . -597) 111123) ((-674 . -1131) 111102) ((-1093 . -25) T) ((-57 . -33) T) ((-490 . -33) T) ((-488 . -33) T) ((-431 . -304) 111081) ((-305 . -351) 111065) ((-470 . -33) T) ((-469 . -33) T) ((-935 . -1067) NIL) ((-584 . -97) T) ((-560 . -97) T) ((-674 . -517) 110996) ((-333 . -669) T) ((-330 . -669) T) ((-322 . -669) T) ((-243 . -669) T) ((-227 . -669) T) ((-974 . -288) 110904) ((-836 . -1020) 110882) ((-49 . -977) T) ((-1183 . -21) T) ((-1183 . 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-1190) 103421) ((-297 . -429) 103400) ((-317 . -288) 103387) ((-550 . -23) T) ((-405 . -126) T) ((-604 . -594) 103361) ((-225 . -942) 103345) ((-807 . -286) T) ((-1195 . -1185) 103329) ((-643 . -37) 103316) ((-525 . -213) T) ((-468 . -223) T) ((-468 . -213) T) ((-713 . -734) T) ((-713 . -737) T) ((-1066 . -215) 103266) ((-1009 . -844) 103245) ((-112 . -37) 103232) ((-191 . -742) T) ((-190 . -742) T) ((-189 . -742) T) ((-188 . -742) T) ((-807 . -953) 103211) ((-1184 . -464) 103195) ((-724 . -844) 103174) ((-722 . -844) 103153) ((-1101 . -1127) T) ((-431 . -844) 103132) ((-680 . -464) 103116) ((-1009 . -594) 103041) ((-724 . -594) 102966) ((-573 . -983) 102953) ((-455 . -1127) T) ((-321 . -346) T) ((-132 . -464) 102935) ((-722 . -594) 102860) ((-1057 . -1127) T) ((-438 . -594) 102831) ((-243 . -821) 102690) ((-227 . -821) NIL) ((-113 . -983) 102635) ((-431 . -594) 102560) ((-610 . -968) 102537) ((-573 . -107) 102522) ((-333 . -968) 102506) ((-330 . -968) 102490) ((-322 . -968) 102474) 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99560) ((-1137 . -466) 99526) ((-294 . -934) 99505) ((-202 . -1020) 99483) ((-297 . -906) 99445) ((-100 . -97) T) ((-47 . -983) 99410) ((-1195 . -97) T) ((-359 . -97) T) ((-47 . -107) 99366) ((-936 . -588) 99348) ((-1159 . -566) 99330) ((-497 . -97) T) ((-473 . -97) T) ((-1051 . -1052) 99314) ((-143 . -1180) 99298) ((-225 . -1127) T) ((-1087 . -1131) 99277) ((-1043 . -1131) 99256) ((-220 . -21) 99167) ((-220 . -25) 99019) ((-123 . -115) 99003) ((-117 . -115) 98987) ((-43 . -687) 98971) ((-1087 . -517) 98882) ((-1043 . -517) 98813) ((-966 . -265) 98788) ((-758 . -126) T) ((-113 . -737) NIL) ((-113 . -734) NIL) ((-333 . -286) T) ((-330 . -286) T) ((-322 . -286) T) ((-1015 . -1127) T) ((-230 . -1032) 98699) ((-229 . -1032) 98610) ((-955 . -977) T) ((-935 . -984) T) ((-321 . -594) 98555) ((-571 . -37) 98539) ((-1184 . -566) 98501) ((-1184 . -567) 98462) ((-1000 . -566) 98444) ((-955 . -223) T) ((-332 . -977) T) ((-757 . -1180) 98414) ((-230 . -23) T) ((-229 . -23) T) ((-920 . -566) 98396) 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-566) 97496) ((-321 . -669) T) ((-30 . -566) 97478) ((-801 . -1020) T) ((-782 . -984) 97457) ((-39 . -594) 97402) ((-205 . -1131) T) ((-385 . -984) T) ((-1074 . -142) 97384) ((-931 . -269) 97335) ((-205 . -517) T) ((-297 . -1154) 97319) ((-297 . -1151) 97289) ((-1101 . -1104) 97268) ((-998 . -566) 97250) ((-593 . -142) 97234) ((-581 . -142) 97180) ((-1101 . -102) 97130) ((-455 . -1104) 97109) ((-462 . -138) T) ((-462 . -136) NIL) ((-1038 . -567) 97024) ((-416 . -566) 97006) ((-198 . -138) T) ((-198 . -136) NIL) ((-1038 . -566) 96988) ((-125 . -97) T) ((-51 . -97) T) ((-1137 . -588) 96940) ((-455 . -102) 96890) ((-926 . -23) T) ((-1195 . -37) 96860) ((-1087 . -1032) T) ((-1043 . -1032) T) ((-988 . -1131) T) ((-793 . -1032) T) ((-887 . -1131) 96839) ((-457 . -1131) 96818) ((-674 . -789) 96797) ((-988 . -517) T) ((-887 . -517) 96728) ((-1087 . -23) T) ((-1043 . -23) T) ((-793 . -23) T) ((-457 . -517) 96659) ((-1058 . -660) 96591) ((-1062 . -486) 96524) ((-966 . -567) NIL) ((-966 . -566) 96506) ((-801 . -660) 96476) ((-1122 . -46) 96445) ((-229 . -126) T) ((-230 . -126) T) ((-1024 . -1020) T) ((-935 . -1020) T) ((-60 . -566) 96427) ((-1082 . -789) NIL) ((-955 . -734) T) ((-955 . -737) T) ((-1199 . -983) 96414) ((-1199 . -107) 96399) ((-805 . -594) 96386) ((-1165 . -25) T) ((-1165 . -21) T) ((-1158 . -21) T) ((-1158 . -25) T) ((-1137 . -21) T) ((-1137 . -25) T) ((-958 . -142) 96370) ((-807 . -762) 96349) ((-807 . -855) T) ((-655 . -265) 96276) ((-551 . -21) T) ((-551 . -25) T) ((-550 . -21) T) ((-39 . -669) T) ((-202 . -486) 96209) ((-550 . -25) T) ((-453 . -142) 96193) ((-440 . -142) 96177) ((-856 . -736) T) ((-856 . -669) T) ((-713 . -735) T) ((-713 . -736) T) ((-475 . -1020) T) ((-713 . -669) T) ((-205 . -341) T) ((-1072 . -1020) 96155) ((-806 . -1131) T) ((-600 . -566) 96137) ((-806 . -517) T) ((-636 . -346) NIL) ((-337 . -1180) 96121) ((-616 . -97) T) ((-331 . -1180) 96105) ((-323 . -1180) 96089) ((-1194 . -1020) T) ((-491 . -789) 96068) ((-759 . -429) 96047) 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93520) ((-966 . -267) 93495) ((-537 . -669) T) ((-525 . -736) T) ((-157 . -341) 93446) ((-525 . -733) T) ((-525 . -669) T) ((-468 . -669) T) ((-1062 . -464) 93430) ((-1009 . -821) NIL) ((-806 . -1032) T) ((-113 . -844) NIL) ((-1193 . -1192) 93406) ((-1191 . -1192) 93385) ((-724 . -821) NIL) ((-722 . -821) 93244) ((-1186 . -25) T) ((-1186 . -21) T) ((-1125 . -97) 93222) ((-1026 . -373) T) ((-573 . -594) 93209) ((-431 . -821) NIL) ((-620 . -97) 93187) ((-1009 . -968) 93016) ((-806 . -23) T) ((-724 . -968) 92877) ((-722 . -968) 92736) ((-113 . -594) 92681) ((-431 . -968) 92559) ((-595 . -968) 92543) ((-576 . -97) T) ((-202 . -464) 92527) ((-1173 . -33) T) ((-584 . -660) 92511) ((-560 . -660) 92495) ((-616 . -37) 92455) ((-297 . -97) T) ((-83 . -566) 92437) ((-49 . -968) 92421) ((-1038 . -983) 92408) ((-1009 . -355) 92392) ((-724 . -355) 92376) ((-58 . -55) 92338) ((-641 . -736) T) ((-641 . -733) T) ((-538 . -968) 92325) ((-489 . -968) 92302) ((-641 . -669) T) ((-302 . -126) T) ((-294 . -977) 92193) ((-291 . -977) T) ((-157 . -1032) T) ((-722 . -355) 92177) ((-44 . -142) 92127) ((-936 . -925) 92109) ((-431 . -355) 92093) ((-385 . -160) T) ((-294 . -223) 92072) ((-291 . -223) T) ((-291 . -213) NIL) ((-273 . -1020) 91855) ((-205 . -126) T) ((-1038 . -107) 91840) ((-157 . -23) T) ((-741 . -138) 91819) ((-741 . -136) 91798) ((-230 . -588) 91706) ((-229 . -588) 91614) ((-297 . -263) 91580) ((-1072 . -486) 91513) ((-1051 . -1020) T) ((-205 . -986) T) ((-757 . -288) 91451) ((-1009 . -835) 91386) ((-724 . -835) 91329) ((-722 . -835) 91313) ((-1193 . -37) 91283) ((-1191 . -37) 91253) ((-1146 . -1032) T) ((-794 . -1032) T) ((-431 . -835) 91230) ((-797 . -1020) T) ((-1146 . -23) T) ((-532 . -1032) T) ((-794 . -23) T) ((-573 . -669) T) ((-333 . -855) T) ((-330 . -855) T) ((-268 . -97) T) ((-322 . -855) T) ((-988 . -126) T) ((-887 . -126) T) ((-113 . -736) NIL) ((-113 . -733) NIL) ((-113 . -669) T) ((-636 . -844) NIL) ((-974 . -486) 91131) ((-457 . -126) T) ((-532 . -23) T) ((-620 . -288) 91069) ((-584 . -704) T) ((-560 . -704) T) ((-1137 . -789) NIL) ((-935 . -269) T) ((-230 . -21) T) ((-636 . -594) 91019) ((-329 . -1020) T) ((-230 . -25) T) ((-229 . -21) T) ((-229 . -25) T) ((-143 . -37) 91003) ((-2 . -97) T) ((-845 . -855) T) ((-458 . -1180) 90973) ((-203 . -968) 90950) ((-1038 . -977) T) ((-654 . -286) T) ((-273 . -660) 90892) ((-643 . -984) T) ((-462 . -429) T) ((-385 . -486) 90804) ((-198 . -429) T) ((-1038 . -213) T) ((-274 . -142) 90754) ((-931 . -567) 90715) ((-931 . -566) 90697) ((-922 . -566) 90679) ((-112 . -984) T) ((-600 . -983) 90663) ((-205 . -466) T) ((-377 . -566) 90645) ((-377 . -567) 90622) ((-981 . -1180) 90592) ((-600 . -107) 90571) ((-1058 . -464) 90555) ((-757 . -37) 90525) ((-61 . -418) T) ((-61 . -373) T) ((-1075 . -97) T) ((-806 . -126) T) ((-459 . -97) 90503) ((-1199 . -346) T) ((-1003 . -97) T) ((-987 . -97) T) ((-329 . -660) 90448) ((-674 . -138) 90427) ((-674 . -136) 90406) ((-955 . -594) 90343) ((-494 . -1020) 90321) ((-337 . -97) T) ((-331 . -97) T) ((-323 . -97) T) ((-103 . -97) T) ((-477 . -1020) T) ((-332 . -594) 90266) ((-1087 . -588) 90214) ((-1043 . -588) 90162) ((-363 . -481) 90141) ((-775 . -787) 90120) ((-357 . -1131) T) ((-636 . -669) T) ((-317 . -984) T) ((-1137 . -925) 90072) ((-161 . -984) T) ((-98 . -566) 90004) ((-1089 . -136) 89983) ((-1089 . -138) 89962) ((-357 . -517) T) ((-1088 . -138) 89941) ((-1088 . -136) 89920) ((-1082 . -136) 89827) ((-385 . -269) T) ((-1082 . -138) 89734) ((-1044 . -138) 89713) ((-1044 . -136) 89692) ((-297 . -37) 89533) ((-157 . -126) T) ((-291 . -737) NIL) ((-291 . -734) NIL) ((-600 . -977) T) ((-47 . -594) 89498) ((-926 . -21) T) ((-123 . -942) 89482) ((-117 . -942) 89466) ((-926 . -25) T) ((-836 . -115) 89450) ((-1074 . -97) T) ((-758 . -789) 89429) ((-1146 . -126) T) ((-1087 . -25) T) ((-1087 . -21) T) ((-794 . -126) T) ((-1043 . -25) T) ((-1043 . -21) T) ((-793 . -25) T) ((-793 . -21) T) ((-724 . -286) 89408) ((-593 . -97) 89386) ((-581 . -97) T) ((-1075 . -288) 89181) ((-532 . -126) T) ((-571 . -787) 89160) ((-1072 . -464) 89144) ((-1066 . -142) 89094) ((-1062 . -566) 89056) ((-1062 . -567) 89017) ((-955 . -733) T) ((-955 . -736) T) ((-955 . -669) T) ((-459 . -288) 88955) ((-430 . -395) 88925) ((-329 . -160) T) ((-268 . -37) 88912) ((-253 . -97) T) ((-252 . -97) T) ((-251 . -97) T) ((-250 . -97) T) ((-249 . -97) T) ((-248 . -97) T) ((-247 . -97) T) ((-321 . -968) 88889) ((-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 . -983) 88712) ((-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) 88521) ((-616 . -211) 88505) ((-538 . -286) T) ((-489 . -286) T) ((-273 . -486) 88454) ((-103 . -288) NIL) ((-70 . -373) T) ((-1033 . -97) 88245) ((-775 . -389) 88229) ((-1038 . -737) T) ((-1038 . -734) T) ((-643 . -1020) T) ((-357 . -341) T) ((-157 . -466) 88207) ((-202 . -566) 88139) ((-128 . -1020) T) ((-112 . -1020) T) ((-47 . -669) T) ((-974 . -464) 88104) ((-132 . -403) 88086) ((-132 . -346) T) ((-958 . -97) T) ((-484 . -481) 88065) ((-453 . -97) T) ((-440 . -97) T) ((-965 . -1032) T) ((-1089 . -34) 88031) ((-1089 . -91) 87997) ((-1089 . -1116) 87963) ((-1089 . -1113) 87929) ((-1074 . -288) NIL) ((-87 . -374) T) ((-87 . -373) T) ((-1003 . -1067) 87908) ((-1088 . -1113) 87874) ((-1088 . -1116) 87840) ((-965 . -23) T) ((-1088 . -91) 87806) ((-532 . -466) T) ((-1088 . -34) 87772) ((-1082 . -1113) 87738) ((-1082 . -1116) 87704) ((-1082 . -91) 87670) ((-339 . -1032) T) ((-337 . -1067) 87649) ((-331 . -1067) 87628) ((-323 . -1067) 87607) ((-1082 . -34) 87573) ((-1044 . -34) 87539) ((-1044 . -91) 87505) ((-103 . -1067) T) ((-1044 . -1116) 87471) ((-775 . -984) 87450) ((-593 . -288) 87388) ((-581 . -288) 87239) ((-1044 . -1113) 87205) ((-655 . -977) T) ((-988 . -588) 87187) ((-1003 . -37) 87055) ((-887 . -588) 87003) 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-789) 86233) ((-229 . -789) 86184) ((-494 . -486) 86117) ((-806 . -588) 86094) ((-453 . -288) 86032) ((-440 . -288) 85970) ((-329 . -269) T) ((-1072 . -1161) 85954) ((-1058 . -566) 85916) ((-1058 . -567) 85877) ((-1056 . -97) T) ((-931 . -983) 85773) ((-39 . -835) 85725) ((-1072 . -558) 85702) ((-1199 . -594) 85689) ((-989 . -142) 85635) ((-807 . -1131) T) ((-931 . -107) 85517) ((-317 . -660) 85501) ((-801 . -566) 85483) ((-161 . -660) 85415) ((-385 . -265) 85373) ((-807 . -517) T) ((-103 . -378) 85355) ((-82 . -362) T) ((-82 . -373) T) ((-643 . -160) T) ((-94 . -669) T) ((-458 . -97) 85146) ((-94 . -450) T) ((-112 . -160) T) ((-1033 . -37) 85116) ((-157 . -588) 85064) ((-981 . -97) T) ((-806 . -25) T) ((-757 . -218) 85043) ((-806 . -21) T) ((-760 . -97) T) ((-392 . -97) T) ((-363 . -97) T) ((-106 . -288) NIL) ((-207 . -97) 85021) ((-123 . -1127) T) ((-117 . -1127) T) ((-965 . -126) T) ((-616 . -345) 85005) ((-931 . -977) T) ((-1146 . -588) 84953) ((-1024 . -566) 84935) ((-935 . -566) 84917) ((-487 . -23) T) ((-482 . -23) T) ((-321 . -286) T) ((-480 . -23) T) ((-300 . -126) T) ((-3 . -1020) T) ((-935 . -567) 84901) ((-931 . -223) 84880) ((-931 . -213) 84859) ((-1199 . -669) T) ((-1165 . -136) 84838) ((-775 . -1020) T) ((-1165 . -138) 84817) ((-1158 . -138) 84796) ((-1158 . -136) 84775) ((-1157 . -1131) 84754) ((-1137 . -136) 84661) ((-1137 . -138) 84568) ((-1136 . -1131) 84547) ((-357 . -126) T) ((-525 . -821) 84529) ((0 . -1020) T) ((-161 . -160) T) ((-157 . -21) T) ((-157 . -25) T) ((-48 . -1020) T) ((-1159 . -594) 84434) ((-1157 . -517) 84385) ((-657 . -1032) T) ((-1136 . -517) 84336) ((-525 . -968) 84318) ((-550 . -138) 84297) ((-550 . -136) 84276) ((-468 . -968) 84219) ((-85 . -362) T) ((-85 . -373) T) ((-807 . -341) T) ((-776 . -126) T) ((-769 . -126) T) ((-657 . -23) T) ((-475 . -566) 84201) ((-1195 . -984) T) ((-357 . -986) T) ((-957 . -1020) 84179) ((-836 . -33) T) ((-458 . -288) 84117) ((-1072 . -567) 84078) ((-1072 . -566) 84010) ((-1087 . -789) 83989) 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-1127) T) ((-103 . -211) 82792) ((-1093 . -97) T) ((-454 . -1020) T) ((-494 . -464) 82776) ((-680 . -33) T) ((-458 . -37) 82746) ((-132 . -33) T) ((-113 . -819) 82723) ((-113 . -821) NIL) ((-573 . -968) 82608) ((-592 . -789) 82587) ((-1183 . -97) T) ((-274 . -97) T) ((-655 . -346) 82566) ((-113 . -968) 82543) ((-368 . -660) 82527) ((-571 . -660) 82511) ((-44 . -288) 82315) ((-758 . -136) 82294) ((-758 . -138) 82273) ((-1194 . -360) 82252) ((-761 . -789) T) ((-1175 . -1020) T) ((-1075 . -209) 82199) ((-364 . -789) 82178) ((-1165 . -1116) 82144) ((-1165 . -1113) 82110) ((-1158 . -1113) 82076) ((-487 . -126) T) ((-1158 . -1116) 82042) ((-1137 . -1113) 82008) ((-1137 . -1116) 81974) ((-1165 . -34) 81940) ((-1165 . -91) 81906) ((-584 . -566) 81875) ((-560 . -566) 81844) ((-205 . -789) T) ((-1158 . -91) 81810) ((-1158 . -34) 81776) ((-1157 . -1032) T) ((-1038 . -594) 81763) ((-1137 . -91) 81729) ((-1136 . -1032) T) ((-548 . -142) 81711) ((-1003 . -327) 81690) ((-113 . -355) 81667) ((-113 . -316) 81644) ((-161 . -269) T) ((-1137 . -34) 81610) ((-805 . -286) T) ((-291 . -736) NIL) ((-291 . -733) NIL) ((-294 . -669) 81460) ((-291 . -669) T) ((-451 . -341) 81439) ((-337 . -327) 81418) ((-331 . -327) 81397) ((-323 . -327) 81376) ((-294 . -450) 81355) ((-1157 . -23) T) ((-1136 . -23) T) ((-661 . -1032) T) ((-657 . -126) T) ((-599 . -97) T) ((-454 . -660) 81320) ((-44 . -261) 81270) ((-100 . -1020) T) ((-66 . -566) 81252) ((-800 . -97) T) ((-573 . -835) 81211) ((-1195 . -1020) T) ((-359 . -1020) T) ((-80 . -1127) T) ((-988 . -789) T) ((-887 . -789) 81190) ((-113 . -835) NIL) ((-724 . -855) 81169) ((-656 . -789) T) ((-497 . -1020) T) ((-473 . -1020) T) ((-333 . -1131) T) ((-330 . -1131) T) ((-322 . -1131) T) ((-243 . -1131) 81148) ((-227 . -1131) 81127) ((-1033 . -211) 81097) ((-457 . -789) 81076) ((-1058 . -983) 81060) ((-368 . -704) T) ((-1074 . -770) T) ((-636 . -1127) T) ((-333 . -517) T) ((-330 . -517) T) ((-322 . -517) T) ((-243 . -517) 80991) ((-227 . -517) 80922) ((-1058 . -107) 80901) ((-430 . -687) 80871) ((-801 . -983) 80841) ((-759 . -37) 80783) ((-636 . -819) 80765) ((-636 . -821) 80747) ((-274 . -288) 80551) ((-845 . -1131) T) ((-616 . -389) 80535) ((-801 . -107) 80500) ((-636 . -968) 80445) ((-936 . -429) T) ((-845 . -517) T) ((-538 . -855) T) ((-451 . -1032) T) ((-489 . -855) T) ((-1072 . -267) 80422) ((-849 . -429) T) ((-63 . -566) 80404) ((-581 . -209) 80350) ((-451 . -23) T) ((-1038 . -736) T) ((-807 . -126) T) ((-1038 . -733) T) ((-1186 . -1188) 80329) ((-1038 . -669) T) ((-600 . -594) 80303) ((-273 . -566) 80045) ((-966 . -33) T) ((-757 . -787) 80024) ((-537 . -286) T) ((-525 . -286) T) ((-468 . -286) T) ((-1195 . -660) 79994) ((-636 . -355) 79976) ((-636 . -316) 79958) ((-454 . -160) T) ((-359 . -660) 79928) ((-806 . -789) NIL) ((-525 . -953) T) ((-468 . -953) T) ((-1051 . -566) 79910) ((-1033 . -218) 79889) ((-195 . -97) T) ((-1066 . -97) T) ((-69 . -566) 79871) ((-1058 . -977) T) ((-1093 . -37) 79768) ((-797 . -566) 79750) ((-525 . -510) T) ((-616 . -984) T) ((-674 . -884) 79703) ((-1058 . -213) 79682) ((-1005 . -1020) T) ((-965 . -25) T) ((-965 . -21) T) ((-935 . -983) 79627) ((-840 . -97) T) ((-801 . -977) T) ((-636 . -835) NIL) ((-333 . -307) 79611) ((-333 . -341) T) ((-330 . -307) 79595) ((-330 . -341) T) ((-322 . -307) 79579) ((-322 . -341) T) ((-462 . -97) T) ((-1183 . -37) 79549) ((-494 . -630) 79499) ((-198 . -97) T) ((-955 . -968) 79381) ((-935 . -107) 79310) ((-1089 . -906) 79279) ((-1088 . -906) 79241) ((-491 . -142) 79225) ((-1003 . -348) 79204) ((-329 . -566) 79186) ((-300 . -21) T) ((-332 . -968) 79163) ((-300 . -25) T) ((-1082 . -906) 79132) ((-1044 . -906) 79099) ((-74 . -566) 79081) ((-641 . -286) T) ((-157 . -789) 79060) ((-845 . -341) T) ((-357 . -25) T) ((-357 . -21) T) ((-845 . -307) 79047) ((-84 . -566) 79029) ((-641 . -953) T) ((-621 . -789) T) ((-1157 . -126) T) ((-1136 . -126) T) ((-836 . -942) 79013) ((-776 . -21) T) ((-47 . -968) 78956) ((-776 . -25) T) ((-769 . -25) T) ((-769 . -21) T) 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-288) 75334) ((-445 . -97) T) ((-550 . -906) 75303) ((-297 . -1020) T) ((-385 . -737) 75282) ((-385 . -734) 75261) ((-473 . -464) 75243) ((-1159 . -968) 75209) ((-1157 . -21) T) ((-1157 . -25) T) ((-1136 . -21) T) ((-1136 . -25) T) ((-757 . -660) 75151) ((-641 . -382) T) ((-1184 . -1127) T) ((-1033 . -389) 75120) ((-935 . -346) NIL) ((-98 . -33) T) ((-680 . -1127) T) ((-43 . -704) T) ((-548 . -97) T) ((-75 . -374) T) ((-75 . -373) T) ((-599 . -602) 75104) ((-132 . -1127) T) ((-806 . -138) T) ((-806 . -136) NIL) ((-329 . -977) T) ((-68 . -361) T) ((-68 . -373) T) ((-1081 . -97) T) ((-616 . -486) 75037) ((-632 . -288) 74975) ((-897 . -37) 74872) ((-678 . -37) 74842) ((-511 . -288) 74646) ((-294 . -1127) T) ((-329 . -213) T) ((-329 . -223) T) ((-291 . -1127) T) ((-268 . -1020) T) ((-1095 . -566) 74628) ((-654 . -1131) T) ((-1072 . -597) 74612) ((-1122 . -517) 74591) ((-654 . -517) T) ((-294 . -819) 74575) ((-294 . -821) 74500) ((-291 . -819) 74461) ((-291 . -821) NIL) ((-741 . -288) 74426) ((-297 . -660) 74267) ((-302 . -301) 74244) ((-460 . -97) T) ((-451 . -25) T) ((-451 . -21) T) ((-396 . -37) 74218) ((-294 . -968) 73886) ((-205 . -1113) T) ((-205 . -1116) T) ((-3 . -566) 73868) ((-291 . -968) 73798) ((-2 . -1020) T) ((-2 . |RecordCategory|) T) ((-775 . -566) 73780) ((-1033 . -984) 73711) ((-537 . -855) T) ((-525 . -762) T) ((-525 . -855) T) ((-468 . -855) T) ((-130 . -968) 73695) ((-205 . -91) T) ((-73 . -418) T) ((-73 . -373) T) ((0 . -566) 73677) ((-157 . -138) 73656) ((-157 . -136) 73607) ((-205 . -34) T) ((-48 . -566) 73589) ((-454 . -984) T) ((-462 . -211) 73571) ((-459 . -902) 73555) ((-458 . -787) 73534) ((-198 . -211) 73516) ((-79 . -418) T) ((-79 . -373) T) ((-1062 . -33) T) ((-757 . -160) 73495) ((-674 . -97) T) ((-957 . -566) 73462) ((-473 . -265) 73437) ((-294 . -355) 73407) ((-291 . -355) 73368) ((-291 . -316) 73329) ((-1007 . -566) 73311) ((-758 . -884) 73258) ((-608 . -126) T) ((-1146 . -136) 73237) ((-1146 . -138) 73216) ((-1089 . -97) T) 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72371) ((-654 . -341) T) ((-473 . -558) 72346) ((-643 . -107) 72331) ((-414 . -97) T) ((-44 . -1065) 72281) ((-112 . -107) 72266) ((-584 . -663) T) ((-560 . -663) T) ((-757 . -486) 72199) ((-966 . -1127) T) ((-878 . -142) 72183) ((-491 . -97) 72133) ((-1009 . -1131) 72112) ((-454 . -566) 72064) ((-454 . -567) 71986) ((-60 . -1127) T) ((-724 . -1131) 71965) ((-722 . -1131) 71944) ((-1087 . -429) 71875) ((-1074 . -1020) T) ((-1058 . -594) 71849) ((-1009 . -517) 71780) ((-458 . -389) 71749) ((-573 . -855) 71728) ((-431 . -1131) 71707) ((-1043 . -429) 71658) ((-376 . -566) 71640) ((-620 . -486) 71573) ((-724 . -517) 71484) ((-722 . -517) 71415) ((-674 . -288) 71402) ((-610 . -25) T) ((-610 . -21) T) ((-431 . -517) 71333) ((-113 . -855) 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) ((-1175 . -566) 71315) ((-1122 . -1032) T) ((-1122 . -23) T) ((-1082 . -288) 71200) ((-1044 . -288) 71187) ((-801 . -594) 71147) ((-1003 . -660) 71015) ((-878 . -913) 70999) ((-268 . -160) T) ((-845 . -21) T) ((-845 . -25) T) ((-807 . -789) 70950) ((-654 . -1032) T) ((-654 . -23) T) ((-593 . -1020) 70928) ((-581 . -563) 70903) ((-581 . -1020) T) ((-538 . -1131) T) ((-489 . -1131) T) ((-538 . -517) T) ((-489 . -517) T) ((-337 . -660) 70855) ((-331 . -660) 70807) ((-161 . -983) 70739) ((-317 . -983) 70723) ((-103 . -660) 70673) ((-161 . -107) 70584) ((-323 . -660) 70536) ((-317 . -107) 70515) ((-253 . -1020) T) ((-252 . -1020) T) ((-251 . -1020) T) ((-250 . -1020) T) ((-643 . -977) T) ((-249 . -1020) T) ((-248 . -1020) T) ((-247 . -1020) T) ((-194 . -1020) T) ((-193 . -1020) T) ((-191 . -1020) T) ((-157 . -1116) 70493) ((-157 . -1113) 70471) ((-190 . -1020) T) ((-189 . -1020) T) ((-112 . -977) T) ((-188 . -1020) T) ((-185 . -1020) T) ((-643 . -213) T) ((-184 . -1020) T) ((-183 . -1020) T) ((-182 . -1020) T) ((-181 . 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. -486) 67873) ((-359 . -360) 67852) ((-1093 . -389) 67836) ((-438 . -23) T) ((-431 . -23) T) ((-459 . -486) 67769) ((-268 . -269) T) ((-1005 . -566) 67751) ((-385 . -844) 67730) ((-49 . -1032) T) ((-955 . -855) T) ((-935 . -669) T) ((-655 . -821) NIL) ((-538 . -1032) T) ((-489 . -1032) T) ((-782 . -594) 67703) ((-1122 . -126) T) ((-1082 . -378) 67655) ((-936 . -288) NIL) ((-757 . -464) 67639) ((-332 . -855) T) ((-1072 . -33) T) ((-385 . -594) 67591) ((-49 . -23) T) ((-654 . -126) T) ((-655 . -968) 67473) ((-538 . -23) T) ((-103 . -486) NIL) ((-489 . -23) T) ((-157 . -387) 67444) ((-124 . -288) NIL) ((-1056 . -1020) T) ((-1186 . -1185) 67428) ((-643 . -737) T) ((-643 . -734) T) ((-1038 . -286) T) ((-357 . -138) T) ((-259 . -566) 67410) ((-1136 . -925) 67380) ((-47 . -855) T) ((-620 . -464) 67364) ((-230 . -1180) 67334) ((-229 . -1180) 67304) ((-1091 . -789) T) ((-1033 . -160) 67283) ((-1038 . -953) T) ((-974 . -33) T) ((-776 . -138) 67262) ((-776 . -136) 67241) ((-680 . -102) 67225) 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. -1065) 56808) ((-473 . -119) T) ((-106 . -558) 56783) ((-193 . -566) 56765) ((-451 . -34) 56731) ((-451 . -91) 56697) ((-191 . -566) 56679) ((-190 . -566) 56661) ((-189 . -566) 56643) ((-188 . -566) 56625) ((-185 . -566) 56607) ((-184 . -566) 56589) ((-183 . -566) 56571) ((-182 . -566) 56553) ((-181 . -566) 56535) ((-180 . -566) 56517) ((-179 . -566) 56499) ((-501 . -1023) 56451) ((-178 . -566) 56433) ((-177 . -566) 56415) ((-44 . -464) 56352) ((-176 . -566) 56334) ((-175 . -566) 56316) ((-757 . -107) 56207) ((-592 . -97) 56157) ((-458 . -265) 56134) ((-1033 . -566) 55866) ((-1021 . -1020) T) ((-974 . -1127) T) ((-573 . -1032) T) ((-1194 . -968) 55850) ((-1087 . -288) 55837) ((-1043 . -288) 55824) ((-113 . -1032) T) ((-761 . -97) T) ((-573 . -23) T) ((-1066 . -486) 55616) ((-364 . -97) T) ((-302 . -97) T) ((-935 . -835) 55568) ((-897 . -1020) T) ((-143 . -977) T) ((-113 . -23) T) ((-674 . -389) 55552) ((-678 . -1020) T) ((-658 . -1020) T) ((-645 . -127) T) ((-430 . -1020) T) ((-294 . 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. -267) 39621) ((-898 . -735) 39574) ((-898 . -736) 39527) ((-757 . -733) 39506) ((-112 . -286) T) ((-89 . -288) 39444) ((-620 . -33) T) ((-511 . -558) 39423) ((-47 . -25) T) ((-47 . -21) T) ((-757 . -736) 39374) ((-757 . -735) 39353) ((-643 . -953) T) ((-599 . -983) 39337) ((-898 . -669) 39236) ((-757 . -669) 39147) ((-898 . -450) 39100) ((-458 . -737) 39051) ((-458 . -734) 39002) ((-845 . -1180) 38989) ((-1093 . -977) T) ((-599 . -107) 38968) ((-1093 . -304) 38945) ((-1114 . -97) 38923) ((-1021 . -566) 38905) ((-643 . -510) T) ((-758 . -1020) T) ((-1183 . -977) T) ((-391 . -1020) T) ((-230 . -984) 38836) ((-229 . -984) 38767) ((-268 . -594) 38754) ((-548 . -265) 38729) ((-632 . -630) 38687) ((-897 . -566) 38669) ((-807 . -97) T) ((-678 . -566) 38651) ((-658 . -566) 38633) ((-1165 . -160) 38584) ((-1158 . -160) 38515) ((-1137 . -160) 38446) ((-641 . -789) T) ((-936 . -269) T) ((-430 . -566) 38428) ((-576 . -669) T) ((-58 . -1020) 38406) ((-225 . -142) 38390) ((-849 . -269) T) ((-955 . 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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 24140b69..0792e9e0 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3422100674) +(30 . 3424116437) (4258 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -460,646 +460,647 @@ |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |packageCall| |copy!| |pseudoQuotient| |lifting1| - |bernoulliB| |explicitEntries?| |s18dcf| |tablePow| - |fortranLiteralLine| |discriminantEuclidean| |palgint0| |plus| |droot| - |meshPar2Var| |rename!| |diagonalProduct| |OMUnknownSymbol?| |pdct| - |prefixRagits| |lieAlgebra?| |curveColor| |viewWriteAvailable| - |cycleSplit!| |leviCivitaSymbol| |drawComplex| |genericRightNorm| - |boundOfCauchy| |subresultantSequence| |setRealSteps| |addPoint| - |leftRankPolynomial| |cAcosh| |setLabelValue| |exponents| |ran| - |findBinding| |unrankImproperPartitions1| |taylorRep| |plenaryPower| - |deepExpand| |op| |c06gcf| |numberOfImproperPartitions| |negative?| - |error| |complexEigenvectors| |cubic| |aLinear| |antiCommutator| - |yellow| |newTypeLists| |times| |extractSplittingLeaf| |leftUnits| - |palgint| |coefficients| |unitNormalize| |assert| |setEmpty!| - |showAllElements| |Lazard2| |iisin| ~= |identity| |intensity| - |invertibleElseSplit?| |constantOperator| |primitive?| |s17dlf| - |optional?| |htrigs| |rquo| |optimize| |expintegrate| |coerce| |iitan| - |interpolate| |spherical| |lhs| |ord| |quotient| |cyclicEntries| - |viewDeltaXDefault| |univariateSolve| |f01rcf| |construct| |any| - |complex?| |rhs| |representationType| |odd?| |setright!| |kmax| - |generate| |clearTable!| |completeHensel| |startPolynomial| |meatAxe| - |points| |high| |groebnerIdeal| |numberOfNormalPoly| - |rightAlternative?| |integerBound| |separant| |s17akf| |nullSpace| - |romberg| |finite?| |sech2cosh| |showAll?| |rules| |subPolSet?| - |magnitude| |cAtan| |branchIfCan| |identitySquareMatrix| |incrementBy| - |s13adf| |semiSubResultantGcdEuclidean2| |normalise| |innerint| - |s17def| |froot| |width| |argscript| |commaSeparate| - |uncouplingMatrices| |externalList| |expand| |universe| |factorials| - |edf2ef| |compBound| |fortranCompilerName| |e02zaf| |rightQuotient| - |rightNorm| |permutationRepresentation| |minimumDegree| |tab| - |filterWhile| |operation| |lazyEvaluate| |sumOfDivisors| |curryRight| - |consnewpol| |f01qcf| |abs| |maxIndex| |movedPoints| |nil| |simpsono| - |fTable| |shuffle| |filterUntil| |readable?| |identification| |recip| - |lprop| |numerators| |iomode| |OMputInteger| |c06fpf| - |probablyZeroDim?| |pToDmp| |condition| |select| |ODESolve| - |UnVectorise| |doubleDisc| 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|semiIndiceSubResultantEuclidean| - |genericRightDiscriminant| |summation| |leftExactQuotient| |UP2ifCan| - |getOperands| |changeVar| |pi| |bfEntry| |sorted?| |deref| - |linearPart| |alphanumeric| |gbasis| |s17dhf| |infinity| - |lastSubResultantElseSplit| |prefix?| |cardinality| |symmetricSquare| - |useEisensteinCriterion| |prinpolINFO| |pomopo!| |mainValue| |cExp| - |unvectorise| |dilog| |diagonal| |extendedResultant| |light| - |structuralConstants| |sumOfKthPowerDivisors| |ldf2lst| |Si| - |OMlistCDs| |credPol| |sin| |polyred| - |semiDegreeSubResultantEuclidean| |symFunc| |complexForm| |kernel| - |binaryFunction| |dmpToP| |nonQsign| |graphCurves| |lyndon?| |f01maf| - |null?| |generateIrredPoly| |byte| |draw| |exists?| - |showTheRoutinesTable| |in?| |cos| |leftRecip| |removeSquaresIfCan| - |solveid| |aspFilename| |edf2fi| |slash| |pointColor| |key?| - |linGenPos| |currentSubProgram| |super| ^ |sec2cos| |explogs2trigs| - |viewpoint| |leftRemainder| |lquo| |infix?| |computeCycleEntry| - |mainDefiningPolynomial| |opeval| |stosePrepareSubResAlgo| |sum| - |bipolar| |unitCanonical| |listOfMonoms| |subCase?| |mask| - |musserTrials| |c06eaf| |reducedForm| |prevPrime| |defineProperty| - |makeObject| |intcompBasis| |reducedSystem| |f01brf| |ode1| |repSq| - |tan2trig| |linearAssociatedExp| |lazyPseudoQuotient| - |numericalOptimization| |f02aef| |generalInfiniteProduct| |mr| - |makeMulti| |UpTriBddDenomInv| |remove| |makeTerm| |determinant| - |prinb| |powmod| |cSin| |outputFloating| |coefChoose| - |viewThetaDefault| |over| |implies| |coef| |doubleResultant| - |frobenius| |bubbleSort!| |f07fef| |matrix| |makeSketch| |OMgetObject| - |collect| |BasicMethod| |xor| |last| |OMputEndBVar| |rischDE| - |removeConstantTerm| |firstNumer| |binaryTournament| |OMserve| |Ci| - |setEpilogue!| |assoc| |shufflein| |primes| |clearTheSymbolTable| - |iflist2Result| |factorList| |omError| |quadraticForm| |equality| - |fortranComplex| |modifyPointData| |primlimitedint| |position!| - |solveRetract| |functionIsFracPolynomial?| |palginfieldint| - |clipParametric| |chiSquare1| |box| |exprToUPS| |isQuotient| - |sinIfCan| |size?| |nextIrreduciblePoly| |eigenvalues| |c05adf| |cond| - |rootBound| |mapUnivariateIfCan| |intersect| |ignore?| |realRoots| - |inR?| |scanOneDimSubspaces| |withPredicates| |exquo| |leftMult| - |rewriteSetByReducingWithParticularGenerators| |fortranDoubleComplex| - |generic| |coordinate| |viewSizeDefault| |indicialEquations| |div| - |logIfCan| |alphanumeric?| |optpair| |complexExpand| - |chineseRemainder| |reducedContinuedFraction| |hyperelliptic| |sample| - |quo| |symbolTableOf| |An| |errorInfo| |linSolve| |measure2Result| - |rightUnits| |numberOfPrimitivePoly| |charpol| |palglimint| |hclf| - |height| |clearDenominator| |reduceLODE| |functionIsOscillatory| - |numberOfMonomials| |predicates| |sumOfSquares| |rem| - |variationOfParameters| |pToHdmp| - |generalizedContinuumHypothesisAssumed?| |weights| - |selectOrPolynomials| |OMputVariable| |bsolve| |weakBiRank| |presuper| - |rowEchelon| |bag| |integralMatrix| |changeMeasure| |zero?| - |categoryFrame| |complexIntegrate| |extractIndex| |fortranLinkerArgs| - |iidprod| |sinhIfCan| |OMgetEndApp| |extractPoint| |rightUnit| - |setPrologue!| |resetVariableOrder| |dequeue!| |quote| |monicModulo| - |nonSingularModel| |prepareSubResAlgo| |delta| |lyndonIfCan| - |children| |mirror| |d02cjf| |printCode| |selectOptimizationRoutines| - |setProperties!| |modularGcd| |systemCommand| |isPower| - |mainCoefficients| |scripted?| |polygamma| |duplicates| |makeSin| - |mapBivariate| |oddlambert| |mantissa| |child| |ravel| - |monicLeftDivide| |dmpToHdmp| |pair?| |printInfo!| |makeVariable| - |outputMeasure| |leftUnit| |definingEquations| |parabolic| |reshape| - |upperCase| |printTypes| |curveColorPalette| - |conditionsForIdempotents| |factorAndSplit| - |removeSuperfluousQuasiComponents| |realElementary| - |halfExtendedSubResultantGcd2| |newLine| |iiacsch| - |leftMinimalPolynomial| |outlineRender| |s19adf| |rightRemainder| - |resize| |eigenvector| |rootDirectory| |sdf2lst| - |resultantReduitEuclidean| |standardBasisOfCyclicSubmodule| - |deleteRoutine!| |lexico| |iitanh| |argument| |cyclePartition| - |integer?| |not| |complexSolve| |groebnerFactorize| |algDsolve| - |addPointLast| |shiftRoots| |someBasis| |createThreeSpace| - |lazyResidueClass| |printingInfo?| |lambda| |HermiteIntegrate| - |s14aaf| |factorByRecursion| |rarrow| |factorGroebnerBasis| |equation| - |fillPascalTriangle| |axesColorDefault| |univariatePolynomialsGcds| - |createGenericMatrix| |update| |zoom| |basicSet| |cSech| |cAsinh| - |setref| |nullary| |toseLastSubResultant| |monomial?| |tower| - |univariatePolynomial| |figureUnits| |OMgetEndBVar| |setTex!| - |setOrder| |pascalTriangle| |prindINFO| |outputAsTex| |var1Steps| - |delay| |divideIfCan!| |solveLinearlyOverQ| |product| |acothIfCan| - |lepol| |algintegrate| |computeBasis| |diagonal?| |label| |toScale| - |iifact| |ode| |extendedIntegrate| |nodes| |inHallBasis?| |power!| - |pushdterm| |ScanArabic| |Nul| |prefix| |logGamma| |perfectNthRoot| - |bracket| |vconcat| |poisson| |position| |makeEq| |multiset| - |ScanRoman| |localIntegralBasis| |showFortranOutputStack| |OMsend| - |component| |solveLinearPolynomialEquationByRecursion| |sub| - |subResultantGcd| |dflist| |randomLC| |objects| |palgLODE0| - |incrementKthElement| |fractionFreeGauss!| |exponential| |supersub| - |polyRDE| |base| |mix| |degreeSubResultantEuclidean| |iisec| - |skewSFunction| |permutationGroup| |squareFreePolynomial| - |rationalFunction| |showSummary| |option| |createMultiplicationTable| - |cos2sec| |indices| |oddInfiniteProduct| |iroot| |iiacoth| |normal| - |OMputEndAttr| |qqq| |iibinom| |OMgetType| |binomThmExpt| - |commutativeEquality| |second| UTS2UP |sh| |bits| |showAttributes| - |setsubMatrix!| |basisOfLeftNucloid| |external?| |increase| |digit?| - |ffactor| |currentCategoryFrame| |resultantEuclidean| |third| - |datalist| |checkPrecision| |getMatch| |cross| 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|collectUnder| |linearDependenceOverZ| - |rangePascalTriangle| |dimensionOfIrreducibleRepresentation| |tanSum| - |primintfldpoly| |stopTableGcd!| |overset?| |lowerCase!| RF2UTS - |createPrimitiveElement| |stopTableInvSet!| |obj| - |createLowComplexityTable| |critMonD1| |elRow2!| |integerIfCan| - |cSinh| |printHeader| |selectsecond| |stiffnessAndStabilityFactor| - |double| |matrixGcd| |rombergo| |split| |headReduce| - |commonDenominator| |OMgetFloat| |cache| |level| |fortranLogical| - |extendedEuclidean| |atom?| |numeric| |elementary| |separateDegrees| - |getVariableOrder| |genericLeftMinimalPolynomial| |measure| - |backOldPos| |tab1| |radical| |bitLength| |intPatternMatch| |monom| - |PollardSmallFactor| |cCosh| |supDimElseRittWu?| |supRittWu?| - |hdmpToDmp| |rightFactorIfCan| |resultant| |e01bef| |traverse| |swap| - |listLoops| |getProperty| |cfirst| |cons| |swap!| |OMsupportsSymbol?| - |whileLoop| |evaluate| |lazyPremWithDefault| |getZechTable| |operator| - |infieldIntegrate| |superscript| |common| |nextLatticePermutation| - |coth2trigh| |lfextlimint| |rightMult| |swapRows!| |lllp| |pastel| - |acschIfCan| |monomialIntegrate| |PDESolve| |acscIfCan| |rootSplit| - |setClipValue| |cAsech| |f04adf| GF2FG |impliesOperands| - |expenseOfEvaluationIF| |merge!| |log10| |numberOfFactors| |compdegd| - |declare!| |innerSolve| |mapExpon| |f04faf| |s17adf| |diff| - |linearPolynomials| |graeffe| |vark| |bitand| |f01ref| |prem| |iiasin| - |expintfldpoly| |solveLinear| |internalAugment| |enumerate| |tan2cot| - |integral?| |fill!| |bitior| |setprevious!| |selectAndPolynomials| - |multinomial| |genericRightMinimalPolynomial| |OMbindTCP| |presub| - |middle| |bivariateSLPEBR| |setFieldInfo| |choosemon| - |algebraicDecompose| |seriesSolve| |reseed| |binding| |homogeneous?| - |processTemplate| |multisect| |mesh| |transcendent?| - |positiveRemainder| |e02bdf| |dn| |setPoly| |ramified?| |qfactor| - |curryLeft| |lazyPseudoRemainder| |triangulate| |lowerCase| |df2ef| - |remove!| NOT |safeFloor| |cAcot| |build| |aQuadratic| |setPredicates| - |outputAsScript| |dimension| |t| |low| |nthFlag| |internalIntegrate| - OR |expint| |headReduced?| |alphabetic| |zerosOf| |extractProperty| - |viewDeltaYDefault| |lintgcd| |linear?| |raisePolynomial| |atanIfCan| - AND |corrPoly| |viewWriteDefault| |qelt| |represents| |tanhIfCan| - |readIfCan!| |stoseSquareFreePart| |less?| |OMunhandledSymbol| - |cyclotomic| |compound?| |rewriteIdealWithHeadRemainder| - |zeroSetSplitIntoTriangularSystems| |top!| |irreducibleFactor| - |hconcat| |laplacian| |quasiAlgebraicSet| |eigenMatrix| |init| |void| - |changeWeightLevel| |purelyAlgebraicLeadingMonomial?| |eyeDistance| - |eigenvectors| |multiplyExponents| |xRange| |vertConcat| |blue| - |e04dgf| |rroot| |rewriteSetWithReduction| |quadratic| |addPoint2| - |prod| |removeRedundantFactors| |outputFixed| |realEigenvectors| - |yRange| |scaleRoots| |d01gbf| |xn| |lookup| |listexp| |pointData| - |brace| |stoseInvertible?sqfreg| |OMputError| |region| - |numericalIntegration| |gcdPrimitive| |zRange| |setScreenResolution3D| - |taylorQuoByVar| |removeDuplicates!| |euler| |numFunEvals| - |infRittWu?| |laurentRep| |pointLists| |univariatePolynomials| |space| - |prepareDecompose| |map!| |multMonom| |setPosition| |rowEchelonLocal| - |d01alf| |complexNormalize| |wordsForStrongGenerators| |dmp2rfi| - |approxNthRoot| |null| |laguerre| |getMeasure| |setnext!| |qsetelt!| - F2FG |segment| |sortConstraints| |declare| |assign| |equiv| |index?| - |OMputApp| |mathieu24| |monicDecomposeIfCan| |case| |sizeLess?| - |tanAn| |node| |lSpaceBasis| |redpps| |genericLeftDiscriminant| - |duplicates?| |iteratedInitials| |laguerreL| |acotIfCan| |value| - |mulmod| |B1solve| |Zero| |primextendedint| |initiallyReduce| |f02awf| - |cTanh| |zag| |root| |schema| |bumptab1| |insert!| |rk4a| |front| * - |One| |physicalLength!| |splitNodeOf!| |gcdcofactprim| |knownInfBasis| - |green| |finiteBound| |shiftLeft| |ramifiedAtInfinity?| |stFunc2| - |convergents| |Gamma| |sinhcosh| ~ |mpsode| |approximants| - |perfectSqrt| |lineColorDefault| |scale| |var1StepsDefault| - |makeResult| |expandTrigProducts| |d02raf| |nextsubResultant2| |acsch| - |denomRicDE| |modularFactor| |inverseLaplace| |wholeRagits| - |newSubProgram| |e02baf| |remainder| |bezoutMatrix| |constantOpIfCan| - |partitions| |string?| |alternating| |restorePrecision| |makingStats?| - |viewPhiDefault| |primitiveElement| |epilogue| |write!| - |removeSuperfluousCases| |resetAttributeButtons| |radicalRoots| - |number?| |d02bhf| |s17acf| |cycleRagits| |paren| |wordInGenerators| - |elt| |e04gcf| |s21bdf| |crest| |stirling2| |moebiusMu| |karatsuba| - |acoshIfCan| |subNodeOf?| |palgextint| |Frobenius| Y |showTheIFTable| - |shade| |open| |showScalarValues| |anfactor| |key| |associator| - |decomposeFunc| |monomialIntPoly| |ratpart| |coerceP| |order| |se2rfi| - |tanIfCan| |associative?| |basisOfRightAnnihilator| |options| - |setFormula!| |nullity| |OMgetEndObject| |unexpand| |unit| |pushdown| - |shanksDiscLogAlgorithm| UP2UTS |fixedPoints| |decimal| |f02agf| - |fractRagits| |reverseLex| |selectPDERoutines| |normalizedAssociate| - |principalIdeal| |members| |dim| |preprocess| |setButtonValue| - |iisqrt2| |filename| |c06gqf| |idealiserMatrix| |id| |repeating?| - |constDsolve| |predicate| |showRegion| |indiceSubResultant| - |usingTable?| |pr2dmp| |integers| |normalDeriv| |f04mbf| |s20adf| - |reduced?| |prologue| |dimensions| |factorFraction| |getCurve| |nthr| - |coefficient| |cCsc| |arg1| |normalDenom| |minRowIndex| - |unprotectedRemoveRedundantFactors| |not?| |roman| |table| |round| - |goodnessOfFit| |fortranTypeOf| |lighting| |totalDegree| - |removeRoughlyRedundantFactorsInPol| |arg2| |basisOfLeftAnnihilator| - |parse| |ptFunc| |new| |leastPower| |realZeros| |multiEuclidean| - |binaryTree| |startTableGcd!| |vedf2vef| |removeCoshSq| |psolve| - |factorset| |midpoint| |basisOfLeftNucleus| |tanintegrate| - |mainCharacterization| |conditions| |binarySearchTree| |qinterval| - |numberOfComputedEntries| |s17aff| |rectangularMatrix| |setleaves!| - |iiasinh| |sup| |match| |iicot| |getConstant| - |unrankImproperPartitions0| |inverseIntegralMatrixAtInfinity| |e01saf| - |matrixDimensions| |fullPartialFraction| |certainlySubVariety?| - |maxdeg| |realEigenvalues| |OMgetApp| |complexElementary| - |patternVariable| |lastSubResultant| |binary| |asimpson| - |makeViewport2D| |reducedDiscriminant| |stripCommentsAndBlanks| - |setMinPoints| |extendIfCan| |trunc| |test| |entry| - |integralBasisAtInfinity| |complexRoots| |redPol| |find| |iiacot| - |polar| |subMatrix| |sizePascalTriangle| |moduleSum| |primitivePart| - |nextNormalPrimitivePoly| |rightCharacteristicPolynomial| - |primlimintfrac| |bombieriNorm| |cotIfCan| |getRef| |curry| |sts2stst| - |traceMatrix| |heap| |imaginary| |imagj| |reciprocalPolynomial| - |initial| |RittWuCompare| |insertionSort!| |eq| |center| - |singularitiesOf| |rightDiscriminant| |addMatchRestricted| - |semiSubResultantGcdEuclidean1| |reverse| |escape| |OMconnInDevice| - |leftGcd| |iter| |e02bef| |left| |messagePrint| |nthFactor| |conjug| - |#| |leader| |jacobiIdentity?| |listBranches| |updateStatus!| |any?| - |right| |imagE| |factorSquareFreeByRecursion| |currentScope| - |singularAtInfinity?| |stoseInvertibleSetreg| |decompose| - |zeroDimPrime?| |randomR| |hasHi| |squareTop| |debug| |pleskenSplit| - |iicsch| |modulus| |fractRadix| |nextPartition| |rotatez| |diag| - |cCsch| |removeIrreducibleRedundantFactors| |setOfMinN| |bottom!| - |index| |generalizedEigenvector| |sin?| |iiatan| |cn| |f02fjf| - |quotientByP| |expt| |formula| |setScreenResolution| |quotedOperators| - |OMgetBind| |elements| |updatF| |setMaxPoints| |latex| |exp| - |pointColorPalette| |hasPredicate?| |splitSquarefree| - |primPartElseUnitCanonical!| |rootsOf| |complexLimit| |rst| |pair| - |critT| |stoseInvertibleSetsqfreg| |iilog| |leftExtendedGcd| |genus| - |leadingIndex| |sqfree| |ocf2ocdf| |Lazard| |balancedBinaryTree| - |iicoth| |submod| |reset| |elliptic| |sqfrFactor| |outputArgs| - |roughUnitIdeal?| |definingInequation| |nrows| |edf2efi| - |bivariatePolynomials| |back| |localAbs| |OMopenFile| |redmat| - |rightRank| |fortranDouble| |ncols| |maxint| |oddintegers| - |reduceByQuasiMonic| |write| |splitLinear| |saturate| - |purelyTranscendental?| |optAttributes| |generalPosition| |save| - |quadratic?| |makeCos| |pile| |red| |cscIfCan| |zeroDimensional?| - |leftPower| |SFunction| |isOp| |pointColorDefault| |numberOfDivisors| - |isPlus| |c06gsf| |torsionIfCan| |createNormalElement| |drawToScale| - |gderiv| |schwerpunkt| |algebraicVariables| |showTheFTable| - |minPoints3D| |minPoly| |e01sbf| |rightGcd| |message| |reorder| - |drawCurves| |result| |increasePrecision| |beauzamyBound| |bumprow| - |asecIfCan| |stoseIntegralLastSubResultant| |totalfract| |noKaratsuba| - |subtractIfCan| BY |changeNameToObjf| |loadNativeModule| |mapGen| - |closed?| |dec| |llprop| |e04naf| |trapezoidal| |c05pbf| |print| - |ricDsolve| |argumentListOf| |upperCase?| |symmetricPower| - |blankSeparate| |fractionPart| |coerceS| |OMcloseConn| |OMReadError?| - |sylvesterSequence| |name| |palgLODE| |plus!| |makeop| - |completeEchelonBasis| |prime| |composite| |subscriptedVariables| - |HenselLift| |d01bbf| |evenlambert| |rightScalarTimes!| |hcrf| - |parameters| |c05nbf| |setMinPoints3D| |or| |cPower| |queue| - |morphism| |tableForDiscreteLogarithm| |po| |simplifyLog| |setClosed| - |cAsin| |viewport2D| |LiePoly| |and| |var2StepsDefault| |OMgetAttr| - |even?| |setProperty| F |createMultiplicationMatrix| |unitNormal| - |d01apf| |conditionP| |univariate?| |semiResultantEuclidean2| - |partition| |mindegTerm| |times!| |trivialIdeal?| |tracePowMod| - |quickSort| |fortranReal| |explicitlyFinite?| |charthRoot| |mapmult| - |useSingleFactorBound| |testDim| |root?| |radix| |countRealRoots| - |createPrimitivePoly| |symmetricProduct| |antisymmetric?| |resetNew| - |euclideanNormalForm| |inconsistent?| |relationsIdeal| |retract| - |fixedPoint| |graphs| |pdf2df| |setrest!| |rischNormalize| - |rightPower| |imagi| |transpose| |wrregime| |cyclicGroup| |f04qaf| - |partialQuotients| |tanNa| |rightMinimalPolynomial| - |constantCoefficientRicDE| |accuracyIF| |lfintegrate| |e04fdf| - |f02wef| |typeList| |characteristic| |s19abf| |sayLength| - |OMconnOutDevice| |rowEch| |plotPolar| |forLoop| |bitCoef| |d01asf| - |mainSquareFreePart| |ScanFloatIgnoreSpacesIfCan| |nthRoot| |lambert| - |tryFunctionalDecomposition| |monomials| |ratDenom| - |doublyTransitive?| |leftOne| |cAcsch| |mathieu11| |wreath| |iisqrt3| - |color| |rightOne| |f07fdf| |yCoord| |algebraicCoefficients?| |iipow| - |idealiser| |constantRight| |c06fuf| |euclideanSize| |e02daf| - |drawComplexVectorField| |leftCharacteristicPolynomial| |rCoord| - |cAcoth| |tRange| |d02gaf| |totalLex| |lastSubResultantEuclidean| - |diagonalMatrix| |check| |comparison| |myDegree| |fortran| |content| - |integral| |goodPoint| |clipWithRanges| |associatorDependence| |imagI| - |d01gaf| |degree| |createNormalPrimitivePoly| |roughEqualIdeals?| - |unmakeSUP| |fortranInteger| |OMreadStr| |polarCoordinates| - |appendPoint| |addmod| |pushup| |setTopPredicate| |primitivePart!| - |semiDiscriminantEuclidean| |totalDifferential| |lazyPrem| - |nonLinearPart| |OMgetString| |select!| |element?| |firstDenom| - |showArrayValues| |expPot| |enqueue!| |groebgen| - |irreducibleRepresentation| |tubePoints| |splitDenominator| |isTimes| - |mat| |addMatch| |createRandomElement| |primaryDecomp| |separate| - |c06ekf| |toroidal| |compiledFunction| |mainPrimitivePart| - |OMputSymbol| |gethi| |makeSeries| |rootSimp| |fortranCharacter| - |failed?| |degreeSubResultant| |squareFreePart| - |integralLastSubResultant| |moduloP| |rightExtendedGcd| |hermite| - |transcendentalDecompose| |dominantTerm| |rootPower| |property| - |basisOfCentroid| |c06fqf| |lazyVariations| |pointSizeDefault| - |writeLine!| |lifting| |factorPolynomial| |mainVariable?| |iicosh| - |qPot| |s18adf| |monicRightFactorIfCan| |orthonormalBasis| - |internalInfRittWu?| |inf| = |airyAi| |cycleLength| |nodeOf?| |biRank| - |exprHasLogarithmicWeights| |intermediateResultsIF| |basisOfCenter| - |factorSFBRlcUnit| |prinshINFO| |harmonic| |delete!| |rangeIsFinite| - |algSplitSimple| |units| |f01qef| |selectfirst| |generator| |connect| - |point| < |associates?| |rdregime| |inc| |selectODEIVPRoutines| - |linearAssociatedLog| |hasSolution?| |e02aef| |userOrdered?| > - |totolex| |implies?| |ellipticCylindrical| |internalZeroSetSplit| - |concat!| |hspace| |getGoodPrime| <= |iiacsc| |minset| - |clearTheFTable| |explimitedint| |coercePreimagesImages| |getOrder| - |fixedPointExquo| |series| >= |useEisensteinCriterion?| |legendre| - |iicos| |OMgetEndAttr| |lazyIrreducibleFactors| |extract!| |nextItem| - |factorsOfCyclicGroupSize| |minrank| |perfectNthPower?| |gcdcofact| - |solve| |hMonic| |LyndonBasis| |leftRank| |s18def| |s18aef| |code| - |list| |setColumn!| |real?| |insertRoot!| |orOperands| |ideal| + - |float?| |setValue!| |youngGroup| |car| |att2Result| |controlPanel| - |functionIsContinuousAtEndPoints| |curve| |min| - |f2df| - |RemainderList| |nativeModuleExtension| |basisOfNucleus| |cdr| - |bipolarCylindrical| |script| |leaf?| |BumInSepFFE| / |ksec| |e02agf| - |safeCeiling| |setDifference| |closedCurve?| |initTable!| - |basisOfMiddleNucleus| |notelem| |integralRepresents| |coord| - |varList| |exprex| |setIntersection| |getExplanations| - |extensionDegree| |complexZeros| |insertTop!| |Vectorise| - |SturmHabicht| |extension| |cTan| |setUnion| |tex| |startStats!| - |unit?| |routines| |setlast!| |dot| |f04axf| |apply| |lyndon| - |rewriteIdealWithRemainder| |inRadical?| |makeYoungTableau| |pdf2ef| - |initials| |systemSizeIF| |branchPointAtInfinity?| |failed| |cot2trig| - |exprHasWeightCosWXorSinWX| |OMsupportsCD?| |rationalPoints| |axes| - |leftTraceMatrix| |rule| |size| |factorSquareFreePolynomial| - |tubeRadiusDefault| |differentialVariables| |setAdaptive3D| |d01fcf| - |distance| |isAbsolutelyIrreducible?| |limitedIntegrate| |birth| - |iicsc| |numberOfOperations| |s17dgf| |properties| |nextSubsetGray| - |OMencodingXML| |radicalEigenvector| |mkIntegral| |shift| |ddFact| - |e02ahf| |leadingCoefficientRicDE| |lo| |cycle| |groebSolve| - |precision| |translate| |tValues| |OMputEndBind| |cartesian| |first| - |dictionary| |s15aef| |subspace| |incr| |upDateBranches| |tree| - |inrootof| |OMgetError| |readLine!| |lieAdmissible?| |rest| |updatD| - |parent| |e02dff| |hi| |conjugates| |mainKernel| |s18acf| - |separateFactors| |d03edf| |mightHaveRoots| |copyInto!| - |strongGenerators| |dark| |completeEval| |exprToGenUPS| - |characteristicPolynomial| |integer| |doubleFloatFormat| |subHeight| - |evaluateInverse| |trigs| |critMTonD1| |primintegrate| |transform| - |rightRecip| |rightTraceMatrix| |gradient| |numberOfFractionalTerms| - |henselFact| |subset?| |nil| |infinite| |arbitraryExponent| + |Record| |Union| |lfextlimint| |reverseLex| |mainPrimitivePart| + |tableau| |mantissa| |problemPoints| |equation| |upperCase!| + |nullSpace| |flagFactor| |degree| |printCode| |cross| |parameters| + |nextPrimitivePoly| |void| |leftTraceMatrix| |increment| |makeSin| + |dflist| |hyperelliptic| |generalInfiniteProduct| |testDim| + |rootDirectory| |fractRadix| |sylvesterSequence| |symbolIfCan| + |implies?| |polygon?| |regime| |karatsubaOnce| |error| |sts2stst| + |lazy?| |meshPar2Var| |getlo| |normalDeriv| |unitNormal| |lyndon?| + |create| |laurentIfCan| |assert| |measure| |e04fdf| |primes| + |scalarTypeOf| |nullary| |overbar| |s19acf| |asimpson| |ldf2lst| + |bandedHessian| |f07fef| ~= |s18def| |sturmVariationsOf| + |coefficients| |radicalRoots| RF2UTS |generalizedEigenvectors| + |vedf2vef| |optimize| |triangular?| |coerce| |df2fi| |rightMult| + |countRealRootsMultiple| |e01sbf| |abs| |e04mbf| |perfectSquare?| + |reduceByQuasiMonic| |construct| |nextPrimitiveNormalPoly| + |jordanAdmissible?| |s17dcf| |lhs| + |dimensionOfIrreducibleRepresentation| |initializeGroupForWordProblem| + |less?| |ellipticCylindrical| |completeEval| |csc| |/\\| |sparsityIF| + |cCos| |complete| |rhs| |build| |high| |createNormalPrimitivePoly| + |reduceBasisAtInfinity| |solve1| |asin| |\\/| + |createPrimitiveNormalPoly| |constantRight| |mainVariables| + |remainder| |deref| |traceMatrix| |physicalLength!| + |selectOptimizationRoutines| |acos| |rightOne| |testModulus| + |selectPDERoutines| |root?| |s18aef| |lexico| |gethi| |randomLC| + |makeMulti| |leftScalarTimes!| |atan| |musserTrials| + |seriesToOutputForm| |f02adf| |f04mbf| |iteratedInitials| |nil| + |permanent| |typeLists| |OMencodingSGML| |power| |acot| |width| + |leadingSupport| |factorSquareFreePolynomial| |mapdiv| |ranges| + |rightGcd| |finite?| |outerProduct| |backOldPos| |flexibleArray| + |minPol| |asec| |numberOfHues| |harmonic| |swapRows!| + |toseInvertibleSet| |triangularSystems| |makeViewport2D| |rotatez| + |Si| |f02wef| |sample| |acsc| |bezoutMatrix| |pointLists| |lowerCase?| + |recolor| |number?| |Lazard2| |createPrimitiveElement| |approximate| + |pushdterm| |mapDown!| |makeSketch| |rename!| |sinh| |objectOf| + |d02ejf| |complex| |elliptic| |divergence| |sincos| |var2Steps| + |maxIndex| |nextPrime| |solveLinearPolynomialEquationByFractions| + |checkPrecision| |safetyMargin| |clearTheSymbolTable| |cosh| + |medialSet| |setColumn!| |d01apf| |f02bjf| |radix| |iitanh| + |subResultantsChain| |rootSplit| |dim| |OMunhandledSymbol| + |splitLinear| |removeCoshSq| |tanh| |rightExtendedGcd| |optional| + |pushucoef| |toseLastSubResultant| |scan| |algebraicDecompose| + |aQuadratic| |tanSum| |roughEqualIdeals?| |exprToGenUPS| + |modularGcdPrimitive| |coth| |varselect| |delete!| |powerAssociative?| + |s20adf| |linearPart| |reorder| |null?| |heap| |log| |infiniteProduct| + |graphState| |sech| |c06ecf| |sdf2lst| |cLog| |c06eaf| |lex| |c06fuf| + |merge| |palgLODE0| |alphabetic?| |setProperties!| |csch| |f02fjf| + |substring?| |unitNormalize| |meshFun2Var| |constantOpIfCan| |f07fdf| + |e02adf| |revert| |fracPart| |Ei| |setelt| |compdegd| + |normalizedAssociate| |OMputFloat| |changeThreshhold| |inverseColeman| + |numFunEvals| |tab1| |normInvertible?| |UpTriBddDenomInv| |asinh| + |removeSquaresIfCan| |suffix?| |startTable!| |setVariableOrder| + |gcdprim| |returnTypeOf| |cyclicSubmodule| + |rewriteIdealWithQuasiMonicGenerators| |legendreP| |splitNodeOf!| + |acosh| |copy| |one?| |simpson| |d02bhf| |real?| |squareFreePart| + |cyclotomic| |wronskianMatrix| |internalDecompose| |interpret| |atanh| + |d01aqf| |prefix?| |countRealRoots| |tubeRadiusDefault| |OMwrite| + |adaptive3D?| |branchIfCan| |invmultisect| |internalZeroSetSplit| + |typeList| |acoth| |autoCoerce| |univariatePolynomials| |cycle| + |create3Space| |primintfldpoly| |drawCurves| |primextintfrac| + |generalizedEigenvector| |unmakeSUP| |OMgetObject| |symbolTableOf| + |asech| |headRemainder| |OMgetEndAtp| |crushedSet| |partialNumerators| + |partitions| |parametric?| |quasiComponent| |imaginary| + |iflist2Result| |psolve| |hermite| |conditionP| |reduced?| |s17acf| + |lllip| |commutator| |expenseOfEvaluationIF| |symmetricRemainder| + |diagonalProduct| |taylorIfCan| D |semiSubResultantGcdEuclidean2| + |randnum| |monomial?| |insertRoot!| |hasTopPredicate?| |gcdPrimitive| + |initial| |in?| |incrementKthElement| |linearAssociatedOrder| + |characteristicPolynomial| |setchildren!| |makeSUP| |distdfact| + |movedPoints| |makeSeries| |checkForZero| |bitLength| |saturate| + |postfix| |cAcos| |infix?| |useSingleFactorBound?| |coshIfCan| + |stopTableGcd!| |inverse| |sech2cosh| |identitySquareMatrix| + |OMlistCDs| |makeTerm| |OMputAtp| |mask| |differentialVariables| + |listRepresentation| |alphanumeric| |increasePrecision| |diag| + |firstUncouplingMatrix| |ipow| |brillhartTrials| |and?| + |createPrimitivePoly| |minimumExponent| |c05pbf| |compose| + |ScanArabic| |rename| |stoseInvertible?reg| |dfRange| |baseRDEsys| + |nsqfree| |principalIdeal| |constantToUnaryFunction| |untab| + |infinite?| |compound?| |jordanAlgebra?| |gcdcofactprim| + |leftAlternative?| |continuedFraction| |semiResultantEuclidean1| + |string?| |setClipValue| |infRittWu?| |matrix| |fortranInteger| |An| + |characteristic| ^ |groebSolve| |toseInvertible?| |every?| + |generalSqFr| |generateIrredPoly| |integralLastSubResultant| + |permutation| |OMsetEncoding| |collect| |hermiteH| |weierstrass| + |orOperands| |cycleRagits| |rootSimp| |sin?| |fractionFreeGauss!| + |remove| |factorset| |airyBi| |nary?| |prologue| |iidsum| |simpsono| + |putColorInfo| |removeRoughlyRedundantFactorsInContents| |imagj| + |evenInfiniteProduct| |concat!| |partialDenominators| |univariate?| + |geometric| |overset?| |mr| |isQuotient| |setScreenResolution3D| + |leftRecip| |stopTable!| |last| |doubleFloatFormat| |factorList| + |mindeg| |critB| |univariatePolynomial| |beauzamyBound| |gbasis| + |quoted?| |assoc| |credPol| |iprint| |OMUnknownSymbol?| |getRef| + |imagk| |startTableInvSet!| |alternating| |callForm?| |showAll?| + |merge!| |intPatternMatch| |setAttributeButtonStep| |modularGcd| |sub| + |symmetricProduct| |members| |ideal| |ricDsolve| |Nul| + |groebnerFactorize| |socf2socdf| |purelyTranscendental?| |lagrange| + |imagJ| |nil?| |interval| |getDatabase| |cCsch| |OMreadStr| + |determinant| |hitherPlane| |rightAlternative?| |next| + |genericLeftNorm| |linearlyDependent?| |infLex?| |karatsubaDivide| + |height| |setvalue!| |exquo| |chiSquare| |knownInfBasis| + |degreePartition| |getVariableOrder| |setAdaptive3D| |dimensions| + |fTable| |OMgetInteger| |cAsech| |div| |rewriteIdealWithHeadRemainder| + |basisOfRightNucloid| |palgintegrate| |scopes| |selectFiniteRoutines| + |extendedint| |paren| |fortranCharacter| |quo| |modTree| + |reciprocalPolynomial| |s19abf| |max| |structuralConstants| |delta| + |tValues| |asechIfCan| |lowerCase!| |bumprow| |pureLex| |normalForm| + |hspace| |chiSquare1| |mergeFactors| |figureUnits| + |possiblyNewVariety?| |s17dhf| |restorePrecision| |rem| |exponential| + |BasicMethod| |squareFreeFactors| |c06ebf| |outputList| |e02bcf| + |prime?| |cCot| |pseudoDivide| |taylorQuoByVar| |setleft!| |errorInfo| + |readIfCan!| |semiResultantEuclidean2| |antisymmetric?| |eulerE| + |argumentListOf| |f01mcf| |omError| |midpoint| |qelt| + |SturmHabichtMultiple| |truncate| |expextendedint| |float?| |rootOf| + |subHeight| |pdct| |expr| |zeroDimPrimary?| |elColumn2!| |errorKind| + |tanh2coth| |subPolSet?| |permutations| |returnType!| |d01gaf| + |xRange| |wordInGenerators| |asecIfCan| |logGamma| |sayLength| + |optAttributes| |systemCommand| |lambda| |yRange| + |exteriorDifferential| |belong?| |f2df| |shuffle| |member?| |s17agf| + |mathieu23| |zRange| |aLinear| |expandPower| |zeroVector| + |lastSubResultantElseSplit| |numberOfCycles| |linearMatrix| |green| + |removeSinhSq| |ravel| |map!| |variable| |sum| UP2UTS |qqq| + |upperCase?| |makingStats?| |setfirst!| |reshape| |qsetelt!| |nthCoef| + |lazyPremWithDefault| |firstSubsetGray| |fortran| |OMreceive| + |setValue!| |ptFunc| |s18dcf| |leftFactor| |cot2trig| |simplifyExp| + |csch2sinh| |closed?| |not| |normalizeAtInfinity| |f07aef| + |clearCache| |nor| |getIdentifier| |readable?| |makeUnit| + |selectNonFiniteRoutines| |separateFactors| |OMopenFile| |groebgen| + |smith| |RemainderList| |increase| |lyndonIfCan| |module| |zoom| + |createNormalElement| |tab| |simpleBounds?| |alphanumeric?| + |linearAssociatedExp| |update| |tower| |acsch| |iibinom| |rowEchelon| + |inverseIntegralMatrixAtInfinity| |numberOfComposites| |llprop| + |linearAssociatedLog| |prefix| |chebyshevT| |antiCommutator| + |trapezoidalo| |var2StepsDefault| |row| |objects| |digamma| |root| + |empty?| |kmax| |imagE| |algebraicSort| |d02raf| |base| + |rewriteSetWithReduction| |removeIrreducibleRedundantFactors| + |mainDefiningPolynomial| |move| |s17dlf| |extractBottom!| |twoFactor| + |e02bbf| |OMParseError?| |drawStyle| |byte| |LyndonWordsList| + |normDeriv2| |tanNa| |label| |exprHasWeightCosWXorSinWX| + |getZechTable| |clip| |mathieu22| |bernoulli| |f04adf| + |partialFraction| |tablePow| |leastPower| |realEigenvalues| + |doubleResultant| |fixedPoints| |leftExactQuotient| |minrank| + |nativeModuleExtension| |laurentRep| |lexTriangular| |redmat| |mesh| + |position| |iiatanh| |possiblyInfinite?| |cAcosh| |pop!| |zeroDim?| + |zero| |s13adf| |hue| |subSet| |rk4| |leftOne| |e04jaf| |s19adf| + |nextSublist| |script| |genericLeftTraceForm| |moduloP| |ffactor| + |d03edf| |triangulate| |irreducibleRepresentation| |mathieu12| + |ef2edf| |goto| |e04naf| |And| |iiatan| |hasSolution?| |removeSinSq| + |showSummary| |palgRDE0| |factorsOfDegree| |satisfy?| |drawToScale| + |e04ucf| |digit| |Or| |shellSort| |digits| |children| |option| + |PDESolve| |commonDenominator| |yellow| |lazyEvaluate| |outputForm| + |makeFloatFunction| |tex| |quadratic| |Not| |numberOfFactors| + |lazyPseudoQuotient| |schema| |showAttributes| |entry?| |charClass| + |pomopo!| |exQuo| |OMgetType| |e01saf| |insertMatch| |basisOfNucleus| + |complementaryBasis| |rightMinimalPolynomial| |d01ajf| |normal| + |zeroMatrix| |bandedJacobian| |OMgetAttr| + |factorSquareFreeByRecursion| |multiple?| |nextsubResultant2| + |repeatUntilLoop| |optpair| |coordinates| |pole?| |linear?| |bindings| + |phiCoord| |hash| |stoseInternalLastSubResultant| |previous| + |clearTable!| |internalSubQuasiComponent?| |fortranLiteralLine| + |mapUnivariate| |repeating| |region| |euclideanGroebner| |operator| + |perfectNthPower?| |asinhIfCan| |trapezoidal| |OMserve| |opeval| + |decimal| |OMputSymbol| |setLabelValue| |returns| |UP2ifCan| |count| + |resultantnaif| |concat| |endSubProgram| |rightRank| + |cyclotomicDecomposition| |myDegree| |romberg| |trace2PowMod| |pade| + |cycleEntry| |integralMatrix| |exponent| |complexNumeric| |exp1| + |f02bbf| |multiple| |power!| |ScanRoman| |tubePoints| |cAcsch| + |OMsupportsCD?| |e02akf| |OMputEndObject| |varList| |complexExpand| + |realZeros| |applyQuote| |cycles| |nextPartition| + |reducedDiscriminant| |rightRemainder| |enterPointData| |monomRDE| + |gderiv| |f2st| |kernels| |subResultantGcdEuclidean| |exactQuotient| + |replace| |primitivePart| |zeroSetSplit| |sumOfDivisors| + |LagrangeInterpolation| |basicSet| |denomRicDE| |interpolate| + |addPoint2| |univariate| |mightHaveRoots| |currentCategoryFrame| + |directory| |OMgetFloat| |infieldIntegrate| |matrixDimensions| + |cyclicEqual?| |gcdPolynomial| |stopTableInvSet!| |specialTrigs| + |bumptab1| |ruleset| |fullDisplay| |f01maf| |bag| |noLinearFactor?| + |stop| |twist| |gcdcofact| |indicialEquation| |bipolarCylindrical| + |e02aef| |numericalOptimization| |curry| |acscIfCan| |mainValue| + |completeHensel| |reduction| |squareMatrix| |setPredicates| + |halfExtendedSubResultantGcd1| |sPol| |factor| |f04asf| + |nthFractionalTerm| |elliptic?| |subResultantGcd| |exponents| + |simplifyPower| |cSech| |s13acf| |adaptive?| |prod| |properties| + |sqrt| |Ci| |constantCoefficientRicDE| |suchThat| |c06gbf| + |euclideanSize| |lp| |even?| |splitDenominator| |getOperands| + |coHeight| |rspace| |real| |translate| |discriminantEuclidean| + |stosePrepareSubResAlgo| |integerBound| |redPo| |schwerpunkt| + |indiceSubResultant| |putGraph| |argument| |mathieu11| |pack!| |imag| + |Aleph| |fortranDouble| |f07adf| |changeMeasure| |addiag| + |listYoungTableaus| |csc2sin| |leaf?| |directProduct| |multiEuclidean| + |complexNumericIfCan| |genericLeftMinimalPolynomial| + |numericalIntegration| |isobaric?| |extendedSubResultantGcd| + |singular?| |newTypeLists| |antisymmetricTensors| |stFuncN| |leftZero| + |associatedSystem| |iCompose| |float| |iiacosh| |d01akf| + |expenseOfEvaluation| |superscript| |curryRight| + |stripCommentsAndBlanks| |acothIfCan| |destruct| |copyInto!| + |chineseRemainder| |ran| |orthonormalBasis| |rationalPoints| + |areEquivalent?| |createLowComplexityTable| |fullPartialFraction| + |depth| |infix| |resultantEuclidean| |modularFactor| |critT| |f02agf| + |constant?| |genericRightTrace| |dihedralGroup| |plus| |insert!| + |mirror| |startPolynomial| |OMputObject| |debug3D| |isTimes| + |indiceSubResultantEuclidean| |outputAsScript| |f02aef| + |completeHermite| |integral?| |collectUnder| |contractSolve| |resize| + |solve| |extend| |monomial| |wordInStrongGenerators| |userOrdered?| + |rdregime| |intChoose| |d02kef| |e02daf| |s17ahf| |changeVar| + |autoReduced?| |multivariate| |accuracyIF| |palgint0| |adaptive| + |setProperty| |equiv| |wreath| |usingTable?| |cyclePartition| + |denominator| |variables| |times| |rootOfIrreduciblePoly| + |setEpilogue!| |OMgetApp| |solid?| |hex| |unitCanonical| + |extractSplittingLeaf| |zero?| |algebraicVariables| |maxint| + |frobenius| GE |transcendent?| |normalElement| |internalInfRittWu?| + |cAsinh| |nextLatticePermutation| |d01anf| |overlabel| |binaryTree| GT + |clipSurface| |nthExponent| |unary?| |fill!| |f02akf| |overlap| + |inverseLaplace| |setMinPoints| |reducedContinuedFraction| |f04mcf| LE + |lowerCase| |leadingBasisTerm| |cosIfCan| |critMonD1| |sturmSequence| + |hMonic| |consnewpol| LT |rk4a| |OMencodingUnknown| |secIfCan| |df2st| + |drawComplexVectorField| |stoseInvertibleSetsqfreg| |eigenvector| + |mat| |certainlySubVariety?| |particularSolution| |rules| |taylor| + |getMatch| |strongGenerators| |complexElementary| |raisePolynomial| + |bringDown| |c02aff| |subResultantChain| |match?| |showTheFTable| + |interpretString| |laurent| |roughBasicSet| |internal?| |optional?| + |singleFactorBound| |atoms| |fractRagits| |OMgetVariable| |meatAxe| + |invertibleSet| |puiseux| |totolex| |d02cjf| |sort| + |positiveRemainder| |rationalPoint?| |content| |fi2df| |pr2dmp| |axes| + |dimension| |linearDependenceOverZ| |bipolar| |fintegrate| |call| + |colorDef| |df2ef| |nextNormalPrimitivePoly| |pointSizeDefault| + |bfEntry| |createMultiplicationMatrix| |leftUnits| |wholeRagits| + |integer?| |inv| |realEigenvectors| |droot| |c06frf| |discreteLog| + |clipPointsDefault| |condition| |gramschmidt| |iisqrt3| |rightTrace| + |coth2trigh| |categoryFrame| |cSec| |ground?| |divide| |lfintegrate| + |shufflein| |resultantReduitEuclidean| |setMaxPoints| + |localIntegralBasis| |lowerPolynomial| |critBonD| |anticoord| + |LyndonBasis| |listOfMonoms| |ground| |readLineIfCan!| + |polynomialZeros| |meshPar1Var| |halfExtendedResultant1| |dec| + |fortranLogical| |vark| |clipBoolean| |setref| |tubePointsDefault| + |internalLastSubResultant| |extendIfCan| |monicRightFactorIfCan| + |leadingMonomial| |setProperty!| |approxSqrt| |random| |bubbleSort!| + |yCoord| |pol| |cExp| |iiabs| |virtualDegree| |recoverAfterFail| + |elRow2!| |minPoints3D| |stopMusserTrials| |leadingCoefficient| + |computeBasis| |resultantEuclideannaif| |oddintegers| + |numberOfChildren| |integral| |f01qcf| |patternMatchTimes| |cschIfCan| + |rst| |primitiveMonomials| |decompose| |bfKeys| |startTableGcd!| + |bitTruth| |patternVariable| |entry| |calcRanges| |po| + |multiplyExponents| |rangePascalTriangle| |low| |newSubProgram| + |tan2cot| |reductum| |cap| |writable?| |cAcsc| |vectorise| + |wordsForStrongGenerators| |atanIfCan| |changeName| + |factorGroebnerBasis| |leftRank| |leftCharacteristicPolynomial| + |points| |radicalSolve| |dark| |front| |reducedQPowers| |htrigs| + |writeLine!| |head| |setAdaptive| |retractIfCan| |sorted?| + |fortranCarriageReturn| |generators| |assign| |scaleRoots| + |rightCharacteristicPolynomial| |chebyshevU| |chvar| |OMgetEndObject| + |minPoly| |complexIntegrate| |color| |useSingleFactorBound| + |selectsecond| |perspective| |e02bdf| |basisOfRightNucleus| |latex| + |indices| |integralBasis| |deepestTail| |subQuasiComponent?| + |subCase?| |trueEqual| |OMopenString| |headReduced?| |inGroundField?| + |function| |showFortranOutputStack| |c06gcf| |OMgetBind| + |halfExtendedSubResultantGcd2| |e02baf| |plusInfinity| |terms| |trunc| + |addMatch| |parent| |product| |realSolve| |nilFactor| |f01ref| + |lexGroebner| |diff| |numer| |nthFactor| |makeYoungTableau| + |minusInfinity| |flatten| |basisOfCommutingElements| |outputSpacing| + |d02gaf| |mainMonomial| |extendedEuclidean| |quotientByP| + |rowEchelonLocal| |denom| |column| |cfirst| |principal?| + |expressIdealMember| |eval| |zeroDimPrime?| |denomLODE| |B1solve| + |dequeue!| |true| |innerSolve| |cSin| |unvectorise| |expIfCan| + |simplifyLog| |dimensionsOf| |discriminant| |find| |reducedSystem| + |diagonal?| |semiResultantEuclideannaif| |bezoutDiscriminant| |space| + |linearDependence| |kroneckerDelta| |pi| |vertConcat| |algebraic?| + |isOp| |intersect| |s01eaf| |purelyAlgebraic?| UTS2UP |c06fqf| + |stoseLastSubResultant| |infinity| |buildSyntax| |doubleDisc| + |nthRoot| |separate| |mkIntegral| |stiffnessAndStabilityFactor| + |numberOfComponents| |transpose| |Vectorise| |goodPoint| |newLine| + |option?| |iicos| |element?| |iiasinh| |squareTop| |alphabetic| + |fortranDoubleComplex| LODO2FUN |rightExactQuotient| |useNagFunctions| + |perfectSqrt| |fixPredicate| |elements| |map| |e02zaf| |getBadValues| + |type| |hypergeometric0F1| |ptree| |totalLex| |viewpoint| |imagK| + |symbolTable| |colorFunction| |absolutelyIrreducible?| |kernel| + |linearPolynomials| |unexpand| |semicolonSeparate| |ode| |reflect| + |double| |copy!| |graphStates| |printInfo!| |draw| |pdf2ef| |read!| + |d01alf| |numberOfImproperPartitions| |binaryFunction| |tanh2trigh| + |oneDimensionalArray| ** |rightLcm| |nextColeman| + |pushFortranOutputStack| |minus!| |obj| |getProperties| |conjug| + |ReduceOrder| |wholePart| |complex?| |lllp| |iiacot| |primextendedint| + |lighting| |subscriptedVariables| |popFortranOutputStack| + |sylvesterMatrix| |mkcomm| |insert| |cache| |oddInfiniteProduct| + |Hausdorff| |numberOfMonomials| |henselFact| + |rightRegularRepresentation| |e02dff| |bracket| |shallowCopy| |lcm| + |outputAsFortran| |swap!| |listexp| |OMputVariable| EQ |convert| + |boundOfCauchy| |fmecg| SEGMENT |quote| |symmetricGroup| |sh| + |validExponential| |makeObject| |shift| |outputFloating| + |OMgetEndError| |addBadValue| |lazyVariations| |coerceImages| + |chainSubResultants| |generic| |matrixGcd| |const| + |radicalOfLeftTraceForm| |append| |blue| |cup| |minIndex| |setClosed| + |normal01| |tube| |zerosOf| |ddFact| |f01brf| |associator| |gcd| + |iiacsch| |createNormalPoly| |coef| |fillPascalTriangle| |updatF| + |c06ekf| |pointColorDefault| |exprToXXP| |declare!| |wholeRadix| + |monicCompleteDecompose| |union| |numerator| |unravel| |graeffe| + |unparse| |d02bbf| |removeZero| |lambert| |constant| |laguerreL| + |leftRemainder| |lastSubResultantEuclidean| |pseudoQuotient| |false| + |makeVariable| |setProperties| |unit| |firstDenom| |extractIfCan| + |pleskenSplit| |setErrorBound| |highCommonTerms| |critM| |wrregime| + |getGraph| |SturmHabicht| |search| |recur| |minordet| |rightQuotient| + |shiftRight| |monomRDEsys| |polar| |computeInt| |midpoints| |d02gbf| + |iroot| |representationType| |selectIntegrationRoutines| + |complexNormalize| |extendedIntegrate| |lineColorDefault| |dom| |erf| + |iisin| |edf2efi| |sizeMultiplication| |iisinh| |jacobiIdentity?| + |pastel| |initials| |sup| |OMgetEndAttr| |sqfrFactor| |style| |rank| + |vconcat| |totalDegree| |HenselLift| |kovacic| + |semiResultantReduitEuclidean| |negative?| |dmpToP| |predicates| + |showIntensityFunctions| |bits| |removeRedundantFactorsInContents| + |sinh2csch| |flexible?| |clipParametric| |roughBase?| |child?| + |toroidal| |subset?| |seriesSolve| |iExquo| |rombergo| |conjugates| + |multiEuclideanTree| |ignore?| |integralCoordinates| + |OMsupportsSymbol?| |e02ddf| |subresultantSequence| |dilog| + |rangeIsFinite| |nand| |monicModulo| |initiallyReduce| |close| + |mainVariable| |vector| |coefChoose| |bsolve| |lfunc| + |numberOfDivisors| |sin| |title| |doubleComplex?| |character?| + |lifting1| |OMputEndApp| |decomposeFunc| |differentiate| |palgextint0| + |cAsin| |s18aff| |alternatingGroup| + |removeRoughlyRedundantFactorsInPols| |cos| |linears| |coordinate| + |display| |ode1| |outputMeasure| |e04dgf| |OMgetBVar| |sumOfSquares| + |ridHack1| |tan| |identity| |e02ahf| |lists| |atanhIfCan| + |diagonalMatrix| |extension| |rightTrim| |e| |f02xef| |contours| + |log2| |tryFunctionalDecomposition| |output| |cot| |outputArgs| |tail| + |combineFeatureCompatibility| |cyclicParents| |getSyntaxFormsFromFile| + |leftTrim| |systemSizeIF| |showArrayValues| |xCoord| |scale| |segment| + |cyclicGroup| |bivariatePolynomials| |polCase| |pushdown| + |axesColorDefault| |rightNorm| |f02axf| |sec| |OMputEndAtp| + |deleteProperty!| |enterInCache| |d01bbf| |iiacoth| |square?| |iicot| + |lazyIrreducibleFactors| |reseed| |input| |fprindINFO| |duplicates?| + |removeRoughlyRedundantFactorsInPol| |leftRegularRepresentation| + |leftMinimalPolynomial| |computePowers| |infinityNorm| |frst| |sn| + |mainKernel| |library| |limit| |ParCond| |rotatex| + |complexEigenvectors| |orbit| |groebner| |isPlus| |setPoly| + |noncommutativeJordanAlgebra?| |prinshINFO| |setsubMatrix!| |top| + |leftUnit| |nullary?| |listBranches| |hasoln| + |semiIndiceSubResultantEuclidean| |algSplitSimple| |continue| + |nonSingularModel| |f02awf| |extractProperty| |monomialIntPoly| + |whileLoop| |vspace| |sort!| |jacobian| ~ |repSq| |subMatrix| + |exptMod| |leadingCoefficientRicDE| |e01daf| |weakBiRank| + |viewThetaDefault| |extractClosed| |var1StepsDefault| |nextNormalPoly| + |f04qaf| |rubiksGroup| |set| |viewSizeDefault| |showAllElements| + |cTan| |associatedEquations| |cAtanh| |extract!| |monomials| |submod| + |bernoulliB| |coerceListOfPairs| |poisson| |aromberg| |rroot| + |viewport2D| |OMencodingBinary| |positive?| |minColIndex| + |closedCurve| |split| |orbits| |evenlambert| |symbol?| + |collectQuasiMonic| |setRealSteps| |permutationRepresentation| + |useEisensteinCriterion| |choosemon| |topPredicate| |back| + |generalizedInverse| |expPot| |exponential1| |getConstant| |hdmpToP| + |open| |precision| |conjugate| |rationalIfCan| |lquo| |operation| + |antiAssociative?| |shanksDiscLogAlgorithm| + |univariatePolynomialsGcds| |eisensteinIrreducible?| |c06gsf| + |basisOfLeftAnnihilator| |basisOfLeftNucloid| |rootPoly| + |OMputEndError| |ratpart| |neglist| |cubic| |odd?| |mesh?| |cTanh| + |s18acf| |viewDeltaYDefault| |modifyPoint| |tubePlot| |OMputEndAttr| + |leastAffineMultiple| |sin2csc| |semiLastSubResultantEuclidean| + |moreAlgebraic?| |check| |linear| |definingEquations| + |branchPointAtInfinity?| |genericRightDiscriminant| |updateStatus!| + |d01amf| |printInfo| |createZechTable| |indicialEquations| + |leastMonomial| |startStats!| |outlineRender| |quasiRegular| + |rootRadius| |makeResult| |sizePascalTriangle| |li| |explicitEntries?| + |polynomial| |totalGroebner| |show| |genericRightTraceForm| |e02gaf| + |evaluate| |bit?| |indicialEquationAtInfinity| |localAbs| |makeEq| + |prepareSubResAlgo| |rightScalarTimes!| |ratDenom| |over| + |fixedDivisor| |computeCycleLength| |nextItem| |trace| |sign| + |tan2trig| |headReduce| |SturmHabichtCoefficients| |dioSolve| + |reopen!| |algebraicOf| |subresultantVector| |more?| |comparison| + |partialQuotients| |external?| |pattern| |mainContent| + |removeDuplicates!| |presuper| |enqueue!| |minimumDegree| |addPoint| + |prinpolINFO| |swapColumns!| |s15adf| |parabolic| |second| |LiePoly| + |unaryFunction| |createGenericMatrix| |mergeDifference| |s20acf| + |computeCycleEntry| |lintgcd| |zag| |coerceP| |third| |say| |any?| + |failed?| |torsion?| |torsionIfCan| |unrankImproperPartitions0| + |reify| |basis| |polygon| |s17ajf| |setright!| |e01baf| |magnitude| + |distribute| |contains?| |selectODEIVPRoutines| |unit?| |iiasec| + |c05nbf| |range| |isList| |or?| |any| |finiteBasis| |moduleSum| + |center| |logIfCan| |collectUpper| |andOperands| + |semiSubResultantGcdEuclidean1| |summation| |setOfMinN| + |expandTrigProducts| |heapSort| |makeCrit| |multiset| |hcrf| + |cycleElt| |slex| |resultant| |subst| |factorsOfCyclicGroupSize| + |exists?| |bright| |OMread| |constructorName| |divisors| + |OMUnknownCD?| GF2FG |csubst| |generalLambert| |currentEnv| |algint| + |minRowIndex| |first| |Beta| |se2rfi| |setMaxPoints3D| + |doublyTransitive?| |leftRankPolynomial| |cAtan| |inrootof| + |repeating?| |rest| |innerEigenvectors| |eigenMatrix| |aCubic| + |integralMatrixAtInfinity| |OMconnectTCP| |empty| |substitute| + |janko2| |radicalSimplify| |string| |deepestInitial| + |semiDiscriminantEuclidean| |printTypes| |removeDuplicates| + |oblateSpheroidal| |OMgetEndApp| |status| |order| |debug| + |printingInfo?| |setlast!| |eq?| |universe| |delete| |pdf2df| + |quickSort| |routines| |escape| |setMinPoints3D| |limitPlus| + |qinterval| |c06fpf| |resetBadValues| |diagonals| |numeric| + |upperCase| |cCoth| |setStatus| |leviCivitaSymbol| + |definingPolynomial| |predicate| |outputAsTex| |setCondition!| + |radical| |derivative| |separateDegrees| |findBinding| |convergents| + |quotient| |level| |linGenPos| |idealSimplify| |node?| + |curveColorPalette| |numberOfNormalPoly| |permutationGroup| + |cylindrical| |transform| |countable?| |notOperand| |conical| |e01bef| + |light| |compactFraction| |iiacos| |palglimint| |corrPoly| |inR?| + |unprotectedRemoveRedundantFactors| |regularRepresentation| + |totalDifferential| |decreasePrecision| |tanIfCan| |eigenvalues| + |npcoef| |characteristicSet| |constDsolve| |bumptab| |mapBivariate| + |HermiteIntegrate| |imagI| |dot| |isMult| |coercePreimagesImages| + |LyndonWordsList1| |OMgetError| |equiv?| |subNodeOf?| |lazyGintegrate| + |clikeUniv| |minimalPolynomial| |selectPolynomials| |primlimintfrac| + |intensity| |numberOfOperations| |divideExponents| |coord| + |variationOfParameters| |tanhIfCan| |changeWeightLevel| |bitCoef| + |primlimitedint| |pmintegrate| |uniform01| |extractPoint| |cosSinInfo| + |cPower| |OMputString| |retractable?| |cscIfCan| |log10| + |roughUnitIdeal?| |reducedForm| |getStream| |irreducible?| + |constantLeft| |listOfLists| |hexDigit| |rationalPower| |binding| + |bitand| |var1Steps| |identityMatrix| |copies| |length| |position!| + |associative?| |unrankImproperPartitions1| |factorials| |cons| + |bitior| |ramified?| |fortranReal| |leftDivide| |palgLODE| |scripts| + |leftTrace| |OMconnInDevice| |cRationalPower| |probablyZeroDim?| + |btwFact| |augment| |removeCosSq| |edf2df| |conditionsForIdempotents| + |squareFreePolynomial| |mapCoef| |numberOfComputedEntries| |e01bgf| + |s17dgf| |currentSubProgram| |signAround| |maxPoints| |traverse| + |complement| |rightRecip| |f01qef| |scanOneDimSubspaces| |setrest!| + |palgextint| |f04axf| |s14aaf| |s13aaf| |cyclicEntries| |qroot| + |insertBottom!| |allRootsOf| |exprex| |generic?| + |purelyAlgebraicLeadingMonomial?| |leftLcm| |Gamma| + |invertibleElseSplit?| |print| |roman| |showRegion| |OMlistSymbols| + |pToHdmp| NOT |showTheSymbolTable| |tanQ| |getOrder| |logpart| + |divideIfCan| |pseudoRemainder| |oddlambert| |screenResolution| + |lazyPrem| OR |primeFrobenius| |hclf| |definingInequation| |surface| + |readLine!| |mapMatrixIfCan| |queue| |symmetricDifference| AND + |drawComplex| |lfextendedint| |homogeneous?| |FormatArabic| + |leftFactorIfCan| |df2mf| |t| |taylorRep| |unitsColorDefault| + |leftNorm| |f04maf| |qfactor| |leaves| |getButtonValue| |localReal?| + |plus!| |basisOfRightAnnihilator| |whatInfinity| |c05adf| |singRicDE| + |sechIfCan| |rightUnit| |explicitlyFinite?| |setelt!| |hasHi| + |powerSum| |factorAndSplit| |leftGcd| |shallowExpand| |d01asf| + |OMclose| |name| |declare| |char| |prevPrime| |delay| |factorOfDegree| + |cyclic?| |body| |ldf2vmf| |rationalFunction| |edf2ef| + |zeroDimensional?| |OMsend| |solveLinearPolynomialEquation| + |showTypeInOutput| |inspect| |lookup| |elRow1!| |brace| |setRow!| + |init| |swap| |lyndon| |rightTraceMatrix| |bombieriNorm| |atom?| + |selectfirst| |rischNormalize| |primeFactor| |trigs2explogs| + |Frobenius| |constantOperator| |nonLinearPart| |null| |mvar| |f01bsf| + |pToDmp| |component| |diagonal| |super| |withPredicates| + |genericPosition| |getExplanations| + |generalizedContinuumHypothesisAssumed?| |genericRightNorm| |lazyPquo| + |s17aff| |case| |clipWithRanges| |processTemplate| |nextSubsetGray| + |besselK| |child| |morphism| |node| |stiffnessAndStabilityOfODEIF| + |entries| |eyeDistance| |Zero| |toseSquareFreePart| |curryLeft| + |pushNewContour| |central?| |SturmHabichtSequence| + |rightFactorCandidate| |value| |getMultiplicationMatrix| |One| + |setStatus!| * |sinhcosh| |viewDeltaXDefault| |viewWriteDefault| + |LazardQuotient2| |box| |round| |numberOfVariables| |moebius| |Is| + |factorByRecursion| |rootBound| |printStats!| |makeFR| |ParCondList| + |divideIfCan!| |coth2tanh| |makeop| |createMultiplicationTable| + |setFormula!| |fixedPointExquo| |makeViewport3D| |OMgetSymbol| + |lieAdmissible?| |e02dcf| |uniform| |setLegalFortranSourceExtensions| + |plenaryPower| |f02aff| |clearDenominator| |connect| |innerSolve1| + |charthRoot| |e01sff| |e02bef| |padicFraction| |rotate!| + |solveRetract| |primitive?| |binomThmExpt| |setPrologue!| + |showTheIFTable| |numericIfCan| |rewriteIdealWithRemainder| |quartic| + |tensorProduct| |elt| |badValues| |OMgetAtp| |defineProperty| + |monicLeftDivide| |removeSuperfluousQuasiComponents| |listLoops| Y + |iiperm| |mainSquareFreePart| |maxdeg| |groebner?| |property| + |acotIfCan| |fibonacci| |thetaCoord| |powmod| |changeBase| |compBound| + |leftPower| |leftMult| |rightPower| |multinomial| |extensionDegree| + |weights| |eigenvectors| |gradient| |e01bhf| |multisect| + |currentScope| |key| |OMencodingXML| |push!| |decrease| + |completeEchelonBasis| |tableForDiscreteLogarithm| |iiGamma| + |ODESolve| |rectangularMatrix| |leftDiscriminant| |keys| |besselJ| + |options| |adjoint| |sec2cos| |units| |standardBasisOfCyclicSubmodule| + |ceiling| |compile| |rightRankPolynomial| |f02abf| + |useEisensteinCriterion?| |cosh2sech| |lazyPseudoRemainder| |mapUp!| + |antiCommutative?| |relerror| |id| |s21baf| |algebraicCoefficients?| + |monicDecomposeIfCan| |OMgetString| |getPickedPoints| |critpOrder| + |univariateSolve| |tryFunctionalDecomposition?| |complexZeros| |arg1| + |filename| |removeRedundantFactors| |goodnessOfFit| |term?| |remove!| + |nodeOf?| |realElementary| |rarrow| |padicallyExpand| |removeZeroes| + |associates?| |generalizedContinuumHypothesisAssumed| |arg2| |shade| + |viewDefaults| |powers| |mapmult| |table| |open?| |rootKerSimp| + |nullity| |listConjugateBases| |mpsode| |datalist| |updatD| + |leadingIndex| |lastSubResultant| |not?| |BumInSepFFE| + |solveLinearlyOverQ| |nlde| |new| |deepExpand| |monicDivide| + |bivariate?| |coleman| |maxPoints3D| |rightZero| |conditions| |s19aaf| + |dmpToHdmp| |parse| |getOperator| |characteristicSerie| + |stronglyReduce| |branchPoint?| |messagePrint| |reduceLODE| |weighted| + |lflimitedint| |comp| |match| |code| |block| |singularAtInfinity?| + |explogs2trigs| |resultantReduit| |rquo| |inRadical?| |cos2sec| + |functionIsFracPolynomial?| |closeComponent| |lifting| |dn| |lepol| + |mulmod| |resetVariableOrder| |genericRightMinimalPolynomial| + |initiallyReduced?| |getProperty| |createIrreduciblePoly| + |mapUnivariateIfCan| |maximumExponent| |dmp2rfi| |lo| |leadingIdeal| + |intcompBasis| |commutativeEquality| |iipow| |squareFreeLexTriangular| + |eq| |test| |select!| |selectOrPolynomials| |SFunction| + |ScanFloatIgnoreSpacesIfCan| |rur| |incr| |outputFixed| |ListOfTerms| + |interReduce| |safeFloor| |prime| |iter| |palglimint0| + |ScanFloatIgnoreSpaces| |setleaves!| |powern| |pointColorPalette| |hi| + |packageCall| |jacobi| |imagi| |cyclic| |s21bbf| |UnVectorise| + |fortranCompilerName| |bat| |monicRightDivide| + |rewriteSetByReducingWithParticularGenerators| |LowTriBddDenomInv| + |insertTop!| |quatern| |polarCoordinates| |associatorDependence| + |approximants| |exponentialOrder| |lift| |prem| |directSum| + |radicalEigenvector| |f04arf| |deleteRoutine!| |balancedFactorisation| + |#| |represents| |PollardSmallFactor| |functionIsOscillatory| + |yCoordinates| |printStatement| |formula| |approxNthRoot| |reduce| + |ksec| |screenResolution3D| |term| |fortranTypeOf| |solid| + |showScalarValues| |cyclotomicFactorization| |leader| |positiveSolve| + |sizeLess?| |primPartElseUnitCanonical!| |f01rcf| |argumentList!| |cn| + |trailingCoefficient| |binary| |explicitlyEmpty?| |left| |padecf| + |reverse| |solveLinearPolynomialEquationByRecursion| |polyred| + |biRank| |solveLinear| |numberOfFractionalTerms| |legendre| + |arguments| |factorPolynomial| |arrayStack| |factorFraction| |iiasech| + |expintegrate| |right| |pair?| |exp| |algDsolve| |rotatey| |setnext!| + |clearTheIFTable| |quoByVar| |split!| |mdeg| |symbol| |preprocess| + |rootProduct| |commutative?| |cAcot| |cotIfCan| |pquo| + |palginfieldint| |cot2tan| |univcase| |ref| |groebnerIdeal| |nrows| + |OMputEndBind| |hostPlatform| |algintegrate| |outputGeneral| + |parametersOf| |zeroSetSplitIntoTriangularSystems| |qPot| |sqfree| + |ncols| |hasPredicate?| |d01fcf| |difference| |integer| |factorial| + |parts| |composite| |setImagSteps| |exprToUPS| |supersub| + |integerIfCan| |pow| |OMbindTCP| |reindex| |polyRicDE| |index| + |stoseInvertibleSetreg| |weight| |idealiser| |rootsOf| |dequeue| + |RittWuCompare| |maxRowIndex| |recip| |infieldint| + |quasiMonicPolynomials| |dihedral| |solveid| |iitan| |anfactor| + |tubeRadius| |complexSolve| |quasiMonic?| |deepCopy| |OMputEndBVar| + |tanAn| |iiasin| |double?| |normalizedDivide| |nthFlag| |logical?| + |cCosh| |internalAugment| |argscript| |push| |laguerre| |generate| + |e04gcf| |reset| |OMgetEndBVar| |superHeight| + |stoseIntegralLastSubResultant| |pair| |basisOfLeftNucleus| |top!| + F2FG |linSolve| |zCoord| |exprHasLogarithmicWeights| |composites| + |partition| |resetNew| |subTriSet?| |int| + |semiDegreeSubResultantEuclidean| |stoseInvertibleSet| |getGoodPrime| + |rCoord| |monic?| |prolateSpheroidal| |ocf2ocdf| |incrementBy| + |mainVariable?| |write| |trim| |getCurve| |laplace| |e02agf| + |appendPoint| |e01bff| |s18adf| |quadraticForm| |extractIndex| + |GospersMethod| |expand| |save| |setButtonValue| |rotate| + |viewPhiDefault| |triangSolve| |result| |integralBasisAtInfinity| + |physicalLength| |evaluateInverse| |prefixRagits| |index?| |presub| + |filterWhile| |cycleTail| |arity| |cartesian| |cardinality| + |OMgetEndBind| |prinb| |invertible?| |direction| |bat1| + |transcendenceDegree| |lSpaceBasis| |besselI| |filterUntil| |e04ycf| + |LazardQuotient| |symmetricPower| |youngGroup| |generalPosition| + |cSinh| |addPointLast| |complexLimit| |squareFreePrim| |limitedint| + |inf| |select| |clearFortranOutputStack| |euclideanNormalForm| + |OMreadFile| |abelianGroup| |internalIntegrate| |companionBlocks| + |OMputBind| |octon| |rational| |intermediateResultsIF| |factor1| + |atrapezoidal| |distance| |inverseIntegralMatrix| |alternative?| + |equality| |distFact| |polyRDE| |enumerate| |viewport3D| |extractTop!| + |denominators| |iilog| |loadNativeModule| BY |numFunEvals3D| + |rischDEsys| |totalfract| |message| |finiteBound| |sortConstraints| + |insertionSort!| |cAcoth| |sinIfCan| |Lazard| + |selectSumOfSquaresRoutines| |coerceL| |aspFilename| |invmod| |s14baf| + |digit?| |supDimElseRittWu?| |OMconnOutDevice| |lprop| + |viewZoomDefault| |mainMonomials| |setprevious!| + |sumOfKthPowerDivisors| |subscript| |loopPoints| |s21bdf| + |primitiveElement| |iiacsc| |getCode| |f01qdf| |symFunc| + |fortranLinkerArgs| |factorSquareFree| |middle| |OMmakeConn| |freeOf?| + |invertIfCan| |setTex!| |safeCeiling| |reverse!| |complexRoots| + |irreducibleFactor| |derivationCoordinates| |acosIfCan| |rischDE| |or| + |leftQuotient| |makeRecord| |OMputApp| |att2Result| |nthr| + |mindegTerm| |isPower| |stoseSquareFreePart| |implies| |shiftRoots| + |e02def| |f04atf| |commaSeparate| |transcendentalDecompose| |and| + |redpps| |normalize| |doubleRank| F |dictionary| |lfinfieldint| + |iisech| |aQuartic| |xor| |measure2Result| |topFortranOutputStack| + |removeRedundantFactorsInPols| |normalise| |printHeader| + |basisOfCenter| |airyAi| |iisqrt2| |rationalApproximation| + |matrixConcat3D| |blankSeparate| |addmod| |tanintegrate| + |constantIfCan| |LyndonCoordinates| |rk4qc| |scalarMatrix| + |leftExtendedGcd| |stack| |edf2fi| |sumSquares| |normFactors| + |noKaratsuba| |operators| |lieAlgebra?| |OMputBVar| |expt| |retract| + |balancedBinaryTree| |point?| |fortranLiteral| |isExpt| + |identification| |epilogue| |divisorCascade| |constantKernel| + |mapExpon| |expint| |trigs| |createLowComplexityNormalBasis| FG2F + |f04jgf| |seed| |simplify| |size?| |exprHasAlgebraicWeight| + |singularitiesOf| |quadratic?| |tRange| |bivariateSLPEBR| + |selectAndPolynomials| |unitVector| |inconsistent?| + |isAbsolutelyIrreducible?| |newReduc| |crest| |innerint| |divisor| + |mix| |f02ajf| |symmetric?| |genericLeftDiscriminant| |mathieu24| + |euler| |complexEigenvalues| |showClipRegion| |cothIfCan| + |controlPanel| |iidprod| |numerators| |supRittWu?| |f02aaf| + |prepareDecompose| |linearlyDependentOverZ?| |variable?| + |solveInField| |palgRDE| |primPartElseUnitCanonical| + |symmetricTensors| |mainCoefficients| |domainOf| |curveColor| |redPol| + |list?| |generalTwoFactor| |close!| |normal?| |degreeSubResultant| + |times!| |coefficient| |subtractIfCan| |closedCurve?| |someBasis| + |rightUnits| |rowEch| |dominantTerm| |factorSFBRlcUnit| |cycleLength| + |s15aef| |makeprod| |symmetricSquare| |irreducibleFactors| |minGbasis| + |genericLeftTrace| |elem?| |setScreenResolution| |replaceKthElement| + |setEmpty!| |ratPoly| |setOrder| |ode2| |sncndn| |write!| + |uncouplingMatrices| |hconcat| |pointPlot| |subNode?| |iicoth| |genus| + |bottom!| |has?| |relationsIdeal| |fractionPart| |largest| + |removeConstantTerm| |pushup| |f04faf| |shiftLeft| |viewPosDefault| + |perfectNthRoot| |point| |limitedIntegrate| |hessian| + |functionIsContinuousAtEndPoints| |maxColIndex| |rootPower| + |rightDiscriminant| |spherical| |minset| |setFieldInfo| + |impliesOperands| |c06gqf| |factors| |stirling2| |s21bcf| |minimize| + |f01rdf| |multMonom| |endOfFile?| |brillhartIrreducible?| |generator| + |showTheRoutinesTable| |slash| |rational?| |radicalEigenvalues| + |stronglyReduced?| |inc| |fortranComplex| + |degreeSubResultantEuclidean| |d03eef| |baseRDE| |splitSquarefree| + |pointData| |series| |badNum| |nthRootIfCan| |changeNameToObjf| + |scripted?| |e02ajf| |s17def| |hdmpToDmp| |mainCharacterization| = + |separant| |patternMatch| |iiexp| |comment| |numberOfIrreduciblePoly| + |selectMultiDimensionalRoutines| |e01sef| |initTable!| |makeCos| + |complexForm| |critMTonD1| |nthExpon| |expintfldpoly| |linkToFortran| + |cCsc| |rightDivide| |is?| |cyclicCopy| |quadraticNorm| |mainForm| + |binomial| |relativeApprox| < |getMeasure| |iicsch| |zeroSquareMatrix| + |asinIfCan| |contract| |removeSuperfluousCases| |nextIrreduciblePoly| + |iomode| |laplacian| > |quotedOperators| |rootNormalize| + |completeSmith| |acschIfCan| |min| |pascalTriangle| |subspace| + |coerceS| |c02agf| |ramifiedAtInfinity?| |setTopPredicate| + |leadingExponent| <= |iicosh| |applyRules| |nodes| |makeGraphImage| + |mkPrim| |rdHack1| |curve| |numberOfPrimitivePoly| |s17adf| |norm| + |ratDsolve| >= |mkAnswer| |basisOfMiddleNucleus| |lazyPseudoDivide| + |OMputAttr| |trivialIdeal?| |d01gbf| |FormatRoman| |basisOfCentroid| + |createThreeSpace| |roughSubIdeal?| |floor| |integralDerivationMatrix| + |nonQsign| |moebiusMu| |stoseInvertible?| |mapGen| |maxrank| + |setPosition| |iisec| |clearTheFTable| |plotPolar| |pointColor| + |dAndcExp| |idealiserMatrix| |createRandomElement| |equivOperands| + |normalized?| |splitConstant| |d03faf| |addMatchRestricted| + + |squareFree| |resetAttributeButtons| |checkRur| |fixedPoint| |s14abf| + |hexDigit?| |toScale| |binarySearchTree| |maxrow| - |modifyPointData| + |quasiRegular?| |paraboloidal| |compiledFunction| |normalDenom| + |radicalEigenvectors| |list| |randomR| |polygamma| |rightFactorIfCan| + |firstNumer| |viewWriteAvailable| / |iFTable| |stoseInvertible?sqfreg| + |car| |birth| |OMcloseConn| |ord| |graphImage| |pile| |froot| |s17akf| + |cdr| |mapSolve| |curve?| |refine| |plot| |rule| |monom| + |halfExtendedResultant2| |externalList| |LiePolyIfCan| + |internalIntegrate0| |components| |setDifference| |upDateBranches| + |KrullNumber| |lazyIntegrate| |cond| |quasiAlgebraicSet| + |primintegrate| |OMputInteger| |tracePowMod| |inHallBasis?| + |setIntersection| |sinhIfCan| |stirling1| |shrinkable| + |primitivePart!| |bezoutResultant| |multiplyCoefficients| + |leadingTerm| |prindINFO| |horizConcat| |xn| |setUnion| |s17aef| + |failed| |common| |lazyResidueClass| |charpol| |sequences| |eulerPhi| + |modulus| |apply| |diophantineSystem| |mapExponents| |karatsuba| + |skewSFunction| |internalSubPolSet?| |deriv| |monomialIntegrate| + |key?| |rk4f| |primaryDecomp| |notelem| |cAsec| |stFunc2| |elementary| + |zeroOf| |graphCurves| |size| |besselY| |normalizeIfCan| |duplicates| + |explimitedint| |expandLog| |extendedResultant| |rowEchLocal| |iicsc| + |graphs| |iifact| |OMReadError?| |nextsousResultant2| |tree| + |integrate| |pushuconst| |realRoots| |pmComplexintegrate| |findCycle| + |exactQuotient!| |forLoop| |polyPart| |getMultiplicationTable| + |OMputError| |localUnquote| |cycleSplit!| |stFunc1| |fglmIfCan| + |integers| |integralRepresents| |binaryTournament| |red| + |integralAtInfinity?| |palgint| |minPoints| |acoshIfCan| |radPoly| + |parabolicCylindrical| |op| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 1dbc1705..282516da 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,4916 +1,4916 @@ -(3149566 . 3422100696) -((-1525 (((-108) (-1 (-108) |#2| |#2|) $) 63) (((-108) $) NIL)) (-2224 (($ (-1 (-108) |#2| |#2|) $) 18) (($ $) NIL)) (-1451 ((|#2| $ (-525) |#2|) NIL) ((|#2| $ (-1140 (-525)) |#2|) 34)) (-2899 (($ $) 59)) (-2176 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 40) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 38) ((|#2| (-1 |#2| |#2| |#2|) $) 37)) (-1875 (((-525) (-1 (-108) |#2|) $) 22) (((-525) |#2| $) NIL) (((-525) |#2| $ (-525)) 73)) (-2557 (((-592 |#2|) $) 13)) 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T) ((-23) . T) ((-25) . T) ((-37 #0=(-385 (-525))) -3204 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-37 |#1|) . T) ((-37 $) -3204 (|has| |#1| (-517)) (|has| |#1| (-327)) (|has| |#1| (-341)) (|has| |#1| (-286))) ((-34) |has| |#1| (-1113)) ((-91) |has| |#1| (-1113)) ((-97) . T) ((-107 #0# #0#) -3204 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-107 |#1| |#1|) . T) ((-107 $ $) . T) ((-126) . T) ((-136) -3204 (|has| |#1| (-327)) (|has| |#1| (-136))) ((-138) |has| |#1| (-138)) ((-566 (-798)) . T) ((-160) . T) ((-567 (-157 (-205))) |has| |#1| (-953)) ((-567 (-157 (-357))) |has| |#1| (-953)) ((-567 (-501)) |has| |#1| (-567 (-501))) ((-567 (-827 (-357))) |has| |#1| (-567 (-827 (-357)))) ((-567 (-827 (-525))) |has| |#1| (-567 (-827 (-525)))) ((-567 #1=(-1087 |#1|)) . T) ((-211 |#1|) . 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T) ((-429) -3204 (|has| |#1| (-327)) (|has| |#1| (-341)) (|has| |#1| (-286))) ((-466) |has| |#1| (-1113)) ((-486 (-1091) |#1|) |has| |#1| (-486 (-1091) |#1|)) ((-486 |#1| |#1|) |has| |#1| (-288 |#1|)) ((-517) -3204 (|has| |#1| (-517)) (|has| |#1| (-327)) (|has| |#1| (-341)) (|has| |#1| (-286))) ((-594 #0#) -3204 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-594 |#1|) . T) ((-594 $) . T) ((-588 (-525)) |has| |#1| (-588 (-525))) ((-588 |#1|) . T) ((-660 #0#) -3204 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-660 |#1|) . T) ((-660 $) -3204 (|has| |#1| (-517)) (|has| |#1| (-327)) (|has| |#1| (-341)) (|has| |#1| (-286))) ((-667 |#1| #1#) . T) ((-669) . T) ((-789) |has| |#1| (-789)) ((-835 (-1091)) |has| |#1| (-835 (-1091))) ((-821 (-357)) |has| |#1| (-821 (-357))) ((-821 (-525)) |has| |#1| (-821 (-525))) ((-819 |#1|) . 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T) ((-288 |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((-346) |has| |#2| (-346)) ((-355 |#2|) |has| |#2| (-977)) ((-389 |#2|) |has| |#2| (-1020)) ((-464 |#2|) . T) ((-558 #0# |#2|) . T) ((-486 |#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((-594 |#2|) -3204 (|has| |#2| (-977)) (|has| |#2| (-341)) (|has| |#2| (-160))) ((-594 $) -3204 (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-160))) ((-588 (-525)) -12 (|has| |#2| (-588 (-525))) (|has| |#2| (-977))) ((-588 |#2|) |has| |#2| (-977)) ((-660 |#2|) -3204 (|has| |#2| (-341)) (|has| |#2| (-160))) ((-669) -3204 (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-669)) (|has| |#2| (-160))) ((-733) |has| |#2| (-787)) ((-734) -3204 (|has| |#2| (-787)) (|has| |#2| (-735))) ((-735) |has| |#2| (-735)) ((-736) -3204 (|has| |#2| (-787)) (|has| |#2| (-735))) ((-737) -3204 (|has| |#2| (-787)) (|has| |#2| (-735))) ((-787) |has| |#2| (-787)) ((-789) -3204 (|has| |#2| (-787)) (|has| |#2| (-735))) ((-835 (-1091)) -12 (|has| |#2| (-835 (-1091))) (|has| |#2| (-977))) ((-968 (-385 (-525))) -12 (|has| |#2| (-968 (-385 (-525)))) (|has| |#2| (-1020))) ((-968 (-525)) -12 (|has| |#2| (-968 (-525))) (|has| |#2| (-1020))) ((-968 |#2|) |has| |#2| (-1020)) ((-983 |#2|) -3204 (|has| |#2| (-977)) (|has| |#2| (-341)) (|has| |#2| (-160))) ((-983 $) |has| |#2| (-160)) ((-977) -3204 (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-160))) ((-984) -3204 (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-160))) ((-1032) -3204 (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-669)) (|has| |#2| (-160))) ((-1020) -3204 (|has| |#2| (-1020)) (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-735)) (|has| |#2| (-669)) (|has| |#2| (-346)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-126)) (|has| |#2| (-25))) ((-1127) . 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T) ((-355 |#1|) . T) ((-389 |#1|) . T) ((-429) -3316 (|has| |#1| (-844)) (|has| |#1| (-429))) ((-486 |#2| |#1|) |has| |#1| (-213)) ((-486 |#2| $) |has| |#1| (-213)) ((-486 |#3| |#1|) . T) ((-486 |#3| $) . T) ((-486 $ $) . T) ((-517) -3316 (|has| |#1| (-844)) (|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 $) -3316 (|has| |#1| (-844)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-669) . T) ((-789) |has| |#1| (-789)) ((-835 (-1091)) |has| |#1| (-835 (-1091))) ((-835 |#3|) . T) ((-821 (-357)) -12 (|has| |#1| (-821 (-357))) (|has| |#3| (-821 (-357)))) ((-821 (-525)) -12 (|has| |#1| (-821 (-525))) (|has| |#3| (-821 (-525)))) ((-884 |#1| |#4| |#3|) . 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T) ((-1131) |has| |#1| (-844))) -((-1266 (((-108) $ $) 19 (|has| |#1| (-1020)))) (-3341 ((|#1| $) 54)) (-2804 ((|#1| $) 44)) (-1673 (((-108) $ (-713)) 8)) (-1702 (($) 7 T CONST)) (-2218 (($ $) 60)) (-2899 (($ $) 48)) (-2831 ((|#1| |#1| $) 46)) (-2228 ((|#1| $) 45)) (-2557 (((-592 |#1|) $) 30 (|has| $ (-6 -4255)))) (-2862 (((-108) $ (-713)) 9)) (-3539 (((-592 |#1|) $) 29 (|has| $ (-6 -4255)))) (-2733 (((-108) |#1| $) 27 (-12 (|has| |#1| (-1020)) (|has| $ (-6 -4255))))) (-3391 (($ (-1 |#1| |#1|) $) 34 (|has| $ (-6 -4256)))) (-2554 (($ (-1 |#1| |#1|) $) 35)) (-3335 (((-108) $ (-713)) 10)) (-1496 (((-713) $) 61)) (-3718 (((-1074) $) 22 (|has| |#1| (-1020)))) (-2188 ((|#1| $) 39)) (-4134 ((|#1| |#1| $) 52)) (-3123 ((|#1| |#1| $) 51)) (-3438 (($ |#1| $) 40)) (-1714 (((-713) $) 55)) (-1948 (((-1038) $) 21 (|has| |#1| (-1020)))) (-3440 ((|#1| $) 62)) (-2974 ((|#1| $) 50)) (-2157 ((|#1| $) 49)) (-4078 ((|#1| $) 41)) (-2432 (((-108) (-1 (-108) |#1|) $) 32 (|has| $ (-6 -4255)))) (-2481 (($ $ (-592 (-273 |#1|))) 26 (-12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (($ $ (-273 |#1|)) 25 (-12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (($ $ |#1| |#1|) 24 (-12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (($ $ (-592 |#1|) (-592 |#1|)) 23 (-12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020))))) (-1944 (((-108) $ $) 14)) (-3980 ((|#1| |#1| $) 58)) (-1979 (((-108) $) 11)) (-1471 (($) 12)) (-1747 ((|#1| $) 59)) (-2249 (($) 57) (($ (-592 |#1|)) 56)) (-2822 (((-713) $) 43)) (-1966 (((-713) (-1 (-108) |#1|) $) 31 (|has| $ (-6 -4255))) (((-713) |#1| $) 28 (-12 (|has| |#1| (-1020)) (|has| $ (-6 -4255))))) (-1472 (($ $) 13)) (-1278 (((-798) $) 18 (|has| |#1| (-566 (-798))))) (-3702 ((|#1| $) 53)) (-1732 (($ (-592 |#1|)) 42)) (-3749 ((|#1| $) 63)) (-3679 (((-108) (-1 (-108) |#1|) $) 33 (|has| $ (-6 -4255)))) (-4026 (((-108) $ $) 20 (|has| |#1| (-1020)))) (-3674 (((-713) $) 6 (|has| $ (-6 -4255))))) +((-2616 (*1 *2 *3) (-12 (-4 *4 (-977)) (-4 *3 (-789)) (-4 *5 (-245 *3)) (-4 *6 (-735)) (-5 *2 (-1 *1 (-713))) (-4 *1 (-232 *4 *3 *5 *6)))) (-1547 (*1 *2 *1) (-12 (-4 *1 (-232 *3 *4 *5 *6)) (-4 *3 (-977)) (-4 *4 (-789)) (-4 *5 (-245 *4)) (-4 *6 (-735)) (-5 *2 (-592 *4)))) (-3033 (*1 *2 *1 *3) (-12 (-4 *1 (-232 *4 *3 *5 *6)) (-4 *4 (-977)) (-4 *3 (-789)) (-4 *5 (-245 *3)) (-4 *6 (-735)) (-5 *2 (-713)))) (-3033 (*1 *2 *1) (-12 (-4 *1 (-232 *3 *4 *5 *6)) (-4 *3 (-977)) (-4 *4 (-789)) (-4 *5 (-245 *4)) (-4 *6 (-735)) (-5 *2 (-713)))) (-1214 (*1 *2 *1 *3) (-12 (-4 *1 (-232 *4 *3 *5 *6)) (-4 *4 (-977)) (-4 *3 (-789)) (-4 *5 (-245 *3)) (-4 *6 (-735)) (-5 *2 (-713)))) (-3384 (*1 *2 *1) (-12 (-4 *1 (-232 *3 *4 *5 *6)) (-4 *3 (-977)) (-4 *4 (-789)) (-4 *5 (-245 *4)) (-4 *6 (-735)) (-5 *2 (-592 (-713))))) (-3642 (*1 *2 *1) (-12 (-4 *1 (-232 *3 *4 *5 *6)) (-4 *3 (-977)) (-4 *4 (-789)) (-4 *5 (-245 *4)) (-4 *6 (-735)) (-5 *2 (-713)))) (-3384 (*1 *2 *1 *3) (-12 (-4 *1 (-232 *4 *3 *5 *6)) (-4 *4 (-977)) (-4 *3 (-789)) (-4 *5 (-245 *3)) (-4 *6 (-735)) (-5 *2 (-592 (-713))))) (-3642 (*1 *2 *1 *3) (-12 (-4 *1 (-232 *4 *3 *5 *6)) (-4 *4 (-977)) (-4 *3 (-789)) (-4 *5 (-245 *3)) (-4 *6 (-735)) (-5 *2 (-713)))) (-2109 (*1 *2 *1) (-12 (-4 *1 (-232 *3 *4 *5 *6)) (-4 *3 (-977)) (-4 *4 (-789)) (-4 *5 (-245 *4)) (-4 *6 (-735)) (-5 *2 (-108)))) (-3568 (*1 *2 *1) (-12 (-4 *1 (-232 *3 *4 *2 *5)) (-4 *3 (-977)) (-4 *4 (-789)) (-4 *5 (-735)) (-4 *2 (-245 *4)))) (-1521 (*1 *1 *1) (-12 (-4 *1 (-232 *2 *3 *4 *5)) (-4 *2 (-977)) (-4 *3 (-789)) (-4 *4 (-245 *3)) (-4 *5 (-735)))) (-4016 (*1 *1 *1) (-12 (-4 *1 (-232 *2 *3 *4 *5)) (-4 *2 (-977)) (-4 *3 (-789)) (-4 *4 (-245 *3)) (-4 *5 (-735)))) (-2616 (*1 *2 *1) (-12 (-4 *3 (-213)) (-4 *3 (-977)) (-4 *4 (-789)) (-4 *5 (-245 *4)) (-4 *6 (-735)) (-5 *2 (-1 *1 (-713))) (-4 *1 (-232 *3 *4 *5 *6))))) +(-13 (-884 |t#1| |t#4| |t#3|) (-211 |t#1|) (-968 |t#2|) (-10 -8 (-15 -2616 ((-1 $ (-713)) |t#2|)) (-15 -1547 ((-592 |t#2|) $)) (-15 -3033 ((-713) $ |t#2|)) (-15 -3033 ((-713) $)) (-15 -1214 ((-713) $ |t#2|)) (-15 -3384 ((-592 (-713)) $)) (-15 -3642 ((-713) $)) (-15 -3384 ((-592 (-713)) $ |t#2|)) (-15 -3642 ((-713) $ |t#2|)) (-15 -2109 ((-108) $)) (-15 -3568 (|t#3| $)) (-15 -1521 ($ $)) (-15 -4016 ($ $)) (IF (|has| |t#1| (-213)) (PROGN (-6 (-486 |t#2| |t#1|)) (-6 (-486 |t#2| $)) (-6 (-288 $)) (-15 -2616 ((-1 $ (-713)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-46 |#1| |#4|) . T) ((-25) . T) ((-37 #0=(-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((-37 |#1|) |has| |#1| (-160)) ((-37 $) -3204 (|has| |#1| (-844)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-97) . T) ((-107 #0# #0#) |has| |#1| (-37 (-385 (-525)))) ((-107 |#1| |#1|) . T) ((-107 $ $) -3204 (|has| |#1| (-844)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-160))) ((-126) . T) ((-136) |has| |#1| (-136)) ((-138) |has| |#1| (-138)) ((-566 (-798)) . T) ((-160) -3204 (|has| |#1| (-844)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-160))) ((-567 (-501)) -12 (|has| |#1| (-567 (-501))) (|has| |#3| (-567 (-501)))) ((-567 (-827 (-357))) -12 (|has| |#1| (-567 (-827 (-357)))) (|has| |#3| (-567 (-827 (-357))))) ((-567 (-827 (-525))) -12 (|has| |#1| (-567 (-827 (-525)))) (|has| |#3| (-567 (-827 (-525))))) ((-211 |#1|) . T) ((-213) |has| |#1| (-213)) ((-269) -3204 (|has| |#1| (-844)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-288 $) . T) ((-304 |#1| |#4|) . T) ((-355 |#1|) . T) ((-389 |#1|) . T) ((-429) -3204 (|has| |#1| (-844)) (|has| |#1| (-429))) ((-486 |#2| |#1|) |has| |#1| (-213)) ((-486 |#2| $) |has| |#1| (-213)) ((-486 |#3| |#1|) . T) ((-486 |#3| $) . T) ((-486 $ $) . T) ((-517) -3204 (|has| |#1| (-844)) (|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 $) -3204 (|has| |#1| (-844)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-669) . T) ((-789) |has| |#1| (-789)) ((-835 (-1091)) |has| |#1| (-835 (-1091))) ((-835 |#3|) . T) ((-821 (-357)) -12 (|has| |#1| (-821 (-357))) (|has| |#3| (-821 (-357)))) ((-821 (-525)) -12 (|has| |#1| (-821 (-525))) (|has| |#3| (-821 (-525)))) ((-884 |#1| |#4| |#3|) . T) ((-844) |has| |#1| (-844)) ((-968 (-385 (-525))) |has| |#1| (-968 (-385 (-525)))) ((-968 (-525)) |has| |#1| (-968 (-525))) ((-968 |#1|) . T) ((-968 |#2|) . T) ((-968 |#3|) . T) ((-983 #0#) |has| |#1| (-37 (-385 (-525)))) ((-983 |#1|) . T) ((-983 $) -3204 (|has| |#1| (-844)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-160))) ((-977) . T) ((-984) . T) ((-1032) . T) ((-1020) . T) ((-1131) |has| |#1| (-844))) +((-1257 (((-108) $ $) 19 (|has| |#1| (-1020)))) (-3679 ((|#1| $) 54)) (-2787 ((|#1| $) 44)) (-3887 (((-108) $ (-713)) 8)) (-1351 (($) 7 T CONST)) (-3350 (($ $) 60)) (-3812 (($ $) 48)) (-3392 ((|#1| |#1| $) 46)) (-1881 ((|#1| $) 45)) (-3630 (((-592 |#1|) $) 30 (|has| $ (-6 -4255)))) (-2926 (((-108) $ (-713)) 9)) (-1646 (((-592 |#1|) $) 29 (|has| $ (-6 -4255)))) (-1760 (((-108) |#1| $) 27 (-12 (|has| |#1| (-1020)) (|has| $ (-6 -4255))))) (-1773 (($ (-1 |#1| |#1|) $) 34 (|has| $ (-6 -4256)))) (-2494 (($ (-1 |#1| |#1|) $) 35)) (-1283 (((-108) $ (-713)) 10)) (-3140 (((-713) $) 61)) (-2394 (((-1074) $) 22 (|has| |#1| (-1020)))) (-3260 ((|#1| $) 39)) (-3539 ((|#1| |#1| $) 52)) (-3181 ((|#1| |#1| $) 51)) (-2145 (($ |#1| $) 40)) (-1668 (((-713) $) 55)) (-1957 (((-1038) $) 21 (|has| |#1| (-1020)))) (-2370 ((|#1| $) 62)) (-3768 ((|#1| $) 50)) (-1848 ((|#1| $) 49)) (-2822 ((|#1| $) 41)) (-1586 (((-108) (-1 (-108) |#1|) $) 32 (|has| $ (-6 -4255)))) (-2438 (($ $ (-592 (-273 |#1|))) 26 (-12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (($ $ (-273 |#1|)) 25 (-12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (($ $ |#1| |#1|) 24 (-12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (($ $ (-592 |#1|) (-592 |#1|)) 23 (-12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020))))) (-3037 (((-108) $ $) 14)) (-2934 ((|#1| |#1| $) 58)) (-1837 (((-108) $) 11)) (-3021 (($) 12)) (-2442 ((|#1| $) 59)) (-3645 (($) 57) (($ (-592 |#1|)) 56)) (-2135 (((-713) $) 43)) (-1978 (((-713) (-1 (-108) |#1|) $) 31 (|has| $ (-6 -4255))) (((-713) |#1| $) 28 (-12 (|has| |#1| (-1020)) (|has| $ (-6 -4255))))) (-1460 (($ $) 13)) (-1267 (((-798) $) 18 (|has| |#1| (-566 (-798))))) (-3962 ((|#1| $) 53)) (-2041 (($ (-592 |#1|)) 42)) (-2845 ((|#1| $) 63)) (-2953 (((-108) (-1 (-108) |#1|) $) 33 (|has| $ (-6 -4255)))) (-4015 (((-108) $ $) 20 (|has| |#1| (-1020)))) (-3552 (((-713) $) 6 (|has| $ (-6 -4255))))) (((-233 |#1|) (-131) (-1127)) (T -233)) -((-2249 (*1 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1127)))) (-2249 (*1 *1 *2) (-12 (-5 *2 (-592 *3)) (-4 *3 (-1127)) (-4 *1 (-233 *3)))) (-1714 (*1 *2 *1) (-12 (-4 *1 (-233 *3)) (-4 *3 (-1127)) (-5 *2 (-713)))) (-3341 (*1 *2 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1127)))) (-3702 (*1 *2 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1127)))) (-4134 (*1 *2 *2 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1127)))) (-3123 (*1 *2 *2 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1127)))) (-2974 (*1 *2 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1127)))) (-2157 (*1 *2 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1127)))) (-2899 (*1 *1 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1127))))) -(-13 (-1039 |t#1|) (-927 |t#1|) (-10 -8 (-15 -2249 ($)) (-15 -2249 ($ (-592 |t#1|))) (-15 -1714 ((-713) $)) (-15 -3341 (|t#1| $)) (-15 -3702 (|t#1| $)) (-15 -4134 (|t#1| |t#1| $)) (-15 -3123 (|t#1| |t#1| $)) (-15 -2974 (|t#1| $)) (-15 -2157 (|t#1| $)) (-15 -2899 ($ $)))) -(((-33) . 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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 $) -3204 (|has| |#1| (-844)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-341))) ((-97) . T) ((-107 #1# #1#) |has| |#1| (-37 (-385 (-525)))) ((-107 |#1| |#1|) . T) ((-107 $ $) -3204 (|has| |#1| (-844)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-341)) (|has| |#1| (-160))) ((-126) . T) ((-136) |has| |#1| (-136)) ((-138) |has| |#1| (-138)) ((-566 (-798)) . T) ((-160) -3204 (|has| |#1| (-844)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-341)) (|has| |#1| (-160))) ((-567 (-501)) -12 (|has| (-1005) (-567 (-501))) (|has| |#1| (-567 (-501)))) ((-567 (-827 (-357))) -12 (|has| (-1005) (-567 (-827 (-357)))) (|has| |#1| (-567 (-827 (-357))))) ((-567 (-827 (-525))) -12 (|has| (-1005) (-567 (-827 (-525)))) (|has| |#1| (-567 (-827 (-525))))) ((-211 |#1|) . T) ((-213) . 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3132538 "XPR" 3133629 NIL XPR (NIL T T) -8 NIL NIL) (-1193 3128341 3129962 3130165 "XPOLY" 3130458 NIL XPOLY (NIL T) -8 NIL NIL) (-1192 3126155 3127533 3127587 "XPOLYC" 3127872 NIL XPOLYC (NIL T T) -9 NIL 3127985) (-1191 3122527 3124672 3125060 "XPBWPOLY" 3125813 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1190 3118455 3120768 3120810 "XF" 3121431 NIL XF (NIL T) -9 NIL 3121830) (-1189 3118076 3118164 3118333 "XF-" 3118338 NIL XF- (NIL T T) -8 NIL NIL) (-1188 3113456 3114755 3114809 "XFALG" 3116957 NIL XFALG (NIL T T) -9 NIL 3117744) (-1187 3112593 3112697 3112901 "XEXPPKG" 3113348 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1186 3110692 3112444 3112539 "XDPOLY" 3112544 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1185 3109571 3110181 3110223 "XALG" 3110285 NIL XALG (NIL T) -9 NIL 3110404) (-1184 3103047 3107555 3108048 "WUTSET" 3109163 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1183 3100851 3101658 3102009 "WP" 3102829 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1182 3099737 3099935 3100230 "WFFINTBS" 3100648 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1181 3097617 3098044 3098506 "WEIER" 3099309 NIL WEIER (NIL T) -7 NIL NIL) (-1180 3096766 3097190 3097232 "VSPACE" 3097368 NIL VSPACE (NIL T) -9 NIL 3097442) (-1179 3096604 3096631 3096722 "VSPACE-" 3096727 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1178 3096350 3096393 3096464 "VOID" 3096555 T VOID (NIL) -8 NIL NIL) (-1177 3094486 3094845 3095251 "VIEW" 3095966 T VIEW (NIL) -7 NIL NIL) (-1176 3090911 3091549 3092286 "VIEWDEF" 3093771 T VIEWDEF (NIL) -7 NIL NIL) (-1175 3080249 3082459 3084632 "VIEW3D" 3088760 T VIEW3D (NIL) -8 NIL NIL) (-1174 3072531 3074160 3075739 "VIEW2D" 3078692 T VIEW2D (NIL) -8 NIL NIL) (-1173 3067940 3072301 3072393 "VECTOR" 3072474 NIL VECTOR (NIL T) -8 NIL NIL) (-1172 3066517 3066776 3067094 "VECTOR2" 3067670 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1171 3060057 3064309 3064352 "VECTCAT" 3065340 NIL VECTCAT (NIL T) -9 NIL 3065924) (-1170 3059071 3059325 3059715 "VECTCAT-" 3059720 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1169 3058542 3058712 3058832 "VARIABLE" 3058986 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1168 3058475 3058480 3058510 "UTYPE" 3058515 T UTYPE (NIL) -9 NIL NIL) (-1167 3057310 3057464 3057725 "UTSODETL" 3058301 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1166 3054750 3055210 3055734 "UTSODE" 3056851 NIL UTSODE (NIL T T) -7 NIL NIL) (-1165 3046594 3052390 3052878 "UTS" 3054319 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1164 3037929 3043294 3043336 "UTSCAT" 3044447 NIL UTSCAT (NIL T) -9 NIL 3045204) (-1163 3035284 3036000 3036988 "UTSCAT-" 3036993 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1162 3034915 3034958 3035089 "UTS2" 3035235 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1161 3029191 3031756 3031799 "URAGG" 3033869 NIL URAGG (NIL T) -9 NIL 3034591) (-1160 3026130 3026993 3028116 "URAGG-" 3028121 NIL URAGG- (NIL T T) -8 NIL NIL) (-1159 3021816 3024747 3025218 "UPXSSING" 3025794 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1158 3013707 3020937 3021217 "UPXS" 3021593 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1157 3006736 3013612 3013683 "UPXSCONS" 3013688 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1156 2997025 3003855 3003916 "UPXSCCA" 3004565 NIL UPXSCCA (NIL T T) -9 NIL 3004806) (-1155 2996664 2996749 2996922 "UPXSCCA-" 2996927 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1154 2986865 2993468 2993510 "UPXSCAT" 2994163 NIL UPXSCAT (NIL T) -9 NIL 2994771) (-1153 2986299 2986378 2986555 "UPXS2" 2986780 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1152 2984953 2985206 2985557 "UPSQFREE" 2986042 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1151 2978844 2981899 2981953 "UPSCAT" 2983102 NIL UPSCAT (NIL T T) -9 NIL 2983876) (-1150 2978049 2978256 2978582 "UPSCAT-" 2978587 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1149 2964135 2972172 2972214 "UPOLYC" 2974292 NIL UPOLYC (NIL T) -9 NIL 2975513) (-1148 2955465 2957890 2961036 "UPOLYC-" 2961041 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1147 2955096 2955139 2955270 "UPOLYC2" 2955416 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1146 2946515 2954665 2954802 "UP" 2955006 NIL UP (NIL NIL T) -8 NIL NIL) (-1145 2945858 2945965 2946128 "UPMP" 2946404 NIL UPMP (NIL T T) -7 NIL NIL) (-1144 2945411 2945492 2945631 "UPDIVP" 2945771 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1143 2943979 2944228 2944544 "UPDECOMP" 2945160 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1142 2943214 2943326 2943511 "UPCDEN" 2943863 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1141 2942737 2942806 2942953 "UP2" 2943139 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1140 2941254 2941941 2942218 "UNISEG" 2942495 NIL UNISEG (NIL T) -8 NIL NIL) (-1139 2940469 2940596 2940801 "UNISEG2" 2941097 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1138 2939529 2939709 2939935 "UNIFACT" 2940285 NIL UNIFACT (NIL T) -7 NIL NIL) (-1137 2923425 2938710 2938960 "ULS" 2939336 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1136 2911390 2923330 2923401 "ULSCONS" 2923406 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1135 2894140 2906153 2906214 "ULSCCAT" 2906926 NIL ULSCCAT (NIL T T) -9 NIL 2907222) (-1134 2893191 2893436 2893823 "ULSCCAT-" 2893828 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1133 2883171 2889688 2889730 "ULSCAT" 2890596 NIL ULSCAT (NIL T) -9 NIL 2891326) (-1132 2882605 2882684 2882861 "ULS2" 2883086 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1131 2881003 2881970 2882000 "UFD" 2882212 T UFD (NIL) -9 NIL 2882326) (-1130 2880797 2880843 2880938 "UFD-" 2880943 NIL UFD- (NIL T) -8 NIL NIL) (-1129 2879879 2880062 2880278 "UDVO" 2880603 T UDVO (NIL) -7 NIL NIL) (-1128 2877695 2878104 2878575 "UDPO" 2879443 NIL UDPO (NIL T) -7 NIL NIL) (-1127 2877628 2877633 2877663 "TYPE" 2877668 T TYPE (NIL) -9 NIL NIL) (-1126 2876599 2876801 2877041 "TWOFACT" 2877422 NIL TWOFACT (NIL T) -7 NIL NIL) (-1125 2875537 2875874 2876137 "TUPLE" 2876371 NIL TUPLE (NIL T) -8 NIL NIL) (-1124 2873228 2873747 2874286 "TUBETOOL" 2875020 T TUBETOOL (NIL) -7 NIL NIL) (-1123 2872077 2872282 2872523 "TUBE" 2873021 NIL TUBE (NIL T) -8 NIL NIL) (-1122 2866801 2871055 2871337 "TS" 2871829 NIL TS (NIL T) -8 NIL NIL) (-1121 2855505 2859597 2859693 "TSETCAT" 2864927 NIL TSETCAT (NIL T T T T) -9 NIL 2866458) (-1120 2850240 2851838 2853728 "TSETCAT-" 2853733 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1119 2844503 2845349 2846291 "TRMANIP" 2849376 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1118 2843944 2844007 2844170 "TRIMAT" 2844435 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1117 2841750 2841987 2842350 "TRIGMNIP" 2843693 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1116 2841270 2841383 2841413 "TRIGCAT" 2841626 T TRIGCAT (NIL) -9 NIL NIL) (-1115 2840939 2841018 2841159 "TRIGCAT-" 2841164 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1114 2837838 2839799 2840079 "TREE" 2840694 NIL TREE (NIL T) -8 NIL NIL) (-1113 2837112 2837640 2837670 "TRANFUN" 2837705 T TRANFUN (NIL) -9 NIL 2837771) (-1112 2836391 2836582 2836862 "TRANFUN-" 2836867 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1111 2836195 2836227 2836288 "TOPSP" 2836352 T TOPSP (NIL) -7 NIL NIL) (-1110 2835547 2835662 2835815 "TOOLSIGN" 2836076 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1109 2834208 2834724 2834963 "TEXTFILE" 2835330 T TEXTFILE (NIL) -8 NIL NIL) (-1108 2832073 2832587 2833025 "TEX" 2833792 T TEX (NIL) -8 NIL NIL) (-1107 2831854 2831885 2831957 "TEX1" 2832036 NIL TEX1 (NIL T) -7 NIL NIL) (-1106 2831502 2831565 2831655 "TEMUTL" 2831786 T TEMUTL (NIL) -7 NIL NIL) (-1105 2829656 2829936 2830261 "TBCMPPK" 2831225 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1104 2821545 2827817 2827873 "TBAGG" 2828273 NIL TBAGG (NIL T T) -9 NIL 2828484) (-1103 2816615 2818103 2819857 "TBAGG-" 2819862 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1102 2815999 2816106 2816251 "TANEXP" 2816504 NIL TANEXP (NIL T) -7 NIL NIL) (-1101 2809500 2815856 2815949 "TABLE" 2815954 NIL TABLE (NIL T T) -8 NIL NIL) (-1100 2808912 2809011 2809149 "TABLEAU" 2809397 NIL TABLEAU (NIL T) -8 NIL NIL) (-1099 2803485 2804705 2805953 "TABLBUMP" 2807698 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1098 2802913 2803013 2803141 "SYSTEM" 2803379 T SYSTEM (NIL) -7 NIL NIL) (-1097 2799376 2800071 2800854 "SYSSOLP" 2802164 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1096 2795667 2796375 2797109 "SYNTAX" 2798664 T SYNTAX (NIL) -8 NIL NIL) (-1095 2792801 2793409 2794047 "SYMTAB" 2795051 T SYMTAB (NIL) -8 NIL NIL) (-1094 2788050 2788952 2789935 "SYMS" 2791840 T SYMS (NIL) -8 NIL NIL) (-1093 2785279 2787506 2787735 "SYMPOLY" 2787855 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1092 2784799 2784874 2784996 "SYMFUNC" 2785191 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1091 2780776 2782036 2782858 "SYMBOL" 2783999 T SYMBOL (NIL) -8 NIL NIL) (-1090 2774315 2776004 2777724 "SWITCH" 2779078 T SWITCH (NIL) -8 NIL NIL) (-1089 2767545 2773142 2773444 "SUTS" 2774070 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1088 2759435 2766666 2766946 "SUPXS" 2767322 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1087 2750927 2759056 2759181 "SUP" 2759344 NIL SUP (NIL T) -8 NIL NIL) (-1086 2750086 2750213 2750430 "SUPFRACF" 2750795 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1085 2749711 2749770 2749881 "SUP2" 2750021 NIL SUP2 (NIL T T) -7 NIL NIL) (-1084 2748108 2748382 2748744 "SUMRF" 2749410 NIL SUMRF (NIL T) -7 NIL NIL) (-1083 2747425 2747491 2747689 "SUMFS" 2748029 NIL SUMFS (NIL T T) -7 NIL NIL) (-1082 2731361 2746606 2746856 "SULS" 2747232 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1081 2730683 2730886 2731026 "SUCH" 2731269 NIL SUCH (NIL T T) -8 NIL NIL) (-1080 2724610 2725622 2726580 "SUBSPACE" 2729771 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1079 2724040 2724130 2724294 "SUBRESP" 2724498 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1078 2717409 2718705 2720016 "STTF" 2722776 NIL STTF (NIL T) -7 NIL NIL) (-1077 2711582 2712702 2713849 "STTFNC" 2716309 NIL STTFNC (NIL T) -7 NIL NIL) (-1076 2702922 2704789 2706582 "STTAYLOR" 2709823 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1075 2696166 2702786 2702869 "STRTBL" 2702874 NIL STRTBL (NIL T) -8 NIL NIL) (-1074 2691557 2696121 2696152 "STRING" 2696157 T STRING (NIL) -8 NIL NIL) (-1073 2686446 2690931 2690961 "STRICAT" 2691020 T STRICAT (NIL) -9 NIL 2691082) (-1072 2679160 2683969 2684589 "STREAM" 2685861 NIL STREAM (NIL T) -8 NIL NIL) (-1071 2678670 2678747 2678891 "STREAM3" 2679077 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1070 2677652 2677835 2678070 "STREAM2" 2678483 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1069 2677340 2677392 2677485 "STREAM1" 2677594 NIL STREAM1 (NIL T) -7 NIL NIL) (-1068 2676356 2676537 2676768 "STINPROD" 2677156 NIL STINPROD (NIL T) -7 NIL NIL) (-1067 2675935 2676119 2676149 "STEP" 2676229 T STEP (NIL) -9 NIL 2676307) (-1066 2669478 2675834 2675911 "STBL" 2675916 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1065 2664654 2668701 2668744 "STAGG" 2668897 NIL STAGG (NIL T) -9 NIL 2668986) (-1064 2662356 2662958 2663830 "STAGG-" 2663835 NIL STAGG- (NIL T T) -8 NIL NIL) (-1063 2660551 2662126 2662218 "STACK" 2662299 NIL STACK (NIL T) -8 NIL NIL) (-1062 2653282 2658698 2659153 "SREGSET" 2660181 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1061 2645714 2647082 2648594 "SRDCMPK" 2651888 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1060 2638682 2643155 2643185 "SRAGG" 2644488 T SRAGG (NIL) -9 NIL 2645096) (-1059 2637699 2637954 2638333 "SRAGG-" 2638338 NIL SRAGG- (NIL T) -8 NIL NIL) (-1058 2632148 2636618 2637045 "SQMATRIX" 2637318 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1057 2625900 2628868 2629594 "SPLTREE" 2631494 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1056 2621890 2622556 2623202 "SPLNODE" 2625326 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1055 2620937 2621170 2621200 "SPFCAT" 2621644 T SPFCAT (NIL) -9 NIL NIL) (-1054 2619674 2619884 2620148 "SPECOUT" 2620695 T SPECOUT (NIL) -7 NIL NIL) (-1053 2619435 2619475 2619544 "SPADPRSR" 2619627 T SPADPRSR (NIL) -7 NIL NIL) (-1052 2611458 2613205 2613247 "SPACEC" 2617570 NIL SPACEC (NIL T) -9 NIL 2619386) (-1051 2609629 2611391 2611439 "SPACE3" 2611444 NIL SPACE3 (NIL T) -8 NIL NIL) (-1050 2608381 2608552 2608843 "SORTPAK" 2609434 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1049 2606437 2606740 2607158 "SOLVETRA" 2608045 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1048 2605448 2605670 2605944 "SOLVESER" 2606210 NIL SOLVESER (NIL T) -7 NIL NIL) (-1047 2600668 2601549 2602551 "SOLVERAD" 2604500 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1046 2596483 2597092 2597821 "SOLVEFOR" 2600035 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1045 2590783 2595835 2595931 "SNTSCAT" 2595936 NIL SNTSCAT (NIL T T T T) -9 NIL 2596006) (-1044 2584887 2589114 2589504 "SMTS" 2590473 NIL SMTS (NIL T T T) -8 NIL NIL) (-1043 2579297 2584776 2584852 "SMP" 2584857 NIL SMP (NIL T T) -8 NIL NIL) (-1042 2577456 2577757 2578155 "SMITH" 2578994 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1041 2570421 2574617 2574719 "SMATCAT" 2576059 NIL SMATCAT (NIL NIL T T T) -9 NIL 2576608) (-1040 2567362 2568185 2569362 "SMATCAT-" 2569367 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1039 2565076 2566599 2566642 "SKAGG" 2566903 NIL SKAGG (NIL T) -9 NIL 2567038) (-1038 2561134 2564180 2564458 "SINT" 2564820 T SINT (NIL) -8 NIL NIL) (-1037 2560906 2560944 2561010 "SIMPAN" 2561090 T SIMPAN (NIL) -7 NIL NIL) (-1036 2559744 2559965 2560240 "SIGNRF" 2560665 NIL SIGNRF (NIL T) -7 NIL NIL) (-1035 2558529 2558680 2558970 "SIGNEF" 2559573 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1034 2556219 2556673 2557179 "SHP" 2558070 NIL SHP (NIL T NIL) -7 NIL NIL) (-1033 2550072 2556120 2556196 "SHDP" 2556201 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1032 2549562 2549754 2549784 "SGROUP" 2549936 T SGROUP (NIL) -9 NIL 2550023) (-1031 2549332 2549384 2549488 "SGROUP-" 2549493 NIL SGROUP- (NIL T) -8 NIL NIL) (-1030 2546168 2546865 2547588 "SGCF" 2548631 T SGCF (NIL) -7 NIL NIL) (-1029 2540567 2545619 2545715 "SFRTCAT" 2545720 NIL SFRTCAT (NIL T T T T) -9 NIL 2545758) (-1028 2534027 2535042 2536176 "SFRGCD" 2539550 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1027 2527193 2528264 2529448 "SFQCMPK" 2532960 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1026 2526815 2526904 2527014 "SFORT" 2527134 NIL SFORT (NIL T T) -8 NIL NIL) (-1025 2525960 2526655 2526776 "SEXOF" 2526781 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1024 2525094 2525841 2525909 "SEX" 2525914 T SEX (NIL) -8 NIL NIL) (-1023 2519871 2520560 2520655 "SEXCAT" 2524426 NIL SEXCAT (NIL T T T T T) -9 NIL 2525045) (-1022 2517051 2519805 2519853 "SET" 2519858 NIL SET (NIL T) -8 NIL NIL) (-1021 2515270 2515732 2516037 "SETMN" 2516792 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1020 2514878 2515004 2515034 "SETCAT" 2515151 T SETCAT (NIL) -9 NIL 2515235) (-1019 2514658 2514710 2514809 "SETCAT-" 2514814 NIL SETCAT- (NIL T) -8 NIL NIL) (-1018 2511046 2513120 2513163 "SETAGG" 2514033 NIL SETAGG (NIL T) -9 NIL 2514373) (-1017 2510504 2510620 2510857 "SETAGG-" 2510862 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1016 2509708 2510001 2510062 "SEGXCAT" 2510348 NIL SEGXCAT (NIL T T) -9 NIL 2510468) (-1015 2508764 2509374 2509556 "SEG" 2509561 NIL SEG (NIL T) -8 NIL NIL) (-1014 2507671 2507884 2507927 "SEGCAT" 2508509 NIL SEGCAT (NIL T) -9 NIL 2508747) (-1013 2506720 2507050 2507250 "SEGBIND" 2507506 NIL SEGBIND (NIL T) -8 NIL NIL) (-1012 2506341 2506400 2506513 "SEGBIND2" 2506655 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1011 2505560 2505686 2505890 "SEG2" 2506185 NIL SEG2 (NIL T T) -7 NIL NIL) (-1010 2504997 2505495 2505542 "SDVAR" 2505547 NIL SDVAR (NIL T) -8 NIL NIL) (-1009 2497249 2504770 2504898 "SDPOL" 2504903 NIL SDPOL (NIL T) -8 NIL NIL) (-1008 2495842 2496108 2496427 "SCPKG" 2496964 NIL SCPKG (NIL T) -7 NIL NIL) (-1007 2494979 2495158 2495358 "SCOPE" 2495664 T SCOPE (NIL) -8 NIL NIL) (-1006 2494200 2494333 2494512 "SCACHE" 2494834 NIL SCACHE (NIL T) -7 NIL NIL) (-1005 2493639 2493960 2494045 "SAOS" 2494137 T SAOS (NIL) -8 NIL NIL) (-1004 2493204 2493239 2493412 "SAERFFC" 2493598 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1003 2487098 2493101 2493181 "SAE" 2493186 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1002 2486691 2486726 2486885 "SAEFACT" 2487057 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1001 2485012 2485326 2485727 "RURPK" 2486357 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1000 2483660 2483937 2484246 "RULESET" 2484848 NIL RULESET (NIL T T T) -8 NIL NIL) (-999 2480854 2481357 2481818 "RULE" 2483342 NIL RULE (NIL T T T) -8 NIL NIL) (-998 2480491 2480646 2480727 "RULECOLD" 2480806 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-997 2475383 2476177 2477093 "RSETGCD" 2479690 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-996 2464698 2469750 2469844 "RSETCAT" 2473909 NIL RSETCAT (NIL T T T T) -9 NIL 2475006) (-995 2462629 2463168 2463988 "RSETCAT-" 2463993 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-994 2455051 2456426 2457942 "RSDCMPK" 2461228 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-993 2453069 2453510 2453582 "RRCC" 2454658 NIL RRCC (NIL T T) -9 NIL 2455002) (-992 2452423 2452597 2452873 "RRCC-" 2452878 NIL RRCC- (NIL T T T) -8 NIL NIL) (-991 2426790 2436415 2436479 "RPOLCAT" 2446981 NIL RPOLCAT (NIL T T T) -9 NIL 2450139) (-990 2418294 2420632 2423750 "RPOLCAT-" 2423755 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-989 2409360 2416524 2417004 "ROUTINE" 2417834 T ROUTINE (NIL) -8 NIL NIL) (-988 2406065 2408916 2409063 "ROMAN" 2409233 T ROMAN (NIL) -8 NIL NIL) (-987 2404351 2404936 2405193 "ROIRC" 2405871 NIL ROIRC (NIL T T) -8 NIL NIL) (-986 2400756 2403060 2403088 "RNS" 2403384 T RNS (NIL) -9 NIL 2403654) (-985 2399270 2399653 2400184 "RNS-" 2400257 NIL RNS- (NIL T) -8 NIL NIL) (-984 2398696 2399104 2399132 "RNG" 2399137 T RNG (NIL) -9 NIL 2399158) (-983 2398094 2398456 2398496 "RMODULE" 2398556 NIL RMODULE (NIL T) -9 NIL 2398598) (-982 2396946 2397040 2397370 "RMCAT2" 2397995 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-981 2393660 2396129 2396450 "RMATRIX" 2396681 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-980 2386657 2388891 2389003 "RMATCAT" 2392312 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2393294) (-979 2386036 2386183 2386486 "RMATCAT-" 2386491 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-978 2385606 2385681 2385807 "RINTERP" 2385955 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-977 2384657 2385221 2385249 "RING" 2385359 T RING (NIL) -9 NIL 2385453) (-976 2384452 2384496 2384590 "RING-" 2384595 NIL RING- (NIL T) -8 NIL NIL) (-975 2383300 2383537 2383793 "RIDIST" 2384216 T RIDIST (NIL) -7 NIL NIL) (-974 2374622 2382774 2382977 "RGCHAIN" 2383149 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-973 2371627 2372241 2372909 "RF" 2373986 NIL RF (NIL T) -7 NIL NIL) (-972 2371276 2371339 2371440 "RFFACTOR" 2371558 NIL RFFACTOR (NIL T) -7 NIL NIL) (-971 2371004 2371039 2371134 "RFFACT" 2371235 NIL RFFACT (NIL T) -7 NIL NIL) (-970 2369134 2369498 2369878 "RFDIST" 2370644 T RFDIST (NIL) -7 NIL NIL) (-969 2368592 2368684 2368844 "RETSOL" 2369036 NIL RETSOL (NIL T T) -7 NIL NIL) (-968 2368185 2368265 2368306 "RETRACT" 2368496 NIL RETRACT (NIL T) -9 NIL NIL) (-967 2368037 2368062 2368146 "RETRACT-" 2368151 NIL RETRACT- (NIL T T) -8 NIL NIL) (-966 2360895 2367694 2367819 "RESULT" 2367932 T RESULT (NIL) -8 NIL NIL) (-965 2359480 2360169 2360366 "RESRING" 2360798 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-964 2359120 2359169 2359265 "RESLATC" 2359417 NIL RESLATC (NIL T) -7 NIL NIL) (-963 2358829 2358863 2358968 "REPSQ" 2359079 NIL REPSQ (NIL T) -7 NIL NIL) (-962 2356260 2356840 2357440 "REP" 2358249 T REP (NIL) -7 NIL NIL) (-961 2355961 2355995 2356104 "REPDB" 2356219 NIL REPDB (NIL T) -7 NIL NIL) (-960 2349906 2351285 2352505 "REP2" 2354773 NIL REP2 (NIL T) -7 NIL NIL) (-959 2346312 2346993 2347798 "REP1" 2349133 NIL REP1 (NIL T) -7 NIL NIL) (-958 2339058 2344473 2344925 "REGSET" 2345943 NIL REGSET (NIL T T T T) -8 NIL NIL) (-957 2337879 2338214 2338462 "REF" 2338843 NIL REF (NIL T) -8 NIL NIL) (-956 2337260 2337363 2337528 "REDORDER" 2337763 NIL REDORDER (NIL T T) -7 NIL NIL) (-955 2333229 2336494 2336715 "RECLOS" 2337091 NIL RECLOS (NIL T) -8 NIL NIL) (-954 2332286 2332467 2332680 "REALSOLV" 2333036 T REALSOLV (NIL) -7 NIL NIL) (-953 2332134 2332175 2332203 "REAL" 2332208 T REAL (NIL) -9 NIL 2332243) (-952 2328570 2329372 2330254 "REAL0Q" 2331299 NIL REAL0Q (NIL T) -7 NIL NIL) (-951 2324181 2325169 2326228 "REAL0" 2327551 NIL REAL0 (NIL T) -7 NIL NIL) (-950 2323589 2323661 2323866 "RDIV" 2324103 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-949 2322662 2322836 2323047 "RDIST" 2323411 NIL RDIST (NIL T) -7 NIL NIL) (-948 2321266 2321553 2321922 "RDETRS" 2322370 NIL RDETRS (NIL T T) -7 NIL NIL) (-947 2319079 2319533 2320068 "RDETR" 2320808 NIL RDETR (NIL T T) -7 NIL NIL) (-946 2317687 2317965 2318366 "RDEEFS" 2318795 NIL RDEEFS (NIL T T) -7 NIL NIL) (-945 2316179 2316485 2316914 "RDEEF" 2317375 NIL RDEEF (NIL T T) -7 NIL NIL) (-944 2310464 2313396 2313424 "RCFIELD" 2314701 T RCFIELD (NIL) -9 NIL 2315431) (-943 2308533 2309037 2309730 "RCFIELD-" 2309803 NIL RCFIELD- (NIL T) -8 NIL NIL) (-942 2304865 2306650 2306691 "RCAGG" 2307762 NIL RCAGG (NIL T) -9 NIL 2308227) (-941 2304496 2304590 2304750 "RCAGG-" 2304755 NIL RCAGG- (NIL T T) -8 NIL NIL) (-940 2303818 2303930 2304092 "RATRET" 2304380 NIL RATRET (NIL T) -7 NIL NIL) (-939 2303375 2303442 2303561 "RATFACT" 2303746 NIL RATFACT (NIL T) -7 NIL NIL) (-938 2302690 2302810 2302960 "RANDSRC" 2303245 T RANDSRC (NIL) -7 NIL NIL) (-937 2302427 2302471 2302542 "RADUTIL" 2302639 T RADUTIL (NIL) -7 NIL NIL) (-936 2295434 2301170 2301487 "RADIX" 2302142 NIL RADIX (NIL NIL) -8 NIL NIL) (-935 2287004 2295278 2295406 "RADFF" 2295411 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-934 2286656 2286731 2286759 "RADCAT" 2286916 T RADCAT (NIL) -9 NIL NIL) (-933 2286441 2286489 2286586 "RADCAT-" 2286591 NIL RADCAT- (NIL T) -8 NIL NIL) (-932 2284592 2286216 2286305 "QUEUE" 2286385 NIL QUEUE (NIL T) -8 NIL NIL) (-931 2281089 2284529 2284574 "QUAT" 2284579 NIL QUAT (NIL T) -8 NIL NIL) (-930 2280727 2280770 2280897 "QUATCT2" 2281040 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-929 2274521 2277901 2277941 "QUATCAT" 2278720 NIL QUATCAT (NIL T) -9 NIL 2279485) (-928 2270665 2271702 2273089 "QUATCAT-" 2273183 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-927 2268186 2269750 2269791 "QUAGG" 2270166 NIL QUAGG (NIL T) -9 NIL 2270341) (-926 2267111 2267584 2267756 "QFORM" 2268058 NIL QFORM (NIL NIL T) -8 NIL NIL) (-925 2258408 2263666 2263706 "QFCAT" 2264364 NIL QFCAT (NIL T) -9 NIL 2265357) (-924 2253980 2255181 2256772 "QFCAT-" 2256866 NIL QFCAT- (NIL T T) -8 NIL NIL) (-923 2253618 2253661 2253788 "QFCAT2" 2253931 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-922 2253078 2253188 2253318 "QEQUAT" 2253508 T QEQUAT (NIL) -8 NIL NIL) (-921 2246264 2247335 2248517 "QCMPACK" 2252011 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-920 2243840 2244261 2244689 "QALGSET" 2245919 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-919 2243085 2243259 2243491 "QALGSET2" 2243660 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-918 2241776 2241999 2242316 "PWFFINTB" 2242858 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-917 2239964 2240132 2240485 "PUSHVAR" 2241590 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-916 2235882 2236936 2236977 "PTRANFN" 2238861 NIL PTRANFN (NIL T) -9 NIL NIL) (-915 2234294 2234585 2234906 "PTPACK" 2235593 NIL PTPACK (NIL T) -7 NIL NIL) (-914 2233930 2233987 2234094 "PTFUNC2" 2234231 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-913 2228407 2232748 2232788 "PTCAT" 2233156 NIL PTCAT (NIL T) -9 NIL 2233318) (-912 2228065 2228100 2228224 "PSQFR" 2228366 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-911 2226660 2226958 2227292 "PSEUDLIN" 2227763 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-910 2213467 2215832 2218155 "PSETPK" 2224420 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-909 2206554 2209268 2209362 "PSETCAT" 2212343 NIL PSETCAT (NIL T T T T) -9 NIL 2213157) (-908 2204392 2205026 2205845 "PSETCAT-" 2205850 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-907 2203741 2203906 2203934 "PSCURVE" 2204202 T PSCURVE (NIL) -9 NIL 2204369) (-906 2200193 2201719 2201783 "PSCAT" 2202619 NIL PSCAT (NIL T T T) -9 NIL 2202859) (-905 2199257 2199473 2199872 "PSCAT-" 2199877 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-904 2197909 2198542 2198756 "PRTITION" 2199063 T PRTITION (NIL) -8 NIL NIL) (-903 2187007 2189213 2191401 "PRS" 2195771 NIL PRS (NIL T T) -7 NIL NIL) (-902 2184866 2186358 2186398 "PRQAGG" 2186581 NIL PRQAGG (NIL T) -9 NIL 2186683) (-901 2184437 2184539 2184567 "PROPLOG" 2184752 T PROPLOG (NIL) -9 NIL NIL) (-900 2181560 2182125 2182652 "PROPFRML" 2183942 NIL PROPFRML (NIL T) -8 NIL NIL) (-899 2181020 2181130 2181260 "PROPERTY" 2181450 T PROPERTY (NIL) -8 NIL NIL) (-898 2174794 2179186 2180006 "PRODUCT" 2180246 NIL PRODUCT (NIL T T) -8 NIL NIL) (-897 2172070 2174254 2174487 "PR" 2174605 NIL PR (NIL T T) -8 NIL NIL) (-896 2171866 2171898 2171957 "PRINT" 2172031 T PRINT (NIL) -7 NIL NIL) (-895 2171206 2171323 2171475 "PRIMES" 2171746 NIL PRIMES (NIL T) -7 NIL NIL) (-894 2169271 2169672 2170138 "PRIMELT" 2170785 NIL PRIMELT (NIL T) -7 NIL NIL) (-893 2169000 2169049 2169077 "PRIMCAT" 2169201 T PRIMCAT (NIL) -9 NIL NIL) (-892 2165161 2168938 2168983 "PRIMARR" 2168988 NIL PRIMARR (NIL T) -8 NIL NIL) (-891 2164168 2164346 2164574 "PRIMARR2" 2164979 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-890 2163811 2163867 2163978 "PREASSOC" 2164106 NIL PREASSOC (NIL T T) -7 NIL NIL) (-889 2163286 2163419 2163447 "PPCURVE" 2163652 T PPCURVE (NIL) -9 NIL 2163788) (-888 2160645 2161044 2161636 "POLYROOT" 2162867 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-887 2154551 2160251 2160410 "POLY" 2160518 NIL POLY (NIL T) -8 NIL NIL) (-886 2153936 2153994 2154227 "POLYLIFT" 2154487 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-885 2150221 2150670 2151298 "POLYCATQ" 2153481 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-884 2137262 2142659 2142723 "POLYCAT" 2146208 NIL POLYCAT (NIL T T T) -9 NIL 2148135) (-883 2130713 2132574 2134957 "POLYCAT-" 2134962 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-882 2130302 2130370 2130489 "POLY2UP" 2130639 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-881 2129938 2129995 2130102 "POLY2" 2130239 NIL POLY2 (NIL T T) -7 NIL NIL) (-880 2128623 2128862 2129138 "POLUTIL" 2129712 NIL POLUTIL (NIL T T) -7 NIL NIL) (-879 2126985 2127262 2127592 "POLTOPOL" 2128345 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-878 2122508 2126922 2126967 "POINT" 2126972 NIL POINT (NIL T) -8 NIL NIL) (-877 2120695 2121052 2121427 "PNTHEORY" 2122153 T PNTHEORY (NIL) -7 NIL NIL) (-876 2119123 2119420 2119829 "PMTOOLS" 2120393 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-875 2118716 2118794 2118911 "PMSYM" 2119039 NIL PMSYM (NIL T) -7 NIL NIL) (-874 2118219 2118288 2118462 "PMQFCAT" 2118641 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-873 2117574 2117684 2117840 "PMPRED" 2118096 NIL PMPRED (NIL T) -7 NIL NIL) (-872 2116970 2117056 2117217 "PMPREDFS" 2117475 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-871 2115602 2115810 2116194 "PMPLCAT" 2116732 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-870 2115134 2115213 2115365 "PMLSAGG" 2115517 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-869 2114604 2114680 2114860 "PMKERNEL" 2115052 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-868 2114221 2114296 2114409 "PMINS" 2114523 NIL PMINS (NIL T) -7 NIL NIL) (-867 2113644 2113713 2113928 "PMFS" 2114146 NIL PMFS (NIL T T T) -7 NIL NIL) (-866 2112875 2112993 2113197 "PMDOWN" 2113521 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-865 2112038 2112197 2112379 "PMASS" 2112713 T PMASS (NIL) -7 NIL NIL) (-864 2111312 2111423 2111586 "PMASSFS" 2111924 NIL PMASSFS (NIL T T) -7 NIL NIL) (-863 2110967 2111035 2111129 "PLOTTOOL" 2111238 T PLOTTOOL (NIL) -7 NIL NIL) (-862 2105589 2106778 2107926 "PLOT" 2109839 T PLOT (NIL) -8 NIL NIL) (-861 2101403 2102437 2103358 "PLOT3D" 2104688 T PLOT3D (NIL) -8 NIL NIL) (-860 2100315 2100492 2100727 "PLOT1" 2101207 NIL PLOT1 (NIL T) -7 NIL NIL) (-859 2075709 2080381 2085232 "PLEQN" 2095581 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-858 2075027 2075149 2075329 "PINTERP" 2075574 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-857 2074720 2074767 2074870 "PINTERPA" 2074974 NIL PINTERPA (NIL T T) -7 NIL NIL) (-856 2073959 2074526 2074613 "PI" 2074653 T PI (NIL) -8 NIL NIL) (-855 2072351 2073336 2073364 "PID" 2073546 T PID (NIL) -9 NIL 2073680) (-854 2072076 2072113 2072201 "PICOERCE" 2072308 NIL PICOERCE (NIL T) -7 NIL NIL) (-853 2071396 2071535 2071711 "PGROEB" 2071932 NIL PGROEB (NIL T) -7 NIL NIL) (-852 2066983 2067797 2068702 "PGE" 2070511 T PGE (NIL) -7 NIL NIL) (-851 2065107 2065353 2065719 "PGCD" 2066700 NIL PGCD (NIL T T T T) -7 NIL NIL) (-850 2064445 2064548 2064709 "PFRPAC" 2064991 NIL PFRPAC (NIL T) -7 NIL NIL) (-849 2061060 2062993 2063346 "PFR" 2064124 NIL PFR (NIL T) -8 NIL NIL) (-848 2059433 2059677 2060002 "PFOTOOLS" 2060807 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-847 2057966 2058205 2058556 "PFOQ" 2059190 NIL PFOQ (NIL T T T) -7 NIL NIL) (-846 2056443 2056655 2057017 "PFO" 2057750 NIL PFO (NIL T T T T T) -7 NIL NIL) (-845 2052966 2056332 2056401 "PF" 2056406 NIL PF (NIL NIL) -8 NIL NIL) (-844 2050395 2051676 2051704 "PFECAT" 2052289 T PFECAT (NIL) -9 NIL 2052673) (-843 2049840 2049994 2050208 "PFECAT-" 2050213 NIL PFECAT- (NIL T) -8 NIL NIL) (-842 2048444 2048695 2048996 "PFBRU" 2049589 NIL PFBRU (NIL T T) -7 NIL NIL) (-841 2046311 2046662 2047094 "PFBR" 2048095 NIL PFBR (NIL T T T T) -7 NIL NIL) (-840 2042162 2043687 2044363 "PERM" 2045668 NIL PERM (NIL T) -8 NIL NIL) (-839 2037427 2038369 2039239 "PERMGRP" 2041325 NIL PERMGRP (NIL T) -8 NIL NIL) (-838 2035498 2036491 2036532 "PERMCAT" 2036978 NIL PERMCAT (NIL T) -9 NIL 2037283) (-837 2035153 2035194 2035317 "PERMAN" 2035451 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-836 2032593 2034722 2034853 "PENDTREE" 2035055 NIL PENDTREE (NIL T) -8 NIL NIL) (-835 2030666 2031444 2031485 "PDRING" 2032142 NIL PDRING (NIL T) -9 NIL 2032427) (-834 2029769 2029987 2030349 "PDRING-" 2030354 NIL PDRING- (NIL T T) -8 NIL NIL) (-833 2026910 2027661 2028352 "PDEPROB" 2029098 T PDEPROB (NIL) -8 NIL NIL) (-832 2024473 2024969 2025518 "PDEPACK" 2026381 T PDEPACK (NIL) -7 NIL NIL) (-831 2023385 2023575 2023826 "PDECOMP" 2024272 NIL PDECOMP (NIL T T) -7 NIL NIL) (-830 2020997 2021812 2021840 "PDECAT" 2022625 T PDECAT (NIL) -9 NIL 2023336) (-829 2020750 2020783 2020872 "PCOMP" 2020958 NIL PCOMP (NIL T T) -7 NIL NIL) (-828 2018957 2019553 2019849 "PBWLB" 2020480 NIL PBWLB (NIL T) -8 NIL NIL) (-827 2011465 2013034 2014370 "PATTERN" 2017642 NIL PATTERN (NIL T) -8 NIL NIL) (-826 2011097 2011154 2011263 "PATTERN2" 2011402 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-825 2008854 2009242 2009699 "PATTERN1" 2010686 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-824 2006249 2006803 2007284 "PATRES" 2008419 NIL PATRES (NIL T T) -8 NIL NIL) (-823 2005813 2005880 2006012 "PATRES2" 2006176 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-822 2003710 2004110 2004515 "PATMATCH" 2005482 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-821 2003247 2003430 2003471 "PATMAB" 2003578 NIL PATMAB (NIL T) -9 NIL 2003661) (-820 2001792 2002101 2002359 "PATLRES" 2003052 NIL PATLRES (NIL T T T) -8 NIL NIL) (-819 2001338 2001461 2001502 "PATAB" 2001507 NIL PATAB (NIL T) -9 NIL 2001679) (-818 1998819 1999351 1999924 "PARTPERM" 2000785 T PARTPERM (NIL) -7 NIL NIL) (-817 1998440 1998503 1998605 "PARSURF" 1998750 NIL PARSURF (NIL T) -8 NIL NIL) (-816 1998072 1998129 1998238 "PARSU2" 1998377 NIL PARSU2 (NIL T T) -7 NIL NIL) (-815 1997836 1997876 1997943 "PARSER" 1998025 T PARSER (NIL) -7 NIL NIL) (-814 1997457 1997520 1997622 "PARSCURV" 1997767 NIL PARSCURV (NIL T) -8 NIL NIL) (-813 1997089 1997146 1997255 "PARSC2" 1997394 NIL PARSC2 (NIL T T) -7 NIL NIL) (-812 1996728 1996786 1996883 "PARPCURV" 1997025 NIL PARPCURV (NIL T) -8 NIL NIL) (-811 1996360 1996417 1996526 "PARPC2" 1996665 NIL PARPC2 (NIL T T) -7 NIL NIL) (-810 1995880 1995966 1996085 "PAN2EXPR" 1996261 T PAN2EXPR (NIL) -7 NIL NIL) (-809 1994686 1995001 1995229 "PALETTE" 1995672 T PALETTE (NIL) -8 NIL NIL) (-808 1993154 1993691 1994051 "PAIR" 1994372 NIL PAIR (NIL T T) -8 NIL NIL) (-807 1986996 1992405 1992599 "PADICRC" 1993009 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-806 1980196 1986334 1986518 "PADICRAT" 1986844 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-805 1978500 1980133 1980178 "PADIC" 1980183 NIL PADIC (NIL NIL) -8 NIL NIL) (-804 1975705 1977279 1977319 "PADICCT" 1977900 NIL PADICCT (NIL NIL) -9 NIL 1978182) (-803 1974662 1974862 1975130 "PADEPAC" 1975492 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-802 1973874 1974007 1974213 "PADE" 1974524 NIL PADE (NIL T T T) -7 NIL NIL) (-801 1971877 1972709 1973024 "OWP" 1973642 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-800 1970981 1971477 1971649 "OVAR" 1971745 NIL OVAR (NIL NIL) -8 NIL NIL) (-799 1970245 1970366 1970527 "OUT" 1970840 T OUT (NIL) -7 NIL NIL) (-798 1959299 1961470 1963640 "OUTFORM" 1968095 T OUTFORM (NIL) -8 NIL NIL) (-797 1958707 1959028 1959117 "OSI" 1959230 T OSI (NIL) -8 NIL NIL) (-796 1958238 1958576 1958604 "OSGROUP" 1958609 T OSGROUP (NIL) -9 NIL 1958631) (-795 1956983 1957210 1957495 "ORTHPOL" 1957985 NIL ORTHPOL (NIL T) -7 NIL NIL) (-794 1954354 1956644 1956782 "OREUP" 1956926 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-793 1951750 1954047 1954173 "ORESUP" 1954296 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-792 1949285 1949785 1950345 "OREPCTO" 1951239 NIL OREPCTO (NIL T T) -7 NIL NIL) (-791 1943195 1945401 1945441 "OREPCAT" 1947762 NIL OREPCAT (NIL T) -9 NIL 1948865) (-790 1940343 1941125 1942182 "OREPCAT-" 1942187 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-789 1939521 1939793 1939821 "ORDSET" 1940130 T ORDSET (NIL) -9 NIL 1940294) (-788 1939040 1939162 1939355 "ORDSET-" 1939360 NIL ORDSET- (NIL T) -8 NIL NIL) (-787 1937654 1938455 1938483 "ORDRING" 1938685 T ORDRING (NIL) -9 NIL 1938809) (-786 1937299 1937393 1937537 "ORDRING-" 1937542 NIL ORDRING- (NIL T) -8 NIL NIL) (-785 1936662 1937143 1937171 "ORDMON" 1937176 T ORDMON (NIL) -9 NIL 1937197) (-784 1935824 1935971 1936166 "ORDFUNS" 1936511 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-783 1935336 1935695 1935723 "ORDFIN" 1935728 T ORDFIN (NIL) -9 NIL 1935749) (-782 1931848 1933922 1934331 "ORDCOMP" 1934960 NIL ORDCOMP (NIL T) -8 NIL NIL) (-781 1931114 1931241 1931427 "ORDCOMP2" 1931708 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-780 1927621 1928504 1929341 "OPTPROB" 1930297 T OPTPROB (NIL) -8 NIL NIL) (-779 1924463 1925092 1925786 "OPTPACK" 1926947 T OPTPACK (NIL) -7 NIL NIL) (-778 1922189 1922925 1922953 "OPTCAT" 1923768 T OPTCAT (NIL) -9 NIL 1924414) (-777 1921957 1921996 1922062 "OPQUERY" 1922143 T OPQUERY (NIL) -7 NIL NIL) (-776 1919093 1920284 1920784 "OP" 1921489 NIL OP (NIL T) -8 NIL NIL) (-775 1915858 1917890 1918259 "ONECOMP" 1918757 NIL ONECOMP (NIL T) -8 NIL NIL) (-774 1915163 1915278 1915452 "ONECOMP2" 1915730 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-773 1914582 1914688 1914818 "OMSERVER" 1915053 T OMSERVER (NIL) -7 NIL NIL) (-772 1911471 1914023 1914063 "OMSAGG" 1914124 NIL OMSAGG (NIL T) -9 NIL 1914188) (-771 1910094 1910357 1910639 "OMPKG" 1911209 T OMPKG (NIL) -7 NIL NIL) (-770 1909524 1909627 1909655 "OM" 1909954 T OM (NIL) -9 NIL NIL) (-769 1908063 1909076 1909244 "OMLO" 1909405 NIL OMLO (NIL T T) -8 NIL NIL) (-768 1906993 1907140 1907366 "OMEXPR" 1907889 NIL OMEXPR (NIL T) -7 NIL NIL) (-767 1906311 1906539 1906675 "OMERR" 1906877 T OMERR (NIL) -8 NIL NIL) (-766 1905489 1905732 1905892 "OMERRK" 1906171 T OMERRK (NIL) -8 NIL NIL) (-765 1904967 1905166 1905274 "OMENC" 1905401 T OMENC (NIL) -8 NIL NIL) (-764 1898862 1900047 1901218 "OMDEV" 1903816 T OMDEV (NIL) -8 NIL NIL) (-763 1897931 1898102 1898296 "OMCONN" 1898688 T OMCONN (NIL) -8 NIL NIL) (-762 1896547 1897533 1897561 "OINTDOM" 1897566 T OINTDOM (NIL) -9 NIL 1897587) (-761 1892309 1893539 1894254 "OFMONOID" 1895864 NIL OFMONOID (NIL T) -8 NIL NIL) (-760 1891747 1892246 1892291 "ODVAR" 1892296 NIL ODVAR (NIL T) -8 NIL NIL) (-759 1888872 1891244 1891429 "ODR" 1891622 NIL ODR (NIL T T NIL) -8 NIL NIL) (-758 1881178 1888651 1888775 "ODPOL" 1888780 NIL ODPOL (NIL T) -8 NIL NIL) (-757 1875001 1881050 1881155 "ODP" 1881160 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-756 1873767 1873982 1874257 "ODETOOLS" 1874775 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-755 1870736 1871392 1872108 "ODESYS" 1873100 NIL ODESYS (NIL T T) -7 NIL NIL) (-754 1865640 1866548 1867571 "ODERTRIC" 1869811 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-753 1865066 1865148 1865342 "ODERED" 1865552 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-752 1861968 1862516 1863191 "ODERAT" 1864489 NIL ODERAT (NIL T T) -7 NIL NIL) (-751 1858929 1859393 1859989 "ODEPRRIC" 1861497 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-750 1856798 1857367 1857876 "ODEPROB" 1858440 T ODEPROB (NIL) -8 NIL NIL) (-749 1853323 1853806 1854452 "ODEPRIM" 1856277 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-748 1852576 1852678 1852936 "ODEPAL" 1853215 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-747 1848754 1849535 1850389 "ODEPACK" 1851742 T ODEPACK (NIL) -7 NIL NIL) (-746 1847791 1847898 1848126 "ODEINT" 1848643 NIL ODEINT (NIL T T) -7 NIL NIL) (-745 1841892 1843317 1844764 "ODEIFTBL" 1846364 T ODEIFTBL (NIL) -8 NIL NIL) (-744 1837236 1838022 1838980 "ODEEF" 1841051 NIL ODEEF (NIL T T) -7 NIL NIL) (-743 1836573 1836662 1836891 "ODECONST" 1837141 NIL ODECONST (NIL T T T) -7 NIL NIL) (-742 1834731 1835364 1835392 "ODECAT" 1835995 T ODECAT (NIL) -9 NIL 1836524) (-741 1831603 1834443 1834562 "OCT" 1834644 NIL OCT (NIL T) -8 NIL NIL) (-740 1831241 1831284 1831411 "OCTCT2" 1831554 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-739 1826075 1828513 1828553 "OC" 1829649 NIL OC (NIL T) -9 NIL 1830506) (-738 1823302 1824050 1825040 "OC-" 1825134 NIL OC- (NIL T T) -8 NIL NIL) (-737 1822681 1823123 1823151 "OCAMON" 1823156 T OCAMON (NIL) -9 NIL 1823177) (-736 1822239 1822554 1822582 "OASGP" 1822587 T OASGP (NIL) -9 NIL 1822607) (-735 1821527 1821990 1822018 "OAMONS" 1822058 T OAMONS (NIL) -9 NIL 1822101) (-734 1820968 1821375 1821403 "OAMON" 1821408 T OAMON (NIL) -9 NIL 1821428) (-733 1820273 1820765 1820793 "OAGROUP" 1820798 T OAGROUP (NIL) -9 NIL 1820818) (-732 1819963 1820013 1820101 "NUMTUBE" 1820217 NIL NUMTUBE (NIL T) -7 NIL NIL) (-731 1813536 1815054 1816590 "NUMQUAD" 1818447 T NUMQUAD (NIL) -7 NIL NIL) (-730 1809244 1810232 1811257 "NUMODE" 1812531 T NUMODE (NIL) -7 NIL NIL) (-729 1806648 1807494 1807522 "NUMINT" 1808439 T NUMINT (NIL) -9 NIL 1809195) (-728 1805596 1805793 1806011 "NUMFMT" 1806450 T NUMFMT (NIL) -7 NIL NIL) (-727 1791919 1794856 1797386 "NUMERIC" 1803105 NIL NUMERIC (NIL T) -7 NIL NIL) (-726 1786320 1791372 1791466 "NTSCAT" 1791471 NIL NTSCAT (NIL T T T T) -9 NIL 1791509) (-725 1785514 1785679 1785872 "NTPOLFN" 1786159 NIL NTPOLFN (NIL T) -7 NIL NIL) (-724 1773330 1782356 1783166 "NSUP" 1784736 NIL NSUP (NIL T) -8 NIL NIL) (-723 1772966 1773023 1773130 "NSUP2" 1773267 NIL NSUP2 (NIL T T) -7 NIL NIL) (-722 1762928 1772745 1772875 "NSMP" 1772880 NIL NSMP (NIL T T) -8 NIL NIL) (-721 1761360 1761661 1762018 "NREP" 1762616 NIL NREP (NIL T) -7 NIL NIL) (-720 1759951 1760203 1760561 "NPCOEF" 1761103 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-719 1759017 1759132 1759348 "NORMRETR" 1759832 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-718 1757070 1757360 1757767 "NORMPK" 1758725 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-717 1756755 1756783 1756907 "NORMMA" 1757036 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-716 1756582 1756712 1756741 "NONE" 1756746 T NONE (NIL) -8 NIL NIL) (-715 1756371 1756400 1756469 "NONE1" 1756546 NIL NONE1 (NIL T) -7 NIL NIL) (-714 1755856 1755918 1756103 "NODE1" 1756303 NIL NODE1 (NIL T T) -7 NIL NIL) (-713 1754149 1755019 1755274 "NNI" 1755621 T NNI (NIL) -8 NIL NIL) (-712 1752569 1752882 1753246 "NLINSOL" 1753817 NIL NLINSOL (NIL T) -7 NIL NIL) (-711 1748736 1749704 1750626 "NIPROB" 1751667 T NIPROB (NIL) -8 NIL NIL) (-710 1747465 1747699 1748001 "NFINTBAS" 1748498 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-709 1746173 1746404 1746685 "NCODIV" 1747233 NIL NCODIV (NIL T T) -7 NIL NIL) (-708 1745935 1745972 1746047 "NCNTFRAC" 1746130 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-707 1744115 1744479 1744899 "NCEP" 1745560 NIL NCEP (NIL T) -7 NIL NIL) (-706 1743027 1743766 1743794 "NASRING" 1743904 T NASRING (NIL) -9 NIL 1743978) (-705 1742822 1742866 1742960 "NASRING-" 1742965 NIL NASRING- (NIL T) -8 NIL NIL) (-704 1741976 1742475 1742503 "NARNG" 1742620 T NARNG (NIL) -9 NIL 1742711) (-703 1741668 1741735 1741869 "NARNG-" 1741874 NIL NARNG- (NIL T) -8 NIL NIL) (-702 1740547 1740754 1740989 "NAGSP" 1741453 T NAGSP (NIL) -7 NIL NIL) (-701 1731971 1733617 1735252 "NAGS" 1738932 T NAGS (NIL) -7 NIL NIL) (-700 1730535 1730839 1731166 "NAGF07" 1731664 T NAGF07 (NIL) -7 NIL NIL) (-699 1725117 1726397 1727693 "NAGF04" 1729259 T NAGF04 (NIL) -7 NIL NIL) (-698 1718149 1719747 1721364 "NAGF02" 1723520 T NAGF02 (NIL) -7 NIL NIL) (-697 1713413 1714503 1715610 "NAGF01" 1717062 T NAGF01 (NIL) -7 NIL NIL) (-696 1707073 1708631 1710208 "NAGE04" 1711856 T NAGE04 (NIL) -7 NIL NIL) (-695 1698314 1700417 1702529 "NAGE02" 1704981 T NAGE02 (NIL) -7 NIL NIL) (-694 1694307 1695244 1696198 "NAGE01" 1697380 T NAGE01 (NIL) -7 NIL NIL) (-693 1692114 1692645 1693200 "NAGD03" 1693772 T NAGD03 (NIL) -7 NIL NIL) (-692 1683900 1685819 1687764 "NAGD02" 1690189 T NAGD02 (NIL) -7 NIL NIL) (-691 1677759 1679172 1680600 "NAGD01" 1682492 T NAGD01 (NIL) -7 NIL NIL) (-690 1674016 1674826 1675651 "NAGC06" 1676954 T NAGC06 (NIL) -7 NIL NIL) (-689 1672493 1672822 1673175 "NAGC05" 1673683 T NAGC05 (NIL) -7 NIL NIL) (-688 1671877 1671994 1672136 "NAGC02" 1672371 T NAGC02 (NIL) -7 NIL NIL) (-687 1670939 1671496 1671536 "NAALG" 1671615 NIL NAALG (NIL T) -9 NIL 1671676) (-686 1670774 1670803 1670893 "NAALG-" 1670898 NIL NAALG- (NIL T T) -8 NIL NIL) (-685 1664724 1665832 1667019 "MULTSQFR" 1669670 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-684 1664043 1664118 1664302 "MULTFACT" 1664636 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-683 1657237 1661148 1661200 "MTSCAT" 1662260 NIL MTSCAT (NIL T T) -9 NIL 1662774) (-682 1656949 1657003 1657095 "MTHING" 1657177 NIL MTHING (NIL T) -7 NIL NIL) (-681 1656741 1656774 1656834 "MSYSCMD" 1656909 T MSYSCMD (NIL) -7 NIL NIL) (-680 1652853 1655496 1655816 "MSET" 1656454 NIL MSET (NIL T) -8 NIL NIL) (-679 1649949 1652415 1652456 "MSETAGG" 1652461 NIL MSETAGG (NIL T) -9 NIL 1652495) (-678 1645805 1647347 1648088 "MRING" 1649252 NIL MRING (NIL T T) -8 NIL NIL) (-677 1645375 1645442 1645571 "MRF2" 1645732 NIL MRF2 (NIL T T T) -7 NIL NIL) (-676 1644993 1645028 1645172 "MRATFAC" 1645334 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-675 1642591 1642886 1643317 "MPRFF" 1644698 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-674 1636611 1642446 1642542 "MPOLY" 1642547 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-673 1636101 1636136 1636344 "MPCPF" 1636570 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-672 1635617 1635660 1635843 "MPC3" 1636052 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-671 1634818 1634899 1635118 "MPC2" 1635532 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-670 1633119 1633456 1633846 "MONOTOOL" 1634478 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-669 1632244 1632579 1632607 "MONOID" 1632884 T MONOID (NIL) -9 NIL 1633056) (-668 1631622 1631785 1632028 "MONOID-" 1632033 NIL MONOID- (NIL T) -8 NIL NIL) (-667 1622603 1628589 1628648 "MONOGEN" 1629322 NIL MONOGEN (NIL T T) -9 NIL 1629778) (-666 1619821 1620556 1621556 "MONOGEN-" 1621675 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-665 1618681 1619101 1619129 "MONADWU" 1619521 T MONADWU (NIL) -9 NIL 1619759) (-664 1618053 1618212 1618460 "MONADWU-" 1618465 NIL MONADWU- (NIL T) -8 NIL NIL) (-663 1617439 1617657 1617685 "MONAD" 1617892 T MONAD (NIL) -9 NIL 1618004) (-662 1617124 1617202 1617334 "MONAD-" 1617339 NIL MONAD- (NIL T) -8 NIL NIL) (-661 1615375 1616037 1616316 "MOEBIUS" 1616877 NIL MOEBIUS (NIL T) -8 NIL NIL) (-660 1614769 1615147 1615187 "MODULE" 1615192 NIL MODULE (NIL T) -9 NIL 1615218) (-659 1614337 1614433 1614623 "MODULE-" 1614628 NIL MODULE- (NIL T T) -8 NIL NIL) (-658 1612008 1612703 1613029 "MODRING" 1614162 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-657 1608964 1610129 1610646 "MODOP" 1611540 NIL MODOP (NIL T T) -8 NIL NIL) (-656 1607023 1607475 1607816 "MODMONOM" 1608763 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-655 1596702 1605227 1605649 "MODMON" 1606651 NIL MODMON (NIL T T) -8 NIL NIL) (-654 1593828 1595546 1595822 "MODFIELD" 1596577 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-653 1592832 1593109 1593299 "MMLFORM" 1593658 T MMLFORM (NIL) -8 NIL NIL) (-652 1592358 1592401 1592580 "MMAP" 1592783 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-651 1590595 1591372 1591412 "MLO" 1591829 NIL MLO (NIL T) -9 NIL 1592070) (-650 1587962 1588477 1589079 "MLIFT" 1590076 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-649 1587353 1587437 1587591 "MKUCFUNC" 1587873 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-648 1586952 1587022 1587145 "MKRECORD" 1587276 NIL MKRECORD (NIL T T) -7 NIL NIL) (-647 1586000 1586161 1586389 "MKFUNC" 1586763 NIL MKFUNC (NIL T) -7 NIL NIL) (-646 1585388 1585492 1585648 "MKFLCFN" 1585883 NIL MKFLCFN (NIL T) -7 NIL NIL) (-645 1584814 1585181 1585270 "MKCHSET" 1585332 NIL MKCHSET (NIL T) -8 NIL NIL) (-644 1584091 1584193 1584378 "MKBCFUNC" 1584707 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-643 1580775 1583645 1583781 "MINT" 1583975 T MINT (NIL) -8 NIL NIL) (-642 1579587 1579830 1580107 "MHROWRED" 1580530 NIL MHROWRED (NIL T) -7 NIL NIL) (-641 1574858 1578032 1578456 "MFLOAT" 1579183 T MFLOAT (NIL) -8 NIL NIL) (-640 1574215 1574291 1574462 "MFINFACT" 1574770 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-639 1570530 1571378 1572262 "MESH" 1573351 T MESH (NIL) -7 NIL NIL) (-638 1568892 1569204 1569557 "MDDFACT" 1570217 NIL MDDFACT (NIL T) -7 NIL NIL) (-637 1565735 1568052 1568093 "MDAGG" 1568348 NIL MDAGG (NIL T) -9 NIL 1568491) (-636 1555433 1565028 1565235 "MCMPLX" 1565548 T MCMPLX (NIL) -8 NIL NIL) (-635 1554574 1554720 1554920 "MCDEN" 1555282 NIL MCDEN (NIL T T) -7 NIL NIL) (-634 1552464 1552734 1553114 "MCALCFN" 1554304 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-633 1550086 1550609 1551170 "MATSTOR" 1551935 NIL MATSTOR (NIL T) -7 NIL NIL) (-632 1546095 1549461 1549708 "MATRIX" 1549871 NIL MATRIX (NIL T) -8 NIL NIL) (-631 1541864 1542568 1543304 "MATLIN" 1545452 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-630 1532062 1535200 1535276 "MATCAT" 1540114 NIL MATCAT (NIL T T T) -9 NIL 1541531) (-629 1528427 1529440 1530795 "MATCAT-" 1530800 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-628 1527029 1527182 1527513 "MATCAT2" 1528262 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-627 1525141 1525465 1525849 "MAPPKG3" 1526704 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-626 1524122 1524295 1524517 "MAPPKG2" 1524965 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-625 1522621 1522905 1523232 "MAPPKG1" 1523828 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-624 1522232 1522290 1522413 "MAPHACK3" 1522557 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-623 1521824 1521885 1521999 "MAPHACK2" 1522164 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-622 1521262 1521365 1521507 "MAPHACK1" 1521715 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-621 1519370 1519964 1520267 "MAGMA" 1520991 NIL MAGMA (NIL T) -8 NIL NIL) (-620 1515844 1517614 1518074 "M3D" 1518943 NIL M3D (NIL T) -8 NIL NIL) (-619 1510000 1514215 1514256 "LZSTAGG" 1515038 NIL LZSTAGG (NIL T) -9 NIL 1515333) (-618 1505973 1507131 1508588 "LZSTAGG-" 1508593 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-617 1503089 1503866 1504352 "LWORD" 1505519 NIL LWORD (NIL T) -8 NIL NIL) (-616 1496249 1502860 1502994 "LSQM" 1502999 NIL LSQM (NIL NIL T) -8 NIL NIL) (-615 1495473 1495612 1495840 "LSPP" 1496104 NIL LSPP (NIL T T T T) -7 NIL NIL) (-614 1493285 1493586 1494042 "LSMP" 1495162 NIL LSMP (NIL T T T T) -7 NIL NIL) (-613 1490064 1490738 1491468 "LSMP1" 1492587 NIL LSMP1 (NIL T) -7 NIL NIL) (-612 1483991 1489233 1489274 "LSAGG" 1489336 NIL LSAGG (NIL T) -9 NIL 1489414) (-611 1480686 1481610 1482823 "LSAGG-" 1482828 NIL LSAGG- (NIL T T) -8 NIL NIL) (-610 1478312 1479830 1480079 "LPOLY" 1480481 NIL LPOLY (NIL T T) -8 NIL NIL) (-609 1477894 1477979 1478102 "LPEFRAC" 1478221 NIL LPEFRAC (NIL T) -7 NIL NIL) (-608 1476241 1476988 1477241 "LO" 1477726 NIL LO (NIL T T T) -8 NIL NIL) (-607 1475895 1476007 1476035 "LOGIC" 1476146 T LOGIC (NIL) -9 NIL 1476226) (-606 1475757 1475780 1475851 "LOGIC-" 1475856 NIL LOGIC- (NIL T) -8 NIL NIL) (-605 1474950 1475090 1475283 "LODOOPS" 1475613 NIL LODOOPS (NIL T T) -7 NIL NIL) (-604 1472368 1474867 1474932 "LODO" 1474937 NIL LODO (NIL T NIL) -8 NIL NIL) (-603 1470914 1471149 1471500 "LODOF" 1472115 NIL LODOF (NIL T T) -7 NIL NIL) (-602 1467334 1469770 1469810 "LODOCAT" 1470242 NIL LODOCAT (NIL T) -9 NIL 1470453) (-601 1467068 1467126 1467252 "LODOCAT-" 1467257 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-600 1464382 1466909 1467027 "LODO2" 1467032 NIL LODO2 (NIL T T) -8 NIL NIL) (-599 1461811 1464319 1464364 "LODO1" 1464369 NIL LODO1 (NIL T) -8 NIL NIL) (-598 1460674 1460839 1461150 "LODEEF" 1461634 NIL LODEEF (NIL T T T) -7 NIL NIL) (-597 1455961 1458805 1458846 "LNAGG" 1459793 NIL LNAGG (NIL T) -9 NIL 1460237) (-596 1455108 1455322 1455664 "LNAGG-" 1455669 NIL LNAGG- (NIL T T) -8 NIL NIL) (-595 1451273 1452035 1452673 "LMOPS" 1454524 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-594 1450671 1451033 1451073 "LMODULE" 1451133 NIL LMODULE (NIL T) -9 NIL 1451175) (-593 1447917 1450316 1450439 "LMDICT" 1450581 NIL LMDICT (NIL T) -8 NIL NIL) (-592 1441144 1446863 1447161 "LIST" 1447652 NIL LIST (NIL T) -8 NIL NIL) (-591 1440669 1440743 1440882 "LIST3" 1441064 NIL LIST3 (NIL T T T) -7 NIL NIL) (-590 1439676 1439854 1440082 "LIST2" 1440487 NIL LIST2 (NIL T T) -7 NIL NIL) (-589 1437810 1438122 1438521 "LIST2MAP" 1439323 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-588 1436523 1437203 1437243 "LINEXP" 1437496 NIL LINEXP (NIL T) -9 NIL 1437644) (-587 1435170 1435430 1435727 "LINDEP" 1436275 NIL LINDEP (NIL T T) -7 NIL NIL) (-586 1431867 1432586 1433363 "LIMITRF" 1434425 NIL LIMITRF (NIL T) -7 NIL NIL) (-585 1430147 1430442 1430857 "LIMITPS" 1431562 NIL LIMITPS (NIL T T) -7 NIL NIL) (-584 1424602 1429658 1429886 "LIE" 1429968 NIL LIE (NIL T T) -8 NIL NIL) (-583 1423653 1424096 1424136 "LIECAT" 1424276 NIL LIECAT (NIL T) -9 NIL 1424427) (-582 1423494 1423521 1423609 "LIECAT-" 1423614 NIL LIECAT- (NIL T T) -8 NIL NIL) (-581 1416106 1422943 1423108 "LIB" 1423349 T LIB (NIL) -8 NIL NIL) (-580 1411743 1412624 1413559 "LGROBP" 1415223 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-579 1409609 1409883 1410245 "LF" 1411464 NIL LF (NIL T T) -7 NIL NIL) (-578 1408449 1409141 1409169 "LFCAT" 1409376 T LFCAT (NIL) -9 NIL 1409515) (-577 1405361 1405987 1406673 "LEXTRIPK" 1407815 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-576 1402067 1402931 1403434 "LEXP" 1404941 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-575 1400465 1400778 1401179 "LEADCDET" 1401749 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-574 1399661 1399735 1399962 "LAZM3PK" 1400386 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-573 1394578 1397740 1398277 "LAUPOL" 1399174 NIL LAUPOL (NIL T T) -8 NIL NIL) (-572 1394145 1394189 1394356 "LAPLACE" 1394528 NIL LAPLACE (NIL T T) -7 NIL NIL) (-571 1392073 1393246 1393497 "LA" 1393978 NIL LA (NIL T T T) -8 NIL NIL) (-570 1391136 1391730 1391770 "LALG" 1391831 NIL LALG (NIL T) -9 NIL 1391889) (-569 1390851 1390910 1391045 "LALG-" 1391050 NIL LALG- (NIL T T) -8 NIL NIL) (-568 1389761 1389948 1390245 "KOVACIC" 1390651 NIL KOVACIC (NIL T T) -7 NIL NIL) (-567 1389596 1389620 1389661 "KONVERT" 1389723 NIL KONVERT (NIL T) -9 NIL NIL) (-566 1389431 1389455 1389496 "KOERCE" 1389558 NIL KOERCE (NIL T) -9 NIL NIL) (-565 1387165 1387925 1388318 "KERNEL" 1389070 NIL KERNEL (NIL T) -8 NIL NIL) (-564 1386667 1386748 1386878 "KERNEL2" 1387079 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-563 1380519 1385207 1385261 "KDAGG" 1385638 NIL KDAGG (NIL T T) -9 NIL 1385844) (-562 1380048 1380172 1380377 "KDAGG-" 1380382 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-561 1373223 1379709 1379864 "KAFILE" 1379926 NIL KAFILE (NIL T) -8 NIL NIL) (-560 1367678 1372734 1372962 "JORDAN" 1373044 NIL JORDAN (NIL T T) -8 NIL NIL) (-559 1367407 1367466 1367553 "JAVACODE" 1367611 T JAVACODE (NIL) -8 NIL NIL) (-558 1363707 1365613 1365667 "IXAGG" 1366596 NIL IXAGG (NIL T T) -9 NIL 1367055) (-557 1362626 1362932 1363351 "IXAGG-" 1363356 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-556 1358211 1362548 1362607 "IVECTOR" 1362612 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-555 1356977 1357214 1357480 "ITUPLE" 1357978 NIL ITUPLE (NIL T) -8 NIL NIL) (-554 1355413 1355590 1355896 "ITRIGMNP" 1356799 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-553 1354158 1354362 1354645 "ITFUN3" 1355189 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-552 1353790 1353847 1353956 "ITFUN2" 1354095 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-551 1351592 1352663 1352960 "ITAYLOR" 1353525 NIL ITAYLOR (NIL T) -8 NIL NIL) (-550 1340569 1345767 1346926 "ISUPS" 1350465 NIL ISUPS (NIL T) -8 NIL NIL) (-549 1339673 1339813 1340049 "ISUMP" 1340416 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-548 1334933 1339470 1339549 "ISTRING" 1339626 NIL ISTRING (NIL NIL) -8 NIL NIL) (-547 1334146 1334227 1334442 "IRURPK" 1334847 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-546 1333082 1333283 1333523 "IRSN" 1333926 T IRSN (NIL) -7 NIL NIL) (-545 1331117 1331472 1331907 "IRRF2F" 1332720 NIL IRRF2F (NIL T) -7 NIL NIL) (-544 1330864 1330902 1330978 "IRREDFFX" 1331073 NIL IRREDFFX (NIL T) -7 NIL NIL) (-543 1329479 1329738 1330037 "IROOT" 1330597 NIL IROOT (NIL T) -7 NIL NIL) (-542 1326107 1327158 1327848 "IR" 1328821 NIL IR (NIL T) -8 NIL NIL) (-541 1323720 1324215 1324781 "IR2" 1325585 NIL IR2 (NIL T T) -7 NIL NIL) (-540 1322796 1322909 1323129 "IR2F" 1323603 NIL IR2F (NIL T T) -7 NIL NIL) (-539 1322587 1322621 1322681 "IPRNTPK" 1322756 T IPRNTPK (NIL) -7 NIL NIL) (-538 1319141 1322476 1322545 "IPF" 1322550 NIL IPF (NIL NIL) -8 NIL NIL) (-537 1317458 1319066 1319123 "IPADIC" 1319128 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-536 1316957 1317015 1317204 "INVLAPLA" 1317394 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-535 1306543 1308896 1311282 "INTTR" 1314621 NIL INTTR (NIL T T) -7 NIL NIL) (-534 1302886 1303627 1304490 "INTTOOLS" 1305729 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-533 1302472 1302563 1302680 "INTSLPE" 1302789 T INTSLPE (NIL) -7 NIL NIL) (-532 1300422 1302395 1302454 "INTRVL" 1302459 NIL INTRVL (NIL T) -8 NIL NIL) (-531 1297987 1298499 1299073 "INTRF" 1299907 NIL INTRF (NIL T) -7 NIL NIL) (-530 1297394 1297491 1297632 "INTRET" 1297885 NIL INTRET (NIL T) -7 NIL NIL) (-529 1295375 1295764 1296233 "INTRAT" 1297002 NIL INTRAT (NIL T T) -7 NIL NIL) (-528 1292608 1293191 1293816 "INTPM" 1294860 NIL INTPM (NIL T T) -7 NIL NIL) (-527 1289317 1289916 1290660 "INTPAF" 1291994 NIL INTPAF (NIL T T T) -7 NIL NIL) (-526 1284560 1285506 1286541 "INTPACK" 1288302 T INTPACK (NIL) -7 NIL NIL) (-525 1281414 1284289 1284416 "INT" 1284453 T INT (NIL) -8 NIL NIL) (-524 1280666 1280818 1281026 "INTHERTR" 1281256 NIL INTHERTR (NIL T T) -7 NIL NIL) (-523 1280105 1280185 1280373 "INTHERAL" 1280580 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-522 1277951 1278394 1278851 "INTHEORY" 1279668 T INTHEORY (NIL) -7 NIL NIL) (-521 1269273 1270894 1272672 "INTG0" 1276303 NIL INTG0 (NIL T T T) -7 NIL NIL) (-520 1249846 1254636 1259446 "INTFTBL" 1264483 T INTFTBL (NIL) -8 NIL NIL) (-519 1249095 1249233 1249406 "INTFACT" 1249705 NIL INTFACT (NIL T) -7 NIL NIL) (-518 1246486 1246932 1247495 "INTEF" 1248649 NIL INTEF (NIL T T) -7 NIL NIL) (-517 1244948 1245697 1245725 "INTDOM" 1246026 T INTDOM (NIL) -9 NIL 1246233) (-516 1244317 1244491 1244733 "INTDOM-" 1244738 NIL INTDOM- (NIL T) -8 NIL NIL) (-515 1240810 1242742 1242796 "INTCAT" 1243595 NIL INTCAT (NIL T) -9 NIL 1243914) (-514 1240283 1240385 1240513 "INTBIT" 1240702 T INTBIT (NIL) -7 NIL NIL) (-513 1238958 1239112 1239425 "INTALG" 1240128 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-512 1238415 1238505 1238675 "INTAF" 1238862 NIL INTAF (NIL T T) -7 NIL NIL) (-511 1231869 1238225 1238365 "INTABL" 1238370 NIL INTABL (NIL T T T) -8 NIL NIL) (-510 1226820 1229549 1229577 "INS" 1230545 T INS (NIL) -9 NIL 1231226) (-509 1224060 1224831 1225805 "INS-" 1225878 NIL INS- (NIL T) -8 NIL NIL) (-508 1222839 1223066 1223363 "INPSIGN" 1223813 NIL INPSIGN (NIL T T) -7 NIL NIL) (-507 1221953 1222070 1222267 "INPRODPF" 1222719 NIL INPRODPF (NIL T T) -7 NIL NIL) (-506 1220843 1220960 1221197 "INPRODFF" 1221833 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-505 1219843 1219995 1220255 "INNMFACT" 1220679 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-504 1219040 1219137 1219325 "INMODGCD" 1219742 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-503 1217549 1217793 1218117 "INFSP" 1218785 NIL INFSP (NIL T T T) -7 NIL NIL) (-502 1216733 1216850 1217033 "INFPROD0" 1217429 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-501 1213744 1214902 1215393 "INFORM" 1216250 T INFORM (NIL) -8 NIL NIL) (-500 1213354 1213414 1213512 "INFORM1" 1213679 NIL INFORM1 (NIL T) -7 NIL NIL) (-499 1212877 1212966 1213080 "INFINITY" 1213260 T INFINITY (NIL) -7 NIL NIL) (-498 1211494 1211743 1212064 "INEP" 1212625 NIL INEP (NIL T T T) -7 NIL NIL) (-497 1210770 1211391 1211456 "INDE" 1211461 NIL INDE (NIL T) -8 NIL NIL) (-496 1210334 1210402 1210519 "INCRMAPS" 1210697 NIL INCRMAPS (NIL T) -7 NIL NIL) (-495 1205645 1206570 1207514 "INBFF" 1209422 NIL INBFF (NIL T) -7 NIL NIL) (-494 1202140 1205490 1205593 "IMATRIX" 1205598 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-493 1200852 1200975 1201290 "IMATQF" 1201996 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-492 1199072 1199299 1199636 "IMATLIN" 1200608 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-491 1193698 1198996 1199054 "ILIST" 1199059 NIL ILIST (NIL T NIL) -8 NIL NIL) (-490 1191651 1193558 1193671 "IIARRAY2" 1193676 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-489 1187019 1191562 1191626 "IFF" 1191631 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-488 1182058 1186307 1186495 "IFARRAY" 1186876 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-487 1181265 1181962 1182035 "IFAMON" 1182040 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-486 1180849 1180914 1180968 "IEVALAB" 1181175 NIL IEVALAB (NIL T T) -9 NIL NIL) (-485 1180524 1180592 1180752 "IEVALAB-" 1180757 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-484 1180182 1180438 1180501 "IDPO" 1180506 NIL IDPO (NIL T T) -8 NIL NIL) (-483 1179459 1180071 1180146 "IDPOAMS" 1180151 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-482 1178793 1179348 1179423 "IDPOAM" 1179428 NIL IDPOAM (NIL T T) -8 NIL NIL) (-481 1177879 1178129 1178182 "IDPC" 1178595 NIL IDPC (NIL T T) -9 NIL 1178744) (-480 1177375 1177771 1177844 "IDPAM" 1177849 NIL IDPAM (NIL T T) -8 NIL NIL) (-479 1176778 1177267 1177340 "IDPAG" 1177345 NIL IDPAG (NIL T T) -8 NIL NIL) (-478 1173033 1173881 1174776 "IDECOMP" 1175935 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-477 1165906 1166956 1168003 "IDEAL" 1172069 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-476 1165070 1165182 1165381 "ICDEN" 1165790 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-475 1164169 1164550 1164697 "ICARD" 1164943 T ICARD (NIL) -8 NIL NIL) (-474 1162241 1162554 1162957 "IBPTOOLS" 1163846 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-473 1157855 1161861 1161974 "IBITS" 1162160 NIL IBITS (NIL NIL) -8 NIL NIL) (-472 1154578 1155154 1155849 "IBATOOL" 1157272 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-471 1152358 1152819 1153352 "IBACHIN" 1154113 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-470 1150235 1152204 1152307 "IARRAY2" 1152312 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-469 1146388 1150161 1150218 "IARRAY1" 1150223 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-468 1140326 1144806 1145284 "IAN" 1145930 T IAN (NIL) -8 NIL NIL) (-467 1139837 1139894 1140067 "IALGFACT" 1140263 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-466 1139365 1139478 1139506 "HYPCAT" 1139713 T HYPCAT (NIL) -9 NIL NIL) (-465 1138903 1139020 1139206 "HYPCAT-" 1139211 NIL HYPCAT- (NIL T) -8 NIL NIL) (-464 1135583 1136914 1136955 "HOAGG" 1137936 NIL HOAGG (NIL T) -9 NIL 1138615) (-463 1134177 1134576 1135102 "HOAGG-" 1135107 NIL HOAGG- (NIL T T) -8 NIL NIL) (-462 1128007 1133618 1133784 "HEXADEC" 1134031 T HEXADEC (NIL) -8 NIL NIL) (-461 1126751 1126973 1127236 "HEUGCD" 1127784 NIL HEUGCD (NIL T) -7 NIL NIL) (-460 1125854 1126588 1126718 "HELLFDIV" 1126723 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-459 1124082 1125631 1125719 "HEAP" 1125798 NIL HEAP (NIL T) -8 NIL NIL) (-458 1117949 1123997 1124059 "HDP" 1124064 NIL HDP (NIL NIL T) -8 NIL NIL) (-457 1111661 1117586 1117737 "HDMP" 1117850 NIL HDMP (NIL NIL T) -8 NIL NIL) (-456 1110986 1111125 1111289 "HB" 1111517 T HB (NIL) -7 NIL NIL) (-455 1104483 1110832 1110936 "HASHTBL" 1110941 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-454 1102236 1104111 1104290 "HACKPI" 1104324 T HACKPI (NIL) -8 NIL NIL) (-453 1097932 1102090 1102202 "GTSET" 1102207 NIL GTSET (NIL T T T T) -8 NIL NIL) (-452 1091458 1097810 1097908 "GSTBL" 1097913 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-451 1083691 1090494 1090758 "GSERIES" 1091249 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-450 1082714 1083167 1083195 "GROUP" 1083456 T GROUP (NIL) -9 NIL 1083615) (-449 1081830 1082053 1082397 "GROUP-" 1082402 NIL GROUP- (NIL T) -8 NIL NIL) (-448 1080199 1080518 1080905 "GROEBSOL" 1081507 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-447 1079140 1079402 1079453 "GRMOD" 1079982 NIL GRMOD (NIL T T) -9 NIL 1080150) (-446 1078908 1078944 1079072 "GRMOD-" 1079077 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-445 1074234 1075262 1076262 "GRIMAGE" 1077928 T GRIMAGE (NIL) -8 NIL NIL) (-444 1072701 1072961 1073285 "GRDEF" 1073930 T GRDEF (NIL) -7 NIL NIL) (-443 1072145 1072261 1072402 "GRAY" 1072580 T GRAY (NIL) -7 NIL NIL) (-442 1071379 1071759 1071810 "GRALG" 1071963 NIL GRALG (NIL T T) -9 NIL 1072055) (-441 1071040 1071113 1071276 "GRALG-" 1071281 NIL GRALG- (NIL T T T) -8 NIL NIL) (-440 1067848 1070629 1070805 "GPOLSET" 1070947 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-439 1067204 1067261 1067518 "GOSPER" 1067785 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-438 1062963 1063642 1064168 "GMODPOL" 1066903 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-437 1061968 1062152 1062390 "GHENSEL" 1062775 NIL GHENSEL (NIL T T) -7 NIL NIL) (-436 1056034 1056877 1057903 "GENUPS" 1061052 NIL GENUPS (NIL T T) -7 NIL NIL) (-435 1055731 1055782 1055871 "GENUFACT" 1055977 NIL GENUFACT (NIL T) -7 NIL NIL) (-434 1055143 1055220 1055385 "GENPGCD" 1055649 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-433 1054617 1054652 1054865 "GENMFACT" 1055102 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-432 1053185 1053440 1053747 "GENEEZ" 1054360 NIL GENEEZ (NIL T T) -7 NIL NIL) (-431 1047059 1052798 1052959 "GDMP" 1053108 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-430 1036426 1040820 1041926 "GCNAALG" 1046042 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-429 1034848 1035720 1035748 "GCDDOM" 1036003 T GCDDOM (NIL) -9 NIL 1036160) (-428 1034318 1034445 1034660 "GCDDOM-" 1034665 NIL GCDDOM- (NIL T) -8 NIL NIL) (-427 1032990 1033175 1033479 "GB" 1034097 NIL GB (NIL T T T T) -7 NIL NIL) (-426 1021610 1023936 1026328 "GBINTERN" 1030681 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-425 1019447 1019739 1020160 "GBF" 1021285 NIL GBF (NIL T T T T) -7 NIL NIL) (-424 1018228 1018393 1018660 "GBEUCLID" 1019263 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-423 1017577 1017702 1017851 "GAUSSFAC" 1018099 T GAUSSFAC (NIL) -7 NIL NIL) (-422 1015954 1016256 1016569 "GALUTIL" 1017296 NIL GALUTIL (NIL T) -7 NIL NIL) (-421 1014271 1014545 1014868 "GALPOLYU" 1015681 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-420 1011660 1011950 1012355 "GALFACTU" 1013968 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-419 1003466 1004965 1006573 "GALFACT" 1010092 NIL GALFACT (NIL T) -7 NIL NIL) (-418 1000854 1001512 1001540 "FVFUN" 1002696 T FVFUN (NIL) -9 NIL 1003416) (-417 1000120 1000302 1000330 "FVC" 1000621 T FVC (NIL) -9 NIL 1000804) (-416 999757 999912 999993 "FUNCTION" 1000072 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-415 997427 997978 998467 "FT" 999288 T FT (NIL) -8 NIL NIL) (-414 996245 996728 996931 "FTEM" 997244 T FTEM (NIL) -8 NIL NIL) (-413 994510 994798 995200 "FSUPFACT" 995937 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-412 992907 993196 993528 "FST" 994198 T FST (NIL) -8 NIL NIL) (-411 992082 992188 992382 "FSRED" 992789 NIL FSRED (NIL T T) -7 NIL NIL) (-410 990761 991016 991370 "FSPRMELT" 991797 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-409 987846 988284 988783 "FSPECF" 990324 NIL FSPECF (NIL T T) -7 NIL NIL) (-408 970220 978777 978817 "FS" 982655 NIL FS (NIL T) -9 NIL 984937) (-407 958870 961860 965916 "FS-" 966213 NIL FS- (NIL T T) -8 NIL NIL) (-406 958386 958440 958616 "FSINT" 958811 NIL FSINT (NIL T T) -7 NIL NIL) (-405 956667 957379 957682 "FSERIES" 958165 NIL FSERIES (NIL T T) -8 NIL NIL) (-404 955685 955801 956031 "FSCINT" 956547 NIL FSCINT (NIL T T) -7 NIL NIL) (-403 951920 954630 954671 "FSAGG" 955041 NIL FSAGG (NIL T) -9 NIL 955300) (-402 949682 950283 951079 "FSAGG-" 951174 NIL FSAGG- (NIL T T) -8 NIL NIL) (-401 948724 948867 949094 "FSAGG2" 949535 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-400 946383 946662 947215 "FS2UPS" 948442 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-399 945969 946012 946165 "FS2" 946334 NIL FS2 (NIL T T T T) -7 NIL NIL) (-398 944829 945000 945308 "FS2EXPXP" 945794 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-397 944255 944370 944522 "FRUTIL" 944709 NIL FRUTIL (NIL T) -7 NIL NIL) (-396 935675 939754 941110 "FR" 942931 NIL FR (NIL T) -8 NIL NIL) (-395 930752 933395 933435 "FRNAALG" 934831 NIL FRNAALG (NIL T) -9 NIL 935438) (-394 926430 927501 928776 "FRNAALG-" 929526 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-393 926068 926111 926238 "FRNAAF2" 926381 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-392 924417 924909 925203 "FRMOD" 925881 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-391 922139 922808 923124 "FRIDEAL" 924208 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-390 921338 921425 921712 "FRIDEAL2" 922046 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-389 920596 921004 921045 "FRETRCT" 921050 NIL FRETRCT (NIL T) -9 NIL 921221) (-388 919708 919939 920290 "FRETRCT-" 920295 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-387 916918 918138 918197 "FRAMALG" 919079 NIL FRAMALG (NIL T T) -9 NIL 919371) (-386 915051 915507 916137 "FRAMALG-" 916360 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-385 908953 914526 914802 "FRAC" 914807 NIL FRAC (NIL T) -8 NIL NIL) (-384 908589 908646 908753 "FRAC2" 908890 NIL FRAC2 (NIL T T) -7 NIL NIL) (-383 908225 908282 908389 "FR2" 908526 NIL FR2 (NIL T T) -7 NIL NIL) (-382 902899 905812 905840 "FPS" 906959 T FPS (NIL) -9 NIL 907515) (-381 902348 902457 902621 "FPS-" 902767 NIL FPS- (NIL T) -8 NIL NIL) (-380 899797 901494 901522 "FPC" 901747 T FPC (NIL) -9 NIL 901889) (-379 899590 899630 899727 "FPC-" 899732 NIL FPC- (NIL T) -8 NIL NIL) (-378 898469 899079 899120 "FPATMAB" 899125 NIL FPATMAB (NIL T) -9 NIL 899277) (-377 896169 896645 897071 "FPARFRAC" 898106 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-376 891562 892061 892743 "FORTRAN" 895601 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-375 889234 889734 890273 "FORT" 891043 T FORT (NIL) -7 NIL NIL) (-374 886910 887472 887500 "FORTFN" 888560 T FORTFN (NIL) -9 NIL 889184) (-373 886674 886724 886752 "FORTCAT" 886811 T FORTCAT (NIL) -9 NIL 886873) (-372 884734 885217 885616 "FORMULA" 886295 T FORMULA (NIL) -8 NIL NIL) (-371 884522 884552 884621 "FORMULA1" 884698 NIL FORMULA1 (NIL T) -7 NIL NIL) (-370 884045 884097 884270 "FORDER" 884464 NIL FORDER (NIL T T T T) -7 NIL NIL) (-369 883141 883305 883498 "FOP" 883872 T FOP (NIL) -7 NIL NIL) (-368 881733 882405 882579 "FNLA" 883023 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-367 880402 880791 880819 "FNCAT" 881391 T FNCAT (NIL) -9 NIL 881684) (-366 879968 880361 880389 "FNAME" 880394 T FNAME (NIL) -8 NIL NIL) (-365 878628 879601 879629 "FMTC" 879634 T FMTC (NIL) -9 NIL 879669) (-364 874946 876153 876781 "FMONOID" 878033 NIL FMONOID (NIL T) -8 NIL NIL) (-363 874166 874689 874837 "FM" 874842 NIL FM (NIL T T) -8 NIL NIL) (-362 871590 872236 872264 "FMFUN" 873408 T FMFUN (NIL) -9 NIL 874116) (-361 870859 871040 871068 "FMC" 871358 T FMC (NIL) -9 NIL 871540) (-360 868089 868923 868976 "FMCAT" 870158 NIL FMCAT (NIL T T) -9 NIL 870652) (-359 866984 867857 867956 "FM1" 868034 NIL FM1 (NIL T T) -8 NIL NIL) (-358 864758 865174 865668 "FLOATRP" 866535 NIL FLOATRP (NIL T) -7 NIL NIL) (-357 858244 862414 863044 "FLOAT" 864148 T FLOAT (NIL) -8 NIL NIL) (-356 855682 856182 856760 "FLOATCP" 857711 NIL FLOATCP (NIL T) -7 NIL NIL) (-355 854471 855319 855359 "FLINEXP" 855364 NIL FLINEXP (NIL T) -9 NIL 855457) (-354 853626 853861 854188 "FLINEXP-" 854193 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-353 852702 852846 853070 "FLASORT" 853478 NIL FLASORT (NIL T T) -7 NIL NIL) (-352 849921 850763 850815 "FLALG" 852042 NIL FLALG (NIL T T) -9 NIL 852509) (-351 843706 847408 847449 "FLAGG" 848711 NIL FLAGG (NIL T) -9 NIL 849363) (-350 842432 842771 843261 "FLAGG-" 843266 NIL FLAGG- (NIL T T) -8 NIL NIL) (-349 841474 841617 841844 "FLAGG2" 842285 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-348 838447 839465 839524 "FINRALG" 840652 NIL FINRALG (NIL T T) -9 NIL 841160) (-347 837607 837836 838175 "FINRALG-" 838180 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-346 837014 837227 837255 "FINITE" 837451 T FINITE (NIL) -9 NIL 837558) (-345 829474 831635 831675 "FINAALG" 835342 NIL FINAALG (NIL T) -9 NIL 836795) (-344 824815 825856 827000 "FINAALG-" 828379 NIL FINAALG- (NIL T T) -8 NIL NIL) (-343 824210 824570 824673 "FILE" 824745 NIL FILE (NIL T) -8 NIL NIL) (-342 822895 823207 823261 "FILECAT" 823945 NIL FILECAT (NIL T T) -9 NIL 824161) (-341 820758 822314 822342 "FIELD" 822382 T FIELD (NIL) -9 NIL 822462) (-340 819378 819763 820274 "FIELD-" 820279 NIL FIELD- (NIL T) -8 NIL NIL) (-339 817193 818015 818361 "FGROUP" 819065 NIL FGROUP (NIL T) -8 NIL NIL) (-338 816283 816447 816667 "FGLMICPK" 817025 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-337 812085 816208 816265 "FFX" 816270 NIL FFX (NIL T NIL) -8 NIL NIL) (-336 811686 811747 811882 "FFSLPE" 812018 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-335 807679 808458 809254 "FFPOLY" 810922 NIL FFPOLY (NIL T) -7 NIL NIL) (-334 807183 807219 807428 "FFPOLY2" 807637 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-333 803004 807102 807165 "FFP" 807170 NIL FFP (NIL T NIL) -8 NIL NIL) (-332 798372 802915 802979 "FF" 802984 NIL FF (NIL NIL NIL) -8 NIL NIL) (-331 793468 797715 797905 "FFNBX" 798226 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-330 788325 792551 792809 "FFNBP" 793322 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-329 782928 787609 787820 "FFNB" 788158 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-328 781760 781958 782273 "FFINTBAS" 782725 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-327 777984 780224 780252 "FFIELDC" 780872 T FFIELDC (NIL) -9 NIL 781248) (-326 776647 777017 777514 "FFIELDC-" 777519 NIL FFIELDC- (NIL T) -8 NIL NIL) (-325 776217 776262 776386 "FFHOM" 776589 NIL FFHOM (NIL T T T) -7 NIL NIL) (-324 773915 774399 774916 "FFF" 775732 NIL FFF (NIL T) -7 NIL NIL) (-323 769503 773657 773758 "FFCGX" 773858 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-322 765105 769235 769342 "FFCGP" 769446 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-321 760258 764832 764940 "FFCG" 765041 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-320 742204 751327 751413 "FFCAT" 756578 NIL FFCAT (NIL T T T) -9 NIL 758065) (-319 737402 738449 739763 "FFCAT-" 740993 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-318 736813 736856 737091 "FFCAT2" 737353 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-317 725969 729759 730976 "FEXPR" 735668 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-316 724969 725404 725445 "FEVALAB" 725529 NIL FEVALAB (NIL T) -9 NIL 725790) (-315 724128 724338 724676 "FEVALAB-" 724681 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-314 722721 723511 723714 "FDIV" 724027 NIL FDIV (NIL T T T T) -8 NIL NIL) (-313 719788 720503 720618 "FDIVCAT" 722186 NIL FDIVCAT (NIL T T T T) -9 NIL 722623) (-312 719550 719577 719747 "FDIVCAT-" 719752 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-311 718770 718857 719134 "FDIV2" 719457 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-310 717456 717715 718004 "FCPAK1" 718501 T FCPAK1 (NIL) -7 NIL NIL) (-309 716584 716956 717097 "FCOMP" 717347 NIL FCOMP (NIL T) -8 NIL NIL) (-308 700219 703633 707194 "FC" 713043 T FC (NIL) -8 NIL NIL) (-307 692815 696861 696901 "FAXF" 698703 NIL FAXF (NIL T) -9 NIL 699394) (-306 690094 690749 691574 "FAXF-" 692039 NIL FAXF- (NIL T T) -8 NIL NIL) (-305 685194 689470 689646 "FARRAY" 689951 NIL FARRAY (NIL T) -8 NIL NIL) (-304 680585 682656 682708 "FAMR" 683720 NIL FAMR (NIL T T) -9 NIL 684180) (-303 679476 679778 680212 "FAMR-" 680217 NIL FAMR- (NIL T T T) -8 NIL NIL) (-302 678672 679398 679451 "FAMONOID" 679456 NIL FAMONOID (NIL T) -8 NIL NIL) (-301 676505 677189 677242 "FAMONC" 678183 NIL FAMONC (NIL T T) -9 NIL 678568) (-300 675197 676259 676396 "FAGROUP" 676401 NIL FAGROUP (NIL T) -8 NIL NIL) (-299 673000 673319 673721 "FACUTIL" 674878 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-298 672099 672284 672506 "FACTFUNC" 672810 NIL FACTFUNC (NIL T) -7 NIL NIL) (-297 664419 671350 671562 "EXPUPXS" 671955 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-296 661902 662442 663028 "EXPRTUBE" 663853 T EXPRTUBE (NIL) -7 NIL NIL) (-295 658096 658688 659425 "EXPRODE" 661241 NIL EXPRODE (NIL T T) -7 NIL NIL) (-294 643227 656727 657153 "EXPR" 657702 NIL EXPR (NIL T) -8 NIL NIL) (-293 637639 638226 639038 "EXPR2UPS" 642525 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-292 637275 637332 637439 "EXPR2" 637576 NIL EXPR2 (NIL T T) -7 NIL NIL) (-291 628629 636412 636707 "EXPEXPAN" 637113 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-290 628456 628586 628615 "EXIT" 628620 T EXIT (NIL) -8 NIL NIL) (-289 628083 628145 628258 "EVALCYC" 628388 NIL EVALCYC (NIL T) -7 NIL NIL) (-288 627624 627742 627783 "EVALAB" 627953 NIL EVALAB (NIL T) -9 NIL 628057) (-287 627105 627227 627448 "EVALAB-" 627453 NIL EVALAB- (NIL T T) -8 NIL NIL) (-286 624568 625880 625908 "EUCDOM" 626463 T EUCDOM (NIL) -9 NIL 626813) (-285 622973 623415 624005 "EUCDOM-" 624010 NIL EUCDOM- (NIL T) -8 NIL NIL) (-284 610551 613299 616039 "ESTOOLS" 620253 T ESTOOLS (NIL) -7 NIL NIL) (-283 610187 610244 610351 "ESTOOLS2" 610488 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-282 609938 609980 610060 "ESTOOLS1" 610139 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-281 603876 605600 605628 "ES" 608392 T ES (NIL) -9 NIL 609798) (-280 598823 600110 601927 "ES-" 602091 NIL ES- (NIL T) -8 NIL NIL) (-279 595198 595958 596738 "ESCONT" 598063 T ESCONT (NIL) -7 NIL NIL) (-278 594935 594967 595049 "ESCONT1" 595160 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-277 594610 594660 594760 "ES2" 594879 NIL ES2 (NIL T T) -7 NIL NIL) (-276 594240 594298 594407 "ES1" 594546 NIL ES1 (NIL T T) -7 NIL NIL) (-275 593456 593585 593761 "ERROR" 594084 T ERROR (NIL) -7 NIL NIL) (-274 586959 593315 593406 "EQTBL" 593411 NIL EQTBL (NIL T T) -8 NIL NIL) (-273 579396 582277 583724 "EQ" 585545 NIL -2605 (NIL T) -8 NIL NIL) (-272 579028 579085 579194 "EQ2" 579333 NIL EQ2 (NIL T T) -7 NIL NIL) (-271 574320 575366 576459 "EP" 577967 NIL EP (NIL T) -7 NIL NIL) (-270 572903 573203 573520 "ENV" 574023 T ENV (NIL) -8 NIL NIL) (-269 572063 572627 572655 "ENTIRER" 572660 T ENTIRER (NIL) -9 NIL 572705) (-268 568519 570018 570388 "EMR" 571862 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-267 567663 567848 567902 "ELTAGG" 568282 NIL ELTAGG (NIL T T) -9 NIL 568493) (-266 567382 567444 567585 "ELTAGG-" 567590 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-265 567171 567200 567254 "ELTAB" 567338 NIL ELTAB (NIL T T) -9 NIL NIL) (-264 566297 566443 566642 "ELFUTS" 567022 NIL ELFUTS (NIL T T) -7 NIL NIL) (-263 566039 566095 566123 "ELEMFUN" 566228 T ELEMFUN (NIL) -9 NIL NIL) (-262 565909 565930 565998 "ELEMFUN-" 566003 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-261 560801 564010 564051 "ELAGG" 564991 NIL ELAGG (NIL T) -9 NIL 565454) (-260 559086 559520 560183 "ELAGG-" 560188 NIL ELAGG- (NIL T T) -8 NIL NIL) (-259 557743 558023 558318 "ELABEXPR" 558811 T ELABEXPR (NIL) -8 NIL NIL) (-258 550600 552399 553226 "EFUPXS" 557019 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-257 544039 545840 546650 "EFULS" 549876 NIL EFULS (NIL T T T) -8 NIL NIL) (-256 541470 541828 542306 "EFSTRUC" 543671 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-255 530542 532107 533667 "EF" 539985 NIL EF (NIL T T) -7 NIL NIL) (-254 529643 530027 530176 "EAB" 530413 T EAB (NIL) -8 NIL NIL) (-253 528856 529602 529630 "E04UCFA" 529635 T E04UCFA (NIL) -8 NIL NIL) (-252 528069 528815 528843 "E04NAFA" 528848 T E04NAFA (NIL) -8 NIL NIL) (-251 527282 528028 528056 "E04MBFA" 528061 T E04MBFA (NIL) -8 NIL NIL) (-250 526495 527241 527269 "E04JAFA" 527274 T E04JAFA (NIL) -8 NIL NIL) (-249 525710 526454 526482 "E04GCFA" 526487 T E04GCFA (NIL) -8 NIL NIL) (-248 524925 525669 525697 "E04FDFA" 525702 T E04FDFA (NIL) -8 NIL NIL) (-247 524138 524884 524912 "E04DGFA" 524917 T E04DGFA (NIL) -8 NIL NIL) (-246 518323 519668 521030 "E04AGNT" 522796 T E04AGNT (NIL) -7 NIL NIL) (-245 517050 517530 517570 "DVARCAT" 518045 NIL DVARCAT (NIL T) -9 NIL 518243) (-244 516254 516466 516780 "DVARCAT-" 516785 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-243 509116 516056 516183 "DSMP" 516188 NIL DSMP (NIL T T T) -8 NIL NIL) (-242 503926 505061 506129 "DROPT" 508068 T DROPT (NIL) -8 NIL NIL) (-241 503591 503650 503748 "DROPT1" 503861 NIL DROPT1 (NIL T) -7 NIL NIL) (-240 498706 499832 500969 "DROPT0" 502474 T DROPT0 (NIL) -7 NIL NIL) (-239 497051 497376 497762 "DRAWPT" 498340 T DRAWPT (NIL) -7 NIL NIL) (-238 491638 492561 493640 "DRAW" 496025 NIL DRAW (NIL T) -7 NIL NIL) (-237 491271 491324 491442 "DRAWHACK" 491579 NIL DRAWHACK (NIL T) -7 NIL NIL) (-236 490002 490271 490562 "DRAWCX" 491000 T DRAWCX (NIL) -7 NIL NIL) (-235 489520 489588 489738 "DRAWCURV" 489928 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-234 479991 481950 484065 "DRAWCFUN" 487425 T DRAWCFUN (NIL) -7 NIL NIL) (-233 476805 478687 478728 "DQAGG" 479357 NIL DQAGG (NIL T) -9 NIL 479630) (-232 465312 472050 472132 "DPOLCAT" 473970 NIL DPOLCAT (NIL T T T T) -9 NIL 474514) (-231 460152 461498 463455 "DPOLCAT-" 463460 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-230 452948 460014 460111 "DPMO" 460116 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-229 445647 452729 452895 "DPMM" 452900 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-228 445160 445258 445378 "DOMAIN" 445547 T DOMAIN (NIL) -8 NIL NIL) (-227 438872 444797 444948 "DMP" 445061 NIL DMP (NIL NIL T) -8 NIL NIL) (-226 438472 438528 438672 "DLP" 438810 NIL DLP (NIL T) -7 NIL NIL) (-225 432116 437573 437800 "DLIST" 438277 NIL DLIST (NIL T) -8 NIL NIL) (-224 428963 430972 431013 "DLAGG" 431563 NIL DLAGG (NIL T) -9 NIL 431792) (-223 427673 428365 428393 "DIVRING" 428543 T DIVRING (NIL) -9 NIL 428651) (-222 426661 426914 427307 "DIVRING-" 427312 NIL DIVRING- (NIL T) -8 NIL NIL) (-221 424763 425120 425526 "DISPLAY" 426275 T DISPLAY (NIL) -7 NIL NIL) (-220 418652 424677 424740 "DIRPROD" 424745 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-219 417500 417703 417968 "DIRPROD2" 418445 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-218 407019 413024 413077 "DIRPCAT" 413485 NIL DIRPCAT (NIL NIL T) -9 NIL 414324) (-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))
\ No newline at end of file +((-3 3149738 3149743 3149748 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-2 3149723 3149728 3149733 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1 3149708 3149713 3149718 NIL NIL NIL NIL (NIL) -8 NIL NIL) (0 3149693 3149698 3149703 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1199 3148823 3149568 3149645 "ZMOD" 3149650 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1198 3147933 3148097 3148306 "ZLINDEP" 3148655 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1197 3137337 3139082 3141034 "ZDSOLVE" 3146082 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1196 3136583 3136724 3136913 "YSTREAM" 3137183 NIL YSTREAM (NIL T) -7 NIL NIL) (-1195 3134352 3135888 3136091 "XRPOLY" 3136426 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1194 3130814 3132143 3132725 "XPR" 3133816 NIL XPR (NIL T T) -8 NIL NIL) (-1193 3128528 3130149 3130352 "XPOLY" 3130645 NIL XPOLY (NIL T) -8 NIL NIL) (-1192 3126342 3127720 3127774 "XPOLYC" 3128059 NIL XPOLYC (NIL T T) -9 NIL 3128172) (-1191 3122714 3124859 3125247 "XPBWPOLY" 3126000 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1190 3118642 3120955 3120997 "XF" 3121618 NIL XF (NIL T) -9 NIL 3122017) (-1189 3118263 3118351 3118520 "XF-" 3118525 NIL XF- (NIL T T) -8 NIL NIL) (-1188 3113643 3114942 3114996 "XFALG" 3117144 NIL XFALG (NIL T T) -9 NIL 3117931) (-1187 3112780 3112884 3113088 "XEXPPKG" 3113535 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1186 3110879 3112631 3112726 "XDPOLY" 3112731 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1185 3109758 3110368 3110410 "XALG" 3110472 NIL XALG (NIL T) -9 NIL 3110591) (-1184 3103234 3107742 3108235 "WUTSET" 3109350 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1183 3101038 3101845 3102196 "WP" 3103016 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1182 3099924 3100122 3100417 "WFFINTBS" 3100835 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1181 3097804 3098231 3098693 "WEIER" 3099496 NIL WEIER (NIL T) -7 NIL NIL) (-1180 3096953 3097377 3097419 "VSPACE" 3097555 NIL VSPACE (NIL T) -9 NIL 3097629) (-1179 3096791 3096818 3096909 "VSPACE-" 3096914 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1178 3096537 3096580 3096651 "VOID" 3096742 T VOID (NIL) -8 NIL NIL) (-1177 3094673 3095032 3095438 "VIEW" 3096153 T VIEW (NIL) -7 NIL NIL) (-1176 3091098 3091736 3092473 "VIEWDEF" 3093958 T VIEWDEF (NIL) -7 NIL NIL) (-1175 3080436 3082646 3084819 "VIEW3D" 3088947 T VIEW3D (NIL) -8 NIL NIL) (-1174 3072718 3074347 3075926 "VIEW2D" 3078879 T VIEW2D (NIL) -8 NIL NIL) (-1173 3068127 3072488 3072580 "VECTOR" 3072661 NIL VECTOR (NIL T) -8 NIL NIL) (-1172 3066704 3066963 3067281 "VECTOR2" 3067857 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1171 3060244 3064496 3064539 "VECTCAT" 3065527 NIL VECTCAT (NIL T) -9 NIL 3066111) (-1170 3059258 3059512 3059902 "VECTCAT-" 3059907 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1169 3058729 3058899 3059019 "VARIABLE" 3059173 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1168 3058662 3058667 3058697 "UTYPE" 3058702 T UTYPE (NIL) -9 NIL NIL) (-1167 3057497 3057651 3057912 "UTSODETL" 3058488 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1166 3054937 3055397 3055921 "UTSODE" 3057038 NIL UTSODE (NIL T T) -7 NIL NIL) (-1165 3046781 3052577 3053065 "UTS" 3054506 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1164 3038116 3043481 3043523 "UTSCAT" 3044634 NIL UTSCAT (NIL T) -9 NIL 3045391) (-1163 3035471 3036187 3037175 "UTSCAT-" 3037180 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1162 3035102 3035145 3035276 "UTS2" 3035422 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1161 3029378 3031943 3031986 "URAGG" 3034056 NIL URAGG (NIL T) -9 NIL 3034778) (-1160 3026317 3027180 3028303 "URAGG-" 3028308 NIL URAGG- (NIL T T) -8 NIL NIL) (-1159 3022003 3024934 3025405 "UPXSSING" 3025981 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1158 3013894 3021124 3021404 "UPXS" 3021780 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1157 3006923 3013799 3013870 "UPXSCONS" 3013875 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1156 2997212 3004042 3004103 "UPXSCCA" 3004752 NIL UPXSCCA (NIL T T) -9 NIL 3004993) (-1155 2996851 2996936 2997109 "UPXSCCA-" 2997114 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1154 2987052 2993655 2993697 "UPXSCAT" 2994350 NIL UPXSCAT (NIL T) -9 NIL 2994958) (-1153 2986486 2986565 2986742 "UPXS2" 2986967 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1152 2985140 2985393 2985744 "UPSQFREE" 2986229 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1151 2979031 2982086 2982140 "UPSCAT" 2983289 NIL UPSCAT (NIL T T) -9 NIL 2984063) (-1150 2978236 2978443 2978769 "UPSCAT-" 2978774 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1149 2964322 2972359 2972401 "UPOLYC" 2974479 NIL UPOLYC (NIL T) -9 NIL 2975700) (-1148 2955652 2958077 2961223 "UPOLYC-" 2961228 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1147 2955283 2955326 2955457 "UPOLYC2" 2955603 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1146 2946702 2954852 2954989 "UP" 2955193 NIL UP (NIL NIL T) -8 NIL NIL) (-1145 2946045 2946152 2946315 "UPMP" 2946591 NIL UPMP (NIL T T) -7 NIL NIL) (-1144 2945598 2945679 2945818 "UPDIVP" 2945958 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1143 2944166 2944415 2944731 "UPDECOMP" 2945347 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1142 2943401 2943513 2943698 "UPCDEN" 2944050 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1141 2942924 2942993 2943140 "UP2" 2943326 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1140 2941441 2942128 2942405 "UNISEG" 2942682 NIL UNISEG (NIL T) -8 NIL NIL) (-1139 2940656 2940783 2940988 "UNISEG2" 2941284 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1138 2939716 2939896 2940122 "UNIFACT" 2940472 NIL UNIFACT (NIL T) -7 NIL NIL) (-1137 2923612 2938897 2939147 "ULS" 2939523 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1136 2911577 2923517 2923588 "ULSCONS" 2923593 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1135 2894327 2906340 2906401 "ULSCCAT" 2907113 NIL ULSCCAT (NIL T T) -9 NIL 2907409) (-1134 2893378 2893623 2894010 "ULSCCAT-" 2894015 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1133 2883358 2889875 2889917 "ULSCAT" 2890783 NIL ULSCAT (NIL T) -9 NIL 2891513) (-1132 2882792 2882871 2883048 "ULS2" 2883273 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1131 2881190 2882157 2882187 "UFD" 2882399 T UFD (NIL) -9 NIL 2882513) (-1130 2880984 2881030 2881125 "UFD-" 2881130 NIL UFD- (NIL T) -8 NIL NIL) (-1129 2880066 2880249 2880465 "UDVO" 2880790 T UDVO (NIL) -7 NIL NIL) (-1128 2877882 2878291 2878762 "UDPO" 2879630 NIL UDPO (NIL T) -7 NIL NIL) (-1127 2877815 2877820 2877850 "TYPE" 2877855 T TYPE (NIL) -9 NIL NIL) (-1126 2876786 2876988 2877228 "TWOFACT" 2877609 NIL TWOFACT (NIL T) -7 NIL NIL) (-1125 2875724 2876061 2876324 "TUPLE" 2876558 NIL TUPLE (NIL T) -8 NIL NIL) (-1124 2873415 2873934 2874473 "TUBETOOL" 2875207 T TUBETOOL (NIL) -7 NIL NIL) (-1123 2872264 2872469 2872710 "TUBE" 2873208 NIL TUBE (NIL T) -8 NIL NIL) (-1122 2866988 2871242 2871524 "TS" 2872016 NIL TS (NIL T) -8 NIL NIL) (-1121 2855692 2859784 2859880 "TSETCAT" 2865114 NIL TSETCAT (NIL T T T T) -9 NIL 2866645) (-1120 2850427 2852025 2853915 "TSETCAT-" 2853920 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1119 2844690 2845536 2846478 "TRMANIP" 2849563 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1118 2844131 2844194 2844357 "TRIMAT" 2844622 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1117 2841937 2842174 2842537 "TRIGMNIP" 2843880 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1116 2841457 2841570 2841600 "TRIGCAT" 2841813 T TRIGCAT (NIL) -9 NIL NIL) (-1115 2841126 2841205 2841346 "TRIGCAT-" 2841351 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1114 2838025 2839986 2840266 "TREE" 2840881 NIL TREE (NIL T) -8 NIL NIL) (-1113 2837299 2837827 2837857 "TRANFUN" 2837892 T TRANFUN (NIL) -9 NIL 2837958) (-1112 2836578 2836769 2837049 "TRANFUN-" 2837054 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1111 2836382 2836414 2836475 "TOPSP" 2836539 T TOPSP (NIL) -7 NIL NIL) (-1110 2835734 2835849 2836002 "TOOLSIGN" 2836263 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1109 2834395 2834911 2835150 "TEXTFILE" 2835517 T TEXTFILE (NIL) -8 NIL NIL) (-1108 2832260 2832774 2833212 "TEX" 2833979 T TEX (NIL) -8 NIL NIL) (-1107 2832041 2832072 2832144 "TEX1" 2832223 NIL TEX1 (NIL T) -7 NIL NIL) (-1106 2831689 2831752 2831842 "TEMUTL" 2831973 T TEMUTL (NIL) -7 NIL NIL) (-1105 2829843 2830123 2830448 "TBCMPPK" 2831412 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1104 2821732 2828004 2828060 "TBAGG" 2828460 NIL TBAGG (NIL T T) -9 NIL 2828671) (-1103 2816802 2818290 2820044 "TBAGG-" 2820049 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1102 2816186 2816293 2816438 "TANEXP" 2816691 NIL TANEXP (NIL T) -7 NIL NIL) (-1101 2809687 2816043 2816136 "TABLE" 2816141 NIL TABLE (NIL T T) -8 NIL NIL) (-1100 2809099 2809198 2809336 "TABLEAU" 2809584 NIL TABLEAU (NIL T) -8 NIL NIL) (-1099 2803672 2804892 2806140 "TABLBUMP" 2807885 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1098 2803100 2803200 2803328 "SYSTEM" 2803566 T SYSTEM (NIL) -7 NIL NIL) (-1097 2799563 2800258 2801041 "SYSSOLP" 2802351 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1096 2795854 2796562 2797296 "SYNTAX" 2798851 T SYNTAX (NIL) -8 NIL NIL) (-1095 2792988 2793596 2794234 "SYMTAB" 2795238 T SYMTAB (NIL) -8 NIL NIL) (-1094 2788237 2789139 2790122 "SYMS" 2792027 T SYMS (NIL) -8 NIL NIL) (-1093 2785466 2787693 2787922 "SYMPOLY" 2788042 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1092 2784986 2785061 2785183 "SYMFUNC" 2785378 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1091 2780963 2782223 2783045 "SYMBOL" 2784186 T SYMBOL (NIL) -8 NIL NIL) (-1090 2774502 2776191 2777911 "SWITCH" 2779265 T SWITCH (NIL) -8 NIL NIL) (-1089 2767732 2773329 2773631 "SUTS" 2774257 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1088 2759622 2766853 2767133 "SUPXS" 2767509 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1087 2751114 2759243 2759368 "SUP" 2759531 NIL SUP (NIL T) -8 NIL NIL) (-1086 2750273 2750400 2750617 "SUPFRACF" 2750982 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1085 2749898 2749957 2750068 "SUP2" 2750208 NIL SUP2 (NIL T T) -7 NIL NIL) (-1084 2748295 2748569 2748931 "SUMRF" 2749597 NIL SUMRF (NIL T) -7 NIL NIL) (-1083 2747612 2747678 2747876 "SUMFS" 2748216 NIL SUMFS (NIL T T) -7 NIL NIL) (-1082 2731548 2746793 2747043 "SULS" 2747419 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1081 2730870 2731073 2731213 "SUCH" 2731456 NIL SUCH (NIL T T) -8 NIL NIL) (-1080 2724797 2725809 2726767 "SUBSPACE" 2729958 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1079 2724227 2724317 2724481 "SUBRESP" 2724685 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1078 2717596 2718892 2720203 "STTF" 2722963 NIL STTF (NIL T) -7 NIL NIL) (-1077 2711769 2712889 2714036 "STTFNC" 2716496 NIL STTFNC (NIL T) -7 NIL NIL) (-1076 2703109 2704976 2706769 "STTAYLOR" 2710010 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1075 2696353 2702973 2703056 "STRTBL" 2703061 NIL STRTBL (NIL T) -8 NIL NIL) (-1074 2691744 2696308 2696339 "STRING" 2696344 T STRING (NIL) -8 NIL NIL) (-1073 2686633 2691118 2691148 "STRICAT" 2691207 T STRICAT (NIL) -9 NIL 2691269) (-1072 2679347 2684156 2684776 "STREAM" 2686048 NIL STREAM (NIL T) -8 NIL NIL) (-1071 2678857 2678934 2679078 "STREAM3" 2679264 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1070 2677839 2678022 2678257 "STREAM2" 2678670 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1069 2677527 2677579 2677672 "STREAM1" 2677781 NIL STREAM1 (NIL T) -7 NIL NIL) (-1068 2676543 2676724 2676955 "STINPROD" 2677343 NIL STINPROD (NIL T) -7 NIL NIL) (-1067 2676122 2676306 2676336 "STEP" 2676416 T STEP (NIL) -9 NIL 2676494) (-1066 2669665 2676021 2676098 "STBL" 2676103 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1065 2664841 2668888 2668931 "STAGG" 2669084 NIL STAGG (NIL T) -9 NIL 2669173) (-1064 2662543 2663145 2664017 "STAGG-" 2664022 NIL STAGG- (NIL T T) -8 NIL NIL) (-1063 2660738 2662313 2662405 "STACK" 2662486 NIL STACK (NIL T) -8 NIL NIL) (-1062 2653469 2658885 2659340 "SREGSET" 2660368 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1061 2645901 2647269 2648781 "SRDCMPK" 2652075 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1060 2638869 2643342 2643372 "SRAGG" 2644675 T SRAGG (NIL) -9 NIL 2645283) (-1059 2637886 2638141 2638520 "SRAGG-" 2638525 NIL SRAGG- (NIL T) -8 NIL NIL) (-1058 2632335 2636805 2637232 "SQMATRIX" 2637505 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1057 2626087 2629055 2629781 "SPLTREE" 2631681 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1056 2622077 2622743 2623389 "SPLNODE" 2625513 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1055 2621124 2621357 2621387 "SPFCAT" 2621831 T SPFCAT (NIL) -9 NIL NIL) (-1054 2619861 2620071 2620335 "SPECOUT" 2620882 T SPECOUT (NIL) -7 NIL NIL) (-1053 2619622 2619662 2619731 "SPADPRSR" 2619814 T SPADPRSR (NIL) -7 NIL NIL) (-1052 2611645 2613392 2613434 "SPACEC" 2617757 NIL SPACEC (NIL T) -9 NIL 2619573) (-1051 2609816 2611578 2611626 "SPACE3" 2611631 NIL SPACE3 (NIL T) -8 NIL NIL) (-1050 2608568 2608739 2609030 "SORTPAK" 2609621 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1049 2606624 2606927 2607345 "SOLVETRA" 2608232 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1048 2605635 2605857 2606131 "SOLVESER" 2606397 NIL SOLVESER (NIL T) -7 NIL NIL) (-1047 2600855 2601736 2602738 "SOLVERAD" 2604687 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1046 2596670 2597279 2598008 "SOLVEFOR" 2600222 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1045 2590970 2596022 2596118 "SNTSCAT" 2596123 NIL SNTSCAT (NIL T T T T) -9 NIL 2596193) (-1044 2585074 2589301 2589691 "SMTS" 2590660 NIL SMTS (NIL T T T) -8 NIL NIL) (-1043 2579484 2584963 2585039 "SMP" 2585044 NIL SMP (NIL T T) -8 NIL NIL) (-1042 2577643 2577944 2578342 "SMITH" 2579181 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1041 2570608 2574804 2574906 "SMATCAT" 2576246 NIL SMATCAT (NIL NIL T T T) -9 NIL 2576795) (-1040 2567549 2568372 2569549 "SMATCAT-" 2569554 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1039 2565263 2566786 2566829 "SKAGG" 2567090 NIL SKAGG (NIL T) -9 NIL 2567225) (-1038 2561321 2564367 2564645 "SINT" 2565007 T SINT (NIL) -8 NIL NIL) (-1037 2561093 2561131 2561197 "SIMPAN" 2561277 T SIMPAN (NIL) -7 NIL NIL) (-1036 2559931 2560152 2560427 "SIGNRF" 2560852 NIL SIGNRF (NIL T) -7 NIL NIL) (-1035 2558716 2558867 2559157 "SIGNEF" 2559760 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1034 2556406 2556860 2557366 "SHP" 2558257 NIL SHP (NIL T NIL) -7 NIL NIL) (-1033 2550259 2556307 2556383 "SHDP" 2556388 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1032 2549749 2549941 2549971 "SGROUP" 2550123 T SGROUP (NIL) -9 NIL 2550210) (-1031 2549519 2549571 2549675 "SGROUP-" 2549680 NIL SGROUP- (NIL T) -8 NIL NIL) (-1030 2546355 2547052 2547775 "SGCF" 2548818 T SGCF (NIL) -7 NIL NIL) (-1029 2540754 2545806 2545902 "SFRTCAT" 2545907 NIL SFRTCAT (NIL T T T T) -9 NIL 2545945) (-1028 2534214 2535229 2536363 "SFRGCD" 2539737 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1027 2527380 2528451 2529635 "SFQCMPK" 2533147 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1026 2527002 2527091 2527201 "SFORT" 2527321 NIL SFORT (NIL T T) -8 NIL NIL) (-1025 2526147 2526842 2526963 "SEXOF" 2526968 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1024 2525281 2526028 2526096 "SEX" 2526101 T SEX (NIL) -8 NIL NIL) (-1023 2520058 2520747 2520842 "SEXCAT" 2524613 NIL SEXCAT (NIL T T T T T) -9 NIL 2525232) (-1022 2517238 2519992 2520040 "SET" 2520045 NIL SET (NIL T) -8 NIL NIL) (-1021 2515457 2515919 2516224 "SETMN" 2516979 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1020 2515065 2515191 2515221 "SETCAT" 2515338 T SETCAT (NIL) -9 NIL 2515422) (-1019 2514845 2514897 2514996 "SETCAT-" 2515001 NIL SETCAT- (NIL T) -8 NIL NIL) (-1018 2511233 2513307 2513350 "SETAGG" 2514220 NIL SETAGG (NIL T) -9 NIL 2514560) (-1017 2510691 2510807 2511044 "SETAGG-" 2511049 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1016 2509895 2510188 2510249 "SEGXCAT" 2510535 NIL SEGXCAT (NIL T T) -9 NIL 2510655) (-1015 2508951 2509561 2509743 "SEG" 2509748 NIL SEG (NIL T) -8 NIL NIL) (-1014 2507858 2508071 2508114 "SEGCAT" 2508696 NIL SEGCAT (NIL T) -9 NIL 2508934) (-1013 2506907 2507237 2507437 "SEGBIND" 2507693 NIL SEGBIND (NIL T) -8 NIL NIL) (-1012 2506528 2506587 2506700 "SEGBIND2" 2506842 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1011 2505747 2505873 2506077 "SEG2" 2506372 NIL SEG2 (NIL T T) -7 NIL NIL) (-1010 2505184 2505682 2505729 "SDVAR" 2505734 NIL SDVAR (NIL T) -8 NIL NIL) (-1009 2497436 2504957 2505085 "SDPOL" 2505090 NIL SDPOL (NIL T) -8 NIL NIL) (-1008 2496029 2496295 2496614 "SCPKG" 2497151 NIL SCPKG (NIL T) -7 NIL NIL) (-1007 2495166 2495345 2495545 "SCOPE" 2495851 T SCOPE (NIL) -8 NIL NIL) (-1006 2494387 2494520 2494699 "SCACHE" 2495021 NIL SCACHE (NIL T) -7 NIL NIL) (-1005 2493826 2494147 2494232 "SAOS" 2494324 T SAOS (NIL) -8 NIL NIL) (-1004 2493391 2493426 2493599 "SAERFFC" 2493785 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1003 2487285 2493288 2493368 "SAE" 2493373 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1002 2486878 2486913 2487072 "SAEFACT" 2487244 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1001 2485199 2485513 2485914 "RURPK" 2486544 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1000 2483847 2484124 2484433 "RULESET" 2485035 NIL RULESET (NIL T T T) -8 NIL NIL) (-999 2481041 2481544 2482005 "RULE" 2483529 NIL RULE (NIL T T T) -8 NIL NIL) (-998 2480678 2480833 2480914 "RULECOLD" 2480993 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-997 2475570 2476364 2477280 "RSETGCD" 2479877 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-996 2464885 2469937 2470031 "RSETCAT" 2474096 NIL RSETCAT (NIL T T T T) -9 NIL 2475193) (-995 2462816 2463355 2464175 "RSETCAT-" 2464180 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-994 2455238 2456613 2458129 "RSDCMPK" 2461415 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-993 2453256 2453697 2453769 "RRCC" 2454845 NIL RRCC (NIL T T) -9 NIL 2455189) (-992 2452610 2452784 2453060 "RRCC-" 2453065 NIL RRCC- (NIL T T T) -8 NIL NIL) (-991 2426977 2436602 2436666 "RPOLCAT" 2447168 NIL RPOLCAT (NIL T T T) -9 NIL 2450326) (-990 2418481 2420819 2423937 "RPOLCAT-" 2423942 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-989 2409547 2416711 2417191 "ROUTINE" 2418021 T ROUTINE (NIL) -8 NIL NIL) (-988 2406252 2409103 2409250 "ROMAN" 2409420 T ROMAN (NIL) -8 NIL NIL) (-987 2404538 2405123 2405380 "ROIRC" 2406058 NIL ROIRC (NIL T T) -8 NIL NIL) (-986 2400943 2403247 2403275 "RNS" 2403571 T RNS (NIL) -9 NIL 2403841) (-985 2399457 2399840 2400371 "RNS-" 2400444 NIL RNS- (NIL T) -8 NIL NIL) (-984 2398883 2399291 2399319 "RNG" 2399324 T RNG (NIL) -9 NIL 2399345) (-983 2398281 2398643 2398683 "RMODULE" 2398743 NIL RMODULE (NIL T) -9 NIL 2398785) (-982 2397133 2397227 2397557 "RMCAT2" 2398182 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-981 2393847 2396316 2396637 "RMATRIX" 2396868 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-980 2386844 2389078 2389190 "RMATCAT" 2392499 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2393481) (-979 2386223 2386370 2386673 "RMATCAT-" 2386678 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-978 2385793 2385868 2385994 "RINTERP" 2386142 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-977 2384844 2385408 2385436 "RING" 2385546 T RING (NIL) -9 NIL 2385640) (-976 2384639 2384683 2384777 "RING-" 2384782 NIL RING- (NIL T) -8 NIL NIL) (-975 2383487 2383724 2383980 "RIDIST" 2384403 T RIDIST (NIL) -7 NIL NIL) (-974 2374809 2382961 2383164 "RGCHAIN" 2383336 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-973 2371814 2372428 2373096 "RF" 2374173 NIL RF (NIL T) -7 NIL NIL) (-972 2371463 2371526 2371627 "RFFACTOR" 2371745 NIL RFFACTOR (NIL T) -7 NIL NIL) (-971 2371191 2371226 2371321 "RFFACT" 2371422 NIL RFFACT (NIL T) -7 NIL NIL) (-970 2369321 2369685 2370065 "RFDIST" 2370831 T RFDIST (NIL) -7 NIL NIL) (-969 2368779 2368871 2369031 "RETSOL" 2369223 NIL RETSOL (NIL T T) -7 NIL NIL) (-968 2368372 2368452 2368493 "RETRACT" 2368683 NIL RETRACT (NIL T) -9 NIL NIL) (-967 2368224 2368249 2368333 "RETRACT-" 2368338 NIL RETRACT- (NIL T T) -8 NIL NIL) (-966 2361082 2367881 2368006 "RESULT" 2368119 T RESULT (NIL) -8 NIL NIL) (-965 2359667 2360356 2360553 "RESRING" 2360985 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-964 2359307 2359356 2359452 "RESLATC" 2359604 NIL RESLATC (NIL T) -7 NIL NIL) (-963 2359016 2359050 2359155 "REPSQ" 2359266 NIL REPSQ (NIL T) -7 NIL NIL) (-962 2356447 2357027 2357627 "REP" 2358436 T REP (NIL) -7 NIL NIL) (-961 2356148 2356182 2356291 "REPDB" 2356406 NIL REPDB (NIL T) -7 NIL NIL) (-960 2350093 2351472 2352692 "REP2" 2354960 NIL REP2 (NIL T) -7 NIL NIL) (-959 2346499 2347180 2347985 "REP1" 2349320 NIL REP1 (NIL T) -7 NIL NIL) (-958 2339245 2344660 2345112 "REGSET" 2346130 NIL REGSET (NIL T T T T) -8 NIL NIL) (-957 2338066 2338401 2338649 "REF" 2339030 NIL REF (NIL T) -8 NIL NIL) (-956 2337447 2337550 2337715 "REDORDER" 2337950 NIL REDORDER (NIL T T) -7 NIL NIL) (-955 2333416 2336681 2336902 "RECLOS" 2337278 NIL RECLOS (NIL T) -8 NIL NIL) (-954 2332473 2332654 2332867 "REALSOLV" 2333223 T REALSOLV (NIL) -7 NIL NIL) (-953 2332321 2332362 2332390 "REAL" 2332395 T REAL (NIL) -9 NIL 2332430) (-952 2328757 2329559 2330441 "REAL0Q" 2331486 NIL REAL0Q (NIL T) -7 NIL NIL) (-951 2324368 2325356 2326415 "REAL0" 2327738 NIL REAL0 (NIL T) -7 NIL NIL) (-950 2323776 2323848 2324053 "RDIV" 2324290 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-949 2322849 2323023 2323234 "RDIST" 2323598 NIL RDIST (NIL T) -7 NIL NIL) (-948 2321453 2321740 2322109 "RDETRS" 2322557 NIL RDETRS (NIL T T) -7 NIL NIL) (-947 2319266 2319720 2320255 "RDETR" 2320995 NIL RDETR (NIL T T) -7 NIL NIL) (-946 2317874 2318152 2318553 "RDEEFS" 2318982 NIL RDEEFS (NIL T T) -7 NIL NIL) (-945 2316366 2316672 2317101 "RDEEF" 2317562 NIL RDEEF (NIL T T) -7 NIL NIL) (-944 2310651 2313583 2313611 "RCFIELD" 2314888 T RCFIELD (NIL) -9 NIL 2315618) (-943 2308720 2309224 2309917 "RCFIELD-" 2309990 NIL RCFIELD- (NIL T) -8 NIL NIL) (-942 2305052 2306837 2306878 "RCAGG" 2307949 NIL RCAGG (NIL T) -9 NIL 2308414) (-941 2304683 2304777 2304937 "RCAGG-" 2304942 NIL RCAGG- (NIL T T) -8 NIL NIL) (-940 2304005 2304117 2304279 "RATRET" 2304567 NIL RATRET (NIL T) -7 NIL NIL) (-939 2303562 2303629 2303748 "RATFACT" 2303933 NIL RATFACT (NIL T) -7 NIL NIL) (-938 2302877 2302997 2303147 "RANDSRC" 2303432 T RANDSRC (NIL) -7 NIL NIL) (-937 2302614 2302658 2302729 "RADUTIL" 2302826 T RADUTIL (NIL) -7 NIL NIL) (-936 2295621 2301357 2301674 "RADIX" 2302329 NIL RADIX (NIL NIL) -8 NIL NIL) (-935 2287191 2295465 2295593 "RADFF" 2295598 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-934 2286843 2286918 2286946 "RADCAT" 2287103 T RADCAT (NIL) -9 NIL NIL) (-933 2286628 2286676 2286773 "RADCAT-" 2286778 NIL RADCAT- (NIL T) -8 NIL NIL) (-932 2284779 2286403 2286492 "QUEUE" 2286572 NIL QUEUE (NIL T) -8 NIL NIL) (-931 2281276 2284716 2284761 "QUAT" 2284766 NIL QUAT (NIL T) -8 NIL NIL) (-930 2280914 2280957 2281084 "QUATCT2" 2281227 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-929 2274708 2278088 2278128 "QUATCAT" 2278907 NIL QUATCAT (NIL T) -9 NIL 2279672) (-928 2270852 2271889 2273276 "QUATCAT-" 2273370 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-927 2268373 2269937 2269978 "QUAGG" 2270353 NIL QUAGG (NIL T) -9 NIL 2270528) (-926 2267298 2267771 2267943 "QFORM" 2268245 NIL QFORM (NIL NIL T) -8 NIL NIL) (-925 2258595 2263853 2263893 "QFCAT" 2264551 NIL QFCAT (NIL T) -9 NIL 2265544) (-924 2254167 2255368 2256959 "QFCAT-" 2257053 NIL QFCAT- (NIL T T) -8 NIL NIL) (-923 2253805 2253848 2253975 "QFCAT2" 2254118 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-922 2253265 2253375 2253505 "QEQUAT" 2253695 T QEQUAT (NIL) -8 NIL NIL) (-921 2246451 2247522 2248704 "QCMPACK" 2252198 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-920 2244027 2244448 2244876 "QALGSET" 2246106 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-919 2243272 2243446 2243678 "QALGSET2" 2243847 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-918 2241963 2242186 2242503 "PWFFINTB" 2243045 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-917 2240151 2240319 2240672 "PUSHVAR" 2241777 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-916 2236069 2237123 2237164 "PTRANFN" 2239048 NIL PTRANFN (NIL T) -9 NIL NIL) (-915 2234481 2234772 2235093 "PTPACK" 2235780 NIL PTPACK (NIL T) -7 NIL NIL) (-914 2234117 2234174 2234281 "PTFUNC2" 2234418 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-913 2228594 2232935 2232975 "PTCAT" 2233343 NIL PTCAT (NIL T) -9 NIL 2233505) (-912 2228252 2228287 2228411 "PSQFR" 2228553 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-911 2226847 2227145 2227479 "PSEUDLIN" 2227950 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-910 2213654 2216019 2218342 "PSETPK" 2224607 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-909 2206741 2209455 2209549 "PSETCAT" 2212530 NIL PSETCAT (NIL T T T T) -9 NIL 2213344) (-908 2204579 2205213 2206032 "PSETCAT-" 2206037 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-907 2203928 2204093 2204121 "PSCURVE" 2204389 T PSCURVE (NIL) -9 NIL 2204556) (-906 2200380 2201906 2201970 "PSCAT" 2202806 NIL PSCAT (NIL T T T) -9 NIL 2203046) (-905 2199444 2199660 2200059 "PSCAT-" 2200064 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-904 2198096 2198729 2198943 "PRTITION" 2199250 T PRTITION (NIL) -8 NIL NIL) (-903 2187194 2189400 2191588 "PRS" 2195958 NIL PRS (NIL T T) -7 NIL NIL) (-902 2185053 2186545 2186585 "PRQAGG" 2186768 NIL PRQAGG (NIL T) -9 NIL 2186870) (-901 2184624 2184726 2184754 "PROPLOG" 2184939 T PROPLOG (NIL) -9 NIL NIL) (-900 2181747 2182312 2182839 "PROPFRML" 2184129 NIL PROPFRML (NIL T) -8 NIL NIL) (-899 2181207 2181317 2181447 "PROPERTY" 2181637 T PROPERTY (NIL) -8 NIL NIL) (-898 2174981 2179373 2180193 "PRODUCT" 2180433 NIL PRODUCT (NIL T T) -8 NIL NIL) (-897 2172257 2174441 2174674 "PR" 2174792 NIL PR (NIL T T) -8 NIL NIL) (-896 2172053 2172085 2172144 "PRINT" 2172218 T PRINT (NIL) -7 NIL NIL) (-895 2171393 2171510 2171662 "PRIMES" 2171933 NIL PRIMES (NIL T) -7 NIL NIL) (-894 2169458 2169859 2170325 "PRIMELT" 2170972 NIL PRIMELT (NIL T) -7 NIL NIL) (-893 2169187 2169236 2169264 "PRIMCAT" 2169388 T PRIMCAT (NIL) -9 NIL NIL) (-892 2165348 2169125 2169170 "PRIMARR" 2169175 NIL PRIMARR (NIL T) -8 NIL NIL) (-891 2164355 2164533 2164761 "PRIMARR2" 2165166 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-890 2163998 2164054 2164165 "PREASSOC" 2164293 NIL PREASSOC (NIL T T) -7 NIL NIL) (-889 2163473 2163606 2163634 "PPCURVE" 2163839 T PPCURVE (NIL) -9 NIL 2163975) (-888 2160832 2161231 2161823 "POLYROOT" 2163054 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-887 2154738 2160438 2160597 "POLY" 2160705 NIL POLY (NIL T) -8 NIL NIL) (-886 2154123 2154181 2154414 "POLYLIFT" 2154674 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-885 2150408 2150857 2151485 "POLYCATQ" 2153668 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-884 2137449 2142846 2142910 "POLYCAT" 2146395 NIL POLYCAT (NIL T T T) -9 NIL 2148322) (-883 2130900 2132761 2135144 "POLYCAT-" 2135149 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-882 2130489 2130557 2130676 "POLY2UP" 2130826 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-881 2130125 2130182 2130289 "POLY2" 2130426 NIL POLY2 (NIL T T) -7 NIL NIL) (-880 2128810 2129049 2129325 "POLUTIL" 2129899 NIL POLUTIL (NIL T T) -7 NIL NIL) (-879 2127172 2127449 2127779 "POLTOPOL" 2128532 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-878 2122695 2127109 2127154 "POINT" 2127159 NIL POINT (NIL T) -8 NIL NIL) (-877 2120882 2121239 2121614 "PNTHEORY" 2122340 T PNTHEORY (NIL) -7 NIL NIL) (-876 2119310 2119607 2120016 "PMTOOLS" 2120580 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-875 2118903 2118981 2119098 "PMSYM" 2119226 NIL PMSYM (NIL T) -7 NIL NIL) (-874 2118406 2118475 2118649 "PMQFCAT" 2118828 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-873 2117761 2117871 2118027 "PMPRED" 2118283 NIL PMPRED (NIL T) -7 NIL NIL) (-872 2117157 2117243 2117404 "PMPREDFS" 2117662 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-871 2115789 2115997 2116381 "PMPLCAT" 2116919 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-870 2115321 2115400 2115552 "PMLSAGG" 2115704 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-869 2114791 2114867 2115047 "PMKERNEL" 2115239 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-868 2114408 2114483 2114596 "PMINS" 2114710 NIL PMINS (NIL T) -7 NIL NIL) (-867 2113831 2113900 2114115 "PMFS" 2114333 NIL PMFS (NIL T T T) -7 NIL NIL) (-866 2113062 2113180 2113384 "PMDOWN" 2113708 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-865 2112225 2112384 2112566 "PMASS" 2112900 T PMASS (NIL) -7 NIL NIL) (-864 2111499 2111610 2111773 "PMASSFS" 2112111 NIL PMASSFS (NIL T T) -7 NIL NIL) (-863 2111154 2111222 2111316 "PLOTTOOL" 2111425 T PLOTTOOL (NIL) -7 NIL NIL) (-862 2105776 2106965 2108113 "PLOT" 2110026 T PLOT (NIL) -8 NIL NIL) (-861 2101590 2102624 2103545 "PLOT3D" 2104875 T PLOT3D (NIL) -8 NIL NIL) (-860 2100502 2100679 2100914 "PLOT1" 2101394 NIL PLOT1 (NIL T) -7 NIL NIL) (-859 2075896 2080568 2085419 "PLEQN" 2095768 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-858 2075214 2075336 2075516 "PINTERP" 2075761 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-857 2074907 2074954 2075057 "PINTERPA" 2075161 NIL PINTERPA (NIL T T) -7 NIL NIL) (-856 2074146 2074713 2074800 "PI" 2074840 T PI (NIL) -8 NIL NIL) (-855 2072538 2073523 2073551 "PID" 2073733 T PID (NIL) -9 NIL 2073867) (-854 2072263 2072300 2072388 "PICOERCE" 2072495 NIL PICOERCE (NIL T) -7 NIL NIL) (-853 2071583 2071722 2071898 "PGROEB" 2072119 NIL PGROEB (NIL T) -7 NIL NIL) (-852 2067170 2067984 2068889 "PGE" 2070698 T PGE (NIL) -7 NIL NIL) (-851 2065294 2065540 2065906 "PGCD" 2066887 NIL PGCD (NIL T T T T) -7 NIL NIL) (-850 2064632 2064735 2064896 "PFRPAC" 2065178 NIL PFRPAC (NIL T) -7 NIL NIL) (-849 2061247 2063180 2063533 "PFR" 2064311 NIL PFR (NIL T) -8 NIL NIL) (-848 2059620 2059864 2060189 "PFOTOOLS" 2060994 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-847 2058153 2058392 2058743 "PFOQ" 2059377 NIL PFOQ (NIL T T T) -7 NIL NIL) (-846 2056630 2056842 2057204 "PFO" 2057937 NIL PFO (NIL T T T T T) -7 NIL NIL) (-845 2053153 2056519 2056588 "PF" 2056593 NIL PF (NIL NIL) -8 NIL NIL) (-844 2050582 2051863 2051891 "PFECAT" 2052476 T PFECAT (NIL) -9 NIL 2052860) (-843 2050027 2050181 2050395 "PFECAT-" 2050400 NIL PFECAT- (NIL T) -8 NIL NIL) (-842 2048631 2048882 2049183 "PFBRU" 2049776 NIL PFBRU (NIL T T) -7 NIL NIL) (-841 2046498 2046849 2047281 "PFBR" 2048282 NIL PFBR (NIL T T T T) -7 NIL NIL) (-840 2042349 2043874 2044550 "PERM" 2045855 NIL PERM (NIL T) -8 NIL NIL) (-839 2037614 2038556 2039426 "PERMGRP" 2041512 NIL PERMGRP (NIL T) -8 NIL NIL) (-838 2035685 2036678 2036719 "PERMCAT" 2037165 NIL PERMCAT (NIL T) -9 NIL 2037470) (-837 2035340 2035381 2035504 "PERMAN" 2035638 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-836 2032780 2034909 2035040 "PENDTREE" 2035242 NIL PENDTREE (NIL T) -8 NIL NIL) (-835 2030853 2031631 2031672 "PDRING" 2032329 NIL PDRING (NIL T) -9 NIL 2032614) (-834 2029956 2030174 2030536 "PDRING-" 2030541 NIL PDRING- (NIL T T) -8 NIL NIL) (-833 2027097 2027848 2028539 "PDEPROB" 2029285 T PDEPROB (NIL) -8 NIL NIL) (-832 2024660 2025156 2025705 "PDEPACK" 2026568 T PDEPACK (NIL) -7 NIL NIL) (-831 2023572 2023762 2024013 "PDECOMP" 2024459 NIL PDECOMP (NIL T T) -7 NIL NIL) (-830 2021184 2021999 2022027 "PDECAT" 2022812 T PDECAT (NIL) -9 NIL 2023523) (-829 2020937 2020970 2021059 "PCOMP" 2021145 NIL PCOMP (NIL T T) -7 NIL NIL) (-828 2019144 2019740 2020036 "PBWLB" 2020667 NIL PBWLB (NIL T) -8 NIL NIL) (-827 2011652 2013221 2014557 "PATTERN" 2017829 NIL PATTERN (NIL T) -8 NIL NIL) (-826 2011284 2011341 2011450 "PATTERN2" 2011589 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-825 2009041 2009429 2009886 "PATTERN1" 2010873 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-824 2006436 2006990 2007471 "PATRES" 2008606 NIL PATRES (NIL T T) -8 NIL NIL) (-823 2006000 2006067 2006199 "PATRES2" 2006363 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-822 2003897 2004297 2004702 "PATMATCH" 2005669 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-821 2003434 2003617 2003658 "PATMAB" 2003765 NIL PATMAB (NIL T) -9 NIL 2003848) (-820 2001979 2002288 2002546 "PATLRES" 2003239 NIL PATLRES (NIL T T T) -8 NIL NIL) (-819 2001525 2001648 2001689 "PATAB" 2001694 NIL PATAB (NIL T) -9 NIL 2001866) (-818 1999006 1999538 2000111 "PARTPERM" 2000972 T PARTPERM (NIL) -7 NIL NIL) (-817 1998627 1998690 1998792 "PARSURF" 1998937 NIL PARSURF (NIL T) -8 NIL NIL) (-816 1998259 1998316 1998425 "PARSU2" 1998564 NIL PARSU2 (NIL T T) -7 NIL NIL) (-815 1998023 1998063 1998130 "PARSER" 1998212 T PARSER (NIL) -7 NIL NIL) (-814 1997644 1997707 1997809 "PARSCURV" 1997954 NIL PARSCURV (NIL T) -8 NIL NIL) (-813 1997276 1997333 1997442 "PARSC2" 1997581 NIL PARSC2 (NIL T T) -7 NIL NIL) (-812 1996915 1996973 1997070 "PARPCURV" 1997212 NIL PARPCURV (NIL T) -8 NIL NIL) (-811 1996547 1996604 1996713 "PARPC2" 1996852 NIL PARPC2 (NIL T T) -7 NIL NIL) (-810 1996067 1996153 1996272 "PAN2EXPR" 1996448 T PAN2EXPR (NIL) -7 NIL NIL) (-809 1994873 1995188 1995416 "PALETTE" 1995859 T PALETTE (NIL) -8 NIL NIL) (-808 1993341 1993878 1994238 "PAIR" 1994559 NIL PAIR (NIL T T) -8 NIL NIL) (-807 1987183 1992592 1992786 "PADICRC" 1993196 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-806 1980383 1986521 1986705 "PADICRAT" 1987031 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-805 1978687 1980320 1980365 "PADIC" 1980370 NIL PADIC (NIL NIL) -8 NIL NIL) (-804 1975892 1977466 1977506 "PADICCT" 1978087 NIL PADICCT (NIL NIL) -9 NIL 1978369) (-803 1974849 1975049 1975317 "PADEPAC" 1975679 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-802 1974061 1974194 1974400 "PADE" 1974711 NIL PADE (NIL T T T) -7 NIL NIL) (-801 1972064 1972896 1973211 "OWP" 1973829 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-800 1971168 1971664 1971836 "OVAR" 1971932 NIL OVAR (NIL NIL) -8 NIL NIL) (-799 1970432 1970553 1970714 "OUT" 1971027 T OUT (NIL) -7 NIL NIL) (-798 1959486 1961657 1963827 "OUTFORM" 1968282 T OUTFORM (NIL) -8 NIL NIL) (-797 1958894 1959215 1959304 "OSI" 1959417 T OSI (NIL) -8 NIL NIL) (-796 1958425 1958763 1958791 "OSGROUP" 1958796 T OSGROUP (NIL) -9 NIL 1958818) (-795 1957170 1957397 1957682 "ORTHPOL" 1958172 NIL ORTHPOL (NIL T) -7 NIL NIL) (-794 1954541 1956831 1956969 "OREUP" 1957113 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-793 1951937 1954234 1954360 "ORESUP" 1954483 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-792 1949472 1949972 1950532 "OREPCTO" 1951426 NIL OREPCTO (NIL T T) -7 NIL NIL) (-791 1943382 1945588 1945628 "OREPCAT" 1947949 NIL OREPCAT (NIL T) -9 NIL 1949052) (-790 1940530 1941312 1942369 "OREPCAT-" 1942374 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-789 1939708 1939980 1940008 "ORDSET" 1940317 T ORDSET (NIL) -9 NIL 1940481) (-788 1939227 1939349 1939542 "ORDSET-" 1939547 NIL ORDSET- (NIL T) -8 NIL NIL) (-787 1937841 1938642 1938670 "ORDRING" 1938872 T ORDRING (NIL) -9 NIL 1938996) (-786 1937486 1937580 1937724 "ORDRING-" 1937729 NIL ORDRING- (NIL T) -8 NIL NIL) (-785 1936849 1937330 1937358 "ORDMON" 1937363 T ORDMON (NIL) -9 NIL 1937384) (-784 1936011 1936158 1936353 "ORDFUNS" 1936698 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-783 1935523 1935882 1935910 "ORDFIN" 1935915 T ORDFIN (NIL) -9 NIL 1935936) (-782 1932035 1934109 1934518 "ORDCOMP" 1935147 NIL ORDCOMP (NIL T) -8 NIL NIL) (-781 1931301 1931428 1931614 "ORDCOMP2" 1931895 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-780 1927808 1928691 1929528 "OPTPROB" 1930484 T OPTPROB (NIL) -8 NIL NIL) (-779 1924650 1925279 1925973 "OPTPACK" 1927134 T OPTPACK (NIL) -7 NIL NIL) (-778 1922376 1923112 1923140 "OPTCAT" 1923955 T OPTCAT (NIL) -9 NIL 1924601) (-777 1922144 1922183 1922249 "OPQUERY" 1922330 T OPQUERY (NIL) -7 NIL NIL) (-776 1919280 1920471 1920971 "OP" 1921676 NIL OP (NIL T) -8 NIL NIL) (-775 1916045 1918077 1918446 "ONECOMP" 1918944 NIL ONECOMP (NIL T) -8 NIL NIL) (-774 1915350 1915465 1915639 "ONECOMP2" 1915917 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-773 1914769 1914875 1915005 "OMSERVER" 1915240 T OMSERVER (NIL) -7 NIL NIL) (-772 1911658 1914210 1914250 "OMSAGG" 1914311 NIL OMSAGG (NIL T) -9 NIL 1914375) (-771 1910281 1910544 1910826 "OMPKG" 1911396 T OMPKG (NIL) -7 NIL NIL) (-770 1909711 1909814 1909842 "OM" 1910141 T OM (NIL) -9 NIL NIL) (-769 1908250 1909263 1909431 "OMLO" 1909592 NIL OMLO (NIL T T) -8 NIL NIL) (-768 1907180 1907327 1907553 "OMEXPR" 1908076 NIL OMEXPR (NIL T) -7 NIL NIL) (-767 1906498 1906726 1906862 "OMERR" 1907064 T OMERR (NIL) -8 NIL NIL) (-766 1905676 1905919 1906079 "OMERRK" 1906358 T OMERRK (NIL) -8 NIL NIL) (-765 1905154 1905353 1905461 "OMENC" 1905588 T OMENC (NIL) -8 NIL NIL) (-764 1899049 1900234 1901405 "OMDEV" 1904003 T OMDEV (NIL) -8 NIL NIL) (-763 1898118 1898289 1898483 "OMCONN" 1898875 T OMCONN (NIL) -8 NIL NIL) (-762 1896734 1897720 1897748 "OINTDOM" 1897753 T OINTDOM (NIL) -9 NIL 1897774) (-761 1892496 1893726 1894441 "OFMONOID" 1896051 NIL OFMONOID (NIL T) -8 NIL NIL) (-760 1891934 1892433 1892478 "ODVAR" 1892483 NIL ODVAR (NIL T) -8 NIL NIL) (-759 1889059 1891431 1891616 "ODR" 1891809 NIL ODR (NIL T T NIL) -8 NIL NIL) (-758 1881365 1888838 1888962 "ODPOL" 1888967 NIL ODPOL (NIL T) -8 NIL NIL) (-757 1875188 1881237 1881342 "ODP" 1881347 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-756 1873954 1874169 1874444 "ODETOOLS" 1874962 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-755 1870923 1871579 1872295 "ODESYS" 1873287 NIL ODESYS (NIL T T) -7 NIL NIL) (-754 1865827 1866735 1867758 "ODERTRIC" 1869998 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-753 1865253 1865335 1865529 "ODERED" 1865739 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-752 1862155 1862703 1863378 "ODERAT" 1864676 NIL ODERAT (NIL T T) -7 NIL NIL) (-751 1859116 1859580 1860176 "ODEPRRIC" 1861684 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-750 1856985 1857554 1858063 "ODEPROB" 1858627 T ODEPROB (NIL) -8 NIL NIL) (-749 1853510 1853993 1854639 "ODEPRIM" 1856464 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-748 1852763 1852865 1853123 "ODEPAL" 1853402 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-747 1848941 1849722 1850576 "ODEPACK" 1851929 T ODEPACK (NIL) -7 NIL NIL) (-746 1847978 1848085 1848313 "ODEINT" 1848830 NIL ODEINT (NIL T T) -7 NIL NIL) (-745 1842079 1843504 1844951 "ODEIFTBL" 1846551 T ODEIFTBL (NIL) -8 NIL NIL) (-744 1837423 1838209 1839167 "ODEEF" 1841238 NIL ODEEF (NIL T T) -7 NIL NIL) (-743 1836760 1836849 1837078 "ODECONST" 1837328 NIL ODECONST (NIL T T T) -7 NIL NIL) (-742 1834918 1835551 1835579 "ODECAT" 1836182 T ODECAT (NIL) -9 NIL 1836711) (-741 1831790 1834630 1834749 "OCT" 1834831 NIL OCT (NIL T) -8 NIL NIL) (-740 1831428 1831471 1831598 "OCTCT2" 1831741 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-739 1826262 1828700 1828740 "OC" 1829836 NIL OC (NIL T) -9 NIL 1830693) (-738 1823489 1824237 1825227 "OC-" 1825321 NIL OC- (NIL T T) -8 NIL NIL) (-737 1822868 1823310 1823338 "OCAMON" 1823343 T OCAMON (NIL) -9 NIL 1823364) (-736 1822426 1822741 1822769 "OASGP" 1822774 T OASGP (NIL) -9 NIL 1822794) (-735 1821714 1822177 1822205 "OAMONS" 1822245 T OAMONS (NIL) -9 NIL 1822288) (-734 1821155 1821562 1821590 "OAMON" 1821595 T OAMON (NIL) -9 NIL 1821615) (-733 1820460 1820952 1820980 "OAGROUP" 1820985 T OAGROUP (NIL) -9 NIL 1821005) (-732 1820150 1820200 1820288 "NUMTUBE" 1820404 NIL NUMTUBE (NIL T) -7 NIL NIL) (-731 1813723 1815241 1816777 "NUMQUAD" 1818634 T NUMQUAD (NIL) -7 NIL NIL) (-730 1809431 1810419 1811444 "NUMODE" 1812718 T NUMODE (NIL) -7 NIL NIL) (-729 1806835 1807681 1807709 "NUMINT" 1808626 T NUMINT (NIL) -9 NIL 1809382) (-728 1805783 1805980 1806198 "NUMFMT" 1806637 T NUMFMT (NIL) -7 NIL NIL) (-727 1792106 1795043 1797573 "NUMERIC" 1803292 NIL NUMERIC (NIL T) -7 NIL NIL) (-726 1786507 1791559 1791653 "NTSCAT" 1791658 NIL NTSCAT (NIL T T T T) -9 NIL 1791696) (-725 1785701 1785866 1786059 "NTPOLFN" 1786346 NIL NTPOLFN (NIL T) -7 NIL NIL) (-724 1773517 1782543 1783353 "NSUP" 1784923 NIL NSUP (NIL T) -8 NIL NIL) (-723 1773153 1773210 1773317 "NSUP2" 1773454 NIL NSUP2 (NIL T T) -7 NIL NIL) (-722 1763115 1772932 1773062 "NSMP" 1773067 NIL NSMP (NIL T T) -8 NIL NIL) (-721 1761547 1761848 1762205 "NREP" 1762803 NIL NREP (NIL T) -7 NIL NIL) (-720 1760138 1760390 1760748 "NPCOEF" 1761290 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-719 1759204 1759319 1759535 "NORMRETR" 1760019 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-718 1757257 1757547 1757954 "NORMPK" 1758912 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-717 1756942 1756970 1757094 "NORMMA" 1757223 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-716 1756769 1756899 1756928 "NONE" 1756933 T NONE (NIL) -8 NIL NIL) (-715 1756558 1756587 1756656 "NONE1" 1756733 NIL NONE1 (NIL T) -7 NIL NIL) (-714 1756043 1756105 1756290 "NODE1" 1756490 NIL NODE1 (NIL T T) -7 NIL NIL) (-713 1754336 1755206 1755461 "NNI" 1755808 T NNI (NIL) -8 NIL NIL) (-712 1752756 1753069 1753433 "NLINSOL" 1754004 NIL NLINSOL (NIL T) -7 NIL NIL) (-711 1748923 1749891 1750813 "NIPROB" 1751854 T NIPROB (NIL) -8 NIL NIL) (-710 1747652 1747886 1748188 "NFINTBAS" 1748685 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-709 1746360 1746591 1746872 "NCODIV" 1747420 NIL NCODIV (NIL T T) -7 NIL NIL) (-708 1746122 1746159 1746234 "NCNTFRAC" 1746317 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-707 1744302 1744666 1745086 "NCEP" 1745747 NIL NCEP (NIL T) -7 NIL NIL) (-706 1743214 1743953 1743981 "NASRING" 1744091 T NASRING (NIL) -9 NIL 1744165) (-705 1743009 1743053 1743147 "NASRING-" 1743152 NIL NASRING- (NIL T) -8 NIL NIL) (-704 1742163 1742662 1742690 "NARNG" 1742807 T NARNG (NIL) -9 NIL 1742898) (-703 1741855 1741922 1742056 "NARNG-" 1742061 NIL NARNG- (NIL T) -8 NIL NIL) (-702 1740734 1740941 1741176 "NAGSP" 1741640 T NAGSP (NIL) -7 NIL NIL) (-701 1732158 1733804 1735439 "NAGS" 1739119 T NAGS (NIL) -7 NIL NIL) (-700 1730722 1731026 1731353 "NAGF07" 1731851 T NAGF07 (NIL) -7 NIL NIL) (-699 1725304 1726584 1727880 "NAGF04" 1729446 T NAGF04 (NIL) -7 NIL NIL) (-698 1718336 1719934 1721551 "NAGF02" 1723707 T NAGF02 (NIL) -7 NIL NIL) (-697 1713600 1714690 1715797 "NAGF01" 1717249 T NAGF01 (NIL) -7 NIL NIL) (-696 1707260 1708818 1710395 "NAGE04" 1712043 T NAGE04 (NIL) -7 NIL NIL) (-695 1698501 1700604 1702716 "NAGE02" 1705168 T NAGE02 (NIL) -7 NIL NIL) (-694 1694494 1695431 1696385 "NAGE01" 1697567 T NAGE01 (NIL) -7 NIL NIL) (-693 1692301 1692832 1693387 "NAGD03" 1693959 T NAGD03 (NIL) -7 NIL NIL) (-692 1684087 1686006 1687951 "NAGD02" 1690376 T NAGD02 (NIL) -7 NIL NIL) (-691 1677946 1679359 1680787 "NAGD01" 1682679 T NAGD01 (NIL) -7 NIL NIL) (-690 1674203 1675013 1675838 "NAGC06" 1677141 T NAGC06 (NIL) -7 NIL NIL) (-689 1672680 1673009 1673362 "NAGC05" 1673870 T NAGC05 (NIL) -7 NIL NIL) (-688 1672064 1672181 1672323 "NAGC02" 1672558 T NAGC02 (NIL) -7 NIL NIL) (-687 1671126 1671683 1671723 "NAALG" 1671802 NIL NAALG (NIL T) -9 NIL 1671863) (-686 1670961 1670990 1671080 "NAALG-" 1671085 NIL NAALG- (NIL T T) -8 NIL NIL) (-685 1664911 1666019 1667206 "MULTSQFR" 1669857 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-684 1664230 1664305 1664489 "MULTFACT" 1664823 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-683 1657424 1661335 1661387 "MTSCAT" 1662447 NIL MTSCAT (NIL T T) -9 NIL 1662961) (-682 1657136 1657190 1657282 "MTHING" 1657364 NIL MTHING (NIL T) -7 NIL NIL) (-681 1656928 1656961 1657021 "MSYSCMD" 1657096 T MSYSCMD (NIL) -7 NIL NIL) (-680 1653040 1655683 1656003 "MSET" 1656641 NIL MSET (NIL T) -8 NIL NIL) (-679 1650136 1652602 1652643 "MSETAGG" 1652648 NIL MSETAGG (NIL T) -9 NIL 1652682) (-678 1645992 1647534 1648275 "MRING" 1649439 NIL MRING (NIL T T) -8 NIL NIL) (-677 1645562 1645629 1645758 "MRF2" 1645919 NIL MRF2 (NIL T T T) -7 NIL NIL) (-676 1645180 1645215 1645359 "MRATFAC" 1645521 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-675 1642778 1643073 1643504 "MPRFF" 1644885 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-674 1636798 1642633 1642729 "MPOLY" 1642734 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-673 1636288 1636323 1636531 "MPCPF" 1636757 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-672 1635804 1635847 1636030 "MPC3" 1636239 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-671 1635005 1635086 1635305 "MPC2" 1635719 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-670 1633306 1633643 1634033 "MONOTOOL" 1634665 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-669 1632431 1632766 1632794 "MONOID" 1633071 T MONOID (NIL) -9 NIL 1633243) (-668 1631809 1631972 1632215 "MONOID-" 1632220 NIL MONOID- (NIL T) -8 NIL NIL) (-667 1622790 1628776 1628835 "MONOGEN" 1629509 NIL MONOGEN (NIL T T) -9 NIL 1629965) (-666 1620008 1620743 1621743 "MONOGEN-" 1621862 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-665 1618868 1619288 1619316 "MONADWU" 1619708 T MONADWU (NIL) -9 NIL 1619946) (-664 1618240 1618399 1618647 "MONADWU-" 1618652 NIL MONADWU- (NIL T) -8 NIL NIL) (-663 1617626 1617844 1617872 "MONAD" 1618079 T MONAD (NIL) -9 NIL 1618191) (-662 1617311 1617389 1617521 "MONAD-" 1617526 NIL MONAD- (NIL T) -8 NIL NIL) (-661 1615562 1616224 1616503 "MOEBIUS" 1617064 NIL MOEBIUS (NIL T) -8 NIL NIL) (-660 1614956 1615334 1615374 "MODULE" 1615379 NIL MODULE (NIL T) -9 NIL 1615405) (-659 1614524 1614620 1614810 "MODULE-" 1614815 NIL MODULE- (NIL T T) -8 NIL NIL) (-658 1612195 1612890 1613216 "MODRING" 1614349 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-657 1609151 1610316 1610833 "MODOP" 1611727 NIL MODOP (NIL T T) -8 NIL NIL) (-656 1607210 1607662 1608003 "MODMONOM" 1608950 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-655 1596889 1605414 1605836 "MODMON" 1606838 NIL MODMON (NIL T T) -8 NIL NIL) (-654 1594015 1595733 1596009 "MODFIELD" 1596764 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-653 1593019 1593296 1593486 "MMLFORM" 1593845 T MMLFORM (NIL) -8 NIL NIL) (-652 1592545 1592588 1592767 "MMAP" 1592970 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-651 1590782 1591559 1591599 "MLO" 1592016 NIL MLO (NIL T) -9 NIL 1592257) (-650 1588149 1588664 1589266 "MLIFT" 1590263 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-649 1587540 1587624 1587778 "MKUCFUNC" 1588060 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-648 1587139 1587209 1587332 "MKRECORD" 1587463 NIL MKRECORD (NIL T T) -7 NIL NIL) (-647 1586187 1586348 1586576 "MKFUNC" 1586950 NIL MKFUNC (NIL T) -7 NIL NIL) (-646 1585575 1585679 1585835 "MKFLCFN" 1586070 NIL MKFLCFN (NIL T) -7 NIL NIL) (-645 1585001 1585368 1585457 "MKCHSET" 1585519 NIL MKCHSET (NIL T) -8 NIL NIL) (-644 1584278 1584380 1584565 "MKBCFUNC" 1584894 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-643 1580962 1583832 1583968 "MINT" 1584162 T MINT (NIL) -8 NIL NIL) (-642 1579774 1580017 1580294 "MHROWRED" 1580717 NIL MHROWRED (NIL T) -7 NIL NIL) (-641 1575045 1578219 1578643 "MFLOAT" 1579370 T MFLOAT (NIL) -8 NIL NIL) (-640 1574402 1574478 1574649 "MFINFACT" 1574957 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-639 1570717 1571565 1572449 "MESH" 1573538 T MESH (NIL) -7 NIL NIL) (-638 1569079 1569391 1569744 "MDDFACT" 1570404 NIL MDDFACT (NIL T) -7 NIL NIL) (-637 1565922 1568239 1568280 "MDAGG" 1568535 NIL MDAGG (NIL T) -9 NIL 1568678) (-636 1555620 1565215 1565422 "MCMPLX" 1565735 T MCMPLX (NIL) -8 NIL NIL) (-635 1554761 1554907 1555107 "MCDEN" 1555469 NIL MCDEN (NIL T T) -7 NIL NIL) (-634 1552651 1552921 1553301 "MCALCFN" 1554491 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-633 1550273 1550796 1551357 "MATSTOR" 1552122 NIL MATSTOR (NIL T) -7 NIL NIL) (-632 1546282 1549648 1549895 "MATRIX" 1550058 NIL MATRIX (NIL T) -8 NIL NIL) (-631 1542051 1542755 1543491 "MATLIN" 1545639 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-630 1532249 1535387 1535463 "MATCAT" 1540301 NIL MATCAT (NIL T T T) -9 NIL 1541718) (-629 1528614 1529627 1530982 "MATCAT-" 1530987 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-628 1527216 1527369 1527700 "MATCAT2" 1528449 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-627 1525328 1525652 1526036 "MAPPKG3" 1526891 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-626 1524309 1524482 1524704 "MAPPKG2" 1525152 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-625 1522808 1523092 1523419 "MAPPKG1" 1524015 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-624 1522419 1522477 1522600 "MAPHACK3" 1522744 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-623 1522011 1522072 1522186 "MAPHACK2" 1522351 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-622 1521449 1521552 1521694 "MAPHACK1" 1521902 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-621 1519557 1520151 1520454 "MAGMA" 1521178 NIL MAGMA (NIL T) -8 NIL NIL) (-620 1516031 1517801 1518261 "M3D" 1519130 NIL M3D (NIL T) -8 NIL NIL) (-619 1510187 1514402 1514443 "LZSTAGG" 1515225 NIL LZSTAGG (NIL T) -9 NIL 1515520) (-618 1506160 1507318 1508775 "LZSTAGG-" 1508780 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-617 1503276 1504053 1504539 "LWORD" 1505706 NIL LWORD (NIL T) -8 NIL NIL) (-616 1496436 1503047 1503181 "LSQM" 1503186 NIL LSQM (NIL NIL T) -8 NIL NIL) (-615 1495660 1495799 1496027 "LSPP" 1496291 NIL LSPP (NIL T T T T) -7 NIL NIL) (-614 1493472 1493773 1494229 "LSMP" 1495349 NIL LSMP (NIL T T T T) -7 NIL NIL) (-613 1490251 1490925 1491655 "LSMP1" 1492774 NIL LSMP1 (NIL T) -7 NIL NIL) (-612 1484178 1489420 1489461 "LSAGG" 1489523 NIL LSAGG (NIL T) -9 NIL 1489601) (-611 1480873 1481797 1483010 "LSAGG-" 1483015 NIL LSAGG- (NIL T T) -8 NIL NIL) (-610 1478499 1480017 1480266 "LPOLY" 1480668 NIL LPOLY (NIL T T) -8 NIL NIL) (-609 1478081 1478166 1478289 "LPEFRAC" 1478408 NIL LPEFRAC (NIL T) -7 NIL NIL) (-608 1476428 1477175 1477428 "LO" 1477913 NIL LO (NIL T T T) -8 NIL NIL) (-607 1476082 1476194 1476222 "LOGIC" 1476333 T LOGIC (NIL) -9 NIL 1476413) (-606 1475944 1475967 1476038 "LOGIC-" 1476043 NIL LOGIC- (NIL T) -8 NIL NIL) (-605 1475137 1475277 1475470 "LODOOPS" 1475800 NIL LODOOPS (NIL T T) -7 NIL NIL) (-604 1472555 1475054 1475119 "LODO" 1475124 NIL LODO (NIL T NIL) -8 NIL NIL) (-603 1471101 1471336 1471687 "LODOF" 1472302 NIL LODOF (NIL T T) -7 NIL NIL) (-602 1467521 1469957 1469997 "LODOCAT" 1470429 NIL LODOCAT (NIL T) -9 NIL 1470640) (-601 1467255 1467313 1467439 "LODOCAT-" 1467444 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-600 1464569 1467096 1467214 "LODO2" 1467219 NIL LODO2 (NIL T T) -8 NIL NIL) (-599 1461998 1464506 1464551 "LODO1" 1464556 NIL LODO1 (NIL T) -8 NIL NIL) (-598 1460861 1461026 1461337 "LODEEF" 1461821 NIL LODEEF (NIL T T T) -7 NIL NIL) (-597 1456148 1458992 1459033 "LNAGG" 1459980 NIL LNAGG (NIL T) -9 NIL 1460424) (-596 1455295 1455509 1455851 "LNAGG-" 1455856 NIL LNAGG- (NIL T T) -8 NIL NIL) (-595 1451460 1452222 1452860 "LMOPS" 1454711 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-594 1450858 1451220 1451260 "LMODULE" 1451320 NIL LMODULE (NIL T) -9 NIL 1451362) (-593 1448104 1450503 1450626 "LMDICT" 1450768 NIL LMDICT (NIL T) -8 NIL NIL) (-592 1441331 1447050 1447348 "LIST" 1447839 NIL LIST (NIL T) -8 NIL NIL) (-591 1440856 1440930 1441069 "LIST3" 1441251 NIL LIST3 (NIL T T T) -7 NIL NIL) (-590 1439863 1440041 1440269 "LIST2" 1440674 NIL LIST2 (NIL T T) -7 NIL NIL) (-589 1437997 1438309 1438708 "LIST2MAP" 1439510 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-588 1436710 1437390 1437430 "LINEXP" 1437683 NIL LINEXP (NIL T) -9 NIL 1437831) (-587 1435357 1435617 1435914 "LINDEP" 1436462 NIL LINDEP (NIL T T) -7 NIL NIL) (-586 1432054 1432773 1433550 "LIMITRF" 1434612 NIL LIMITRF (NIL T) -7 NIL NIL) (-585 1430334 1430629 1431044 "LIMITPS" 1431749 NIL LIMITPS (NIL T T) -7 NIL NIL) (-584 1424789 1429845 1430073 "LIE" 1430155 NIL LIE (NIL T T) -8 NIL NIL) (-583 1423840 1424283 1424323 "LIECAT" 1424463 NIL LIECAT (NIL T) -9 NIL 1424614) (-582 1423681 1423708 1423796 "LIECAT-" 1423801 NIL LIECAT- (NIL T T) -8 NIL NIL) (-581 1416293 1423130 1423295 "LIB" 1423536 T LIB (NIL) -8 NIL NIL) (-580 1411930 1412811 1413746 "LGROBP" 1415410 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-579 1409796 1410070 1410432 "LF" 1411651 NIL LF (NIL T T) -7 NIL NIL) (-578 1408636 1409328 1409356 "LFCAT" 1409563 T LFCAT (NIL) -9 NIL 1409702) (-577 1405548 1406174 1406860 "LEXTRIPK" 1408002 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-576 1402254 1403118 1403621 "LEXP" 1405128 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-575 1400652 1400965 1401366 "LEADCDET" 1401936 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-574 1399848 1399922 1400149 "LAZM3PK" 1400573 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-573 1394765 1397927 1398464 "LAUPOL" 1399361 NIL LAUPOL (NIL T T) -8 NIL NIL) (-572 1394332 1394376 1394543 "LAPLACE" 1394715 NIL LAPLACE (NIL T T) -7 NIL NIL) (-571 1392260 1393433 1393684 "LA" 1394165 NIL LA (NIL T T T) -8 NIL NIL) (-570 1391323 1391917 1391957 "LALG" 1392018 NIL LALG (NIL T) -9 NIL 1392076) (-569 1391038 1391097 1391232 "LALG-" 1391237 NIL LALG- (NIL T T) -8 NIL NIL) (-568 1389948 1390135 1390432 "KOVACIC" 1390838 NIL KOVACIC (NIL T T) -7 NIL NIL) (-567 1389783 1389807 1389848 "KONVERT" 1389910 NIL KONVERT (NIL T) -9 NIL NIL) (-566 1389618 1389642 1389683 "KOERCE" 1389745 NIL KOERCE (NIL T) -9 NIL NIL) (-565 1387352 1388112 1388505 "KERNEL" 1389257 NIL KERNEL (NIL T) -8 NIL NIL) (-564 1386854 1386935 1387065 "KERNEL2" 1387266 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-563 1380706 1385394 1385448 "KDAGG" 1385825 NIL KDAGG (NIL T T) -9 NIL 1386031) (-562 1380235 1380359 1380564 "KDAGG-" 1380569 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-561 1373410 1379896 1380051 "KAFILE" 1380113 NIL KAFILE (NIL T) -8 NIL NIL) (-560 1367865 1372921 1373149 "JORDAN" 1373231 NIL JORDAN (NIL T T) -8 NIL NIL) (-559 1367594 1367653 1367740 "JAVACODE" 1367798 T JAVACODE (NIL) -8 NIL NIL) (-558 1363894 1365800 1365854 "IXAGG" 1366783 NIL IXAGG (NIL T T) -9 NIL 1367242) (-557 1362813 1363119 1363538 "IXAGG-" 1363543 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-556 1358398 1362735 1362794 "IVECTOR" 1362799 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-555 1357164 1357401 1357667 "ITUPLE" 1358165 NIL ITUPLE (NIL T) -8 NIL NIL) (-554 1355600 1355777 1356083 "ITRIGMNP" 1356986 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-553 1354345 1354549 1354832 "ITFUN3" 1355376 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-552 1353977 1354034 1354143 "ITFUN2" 1354282 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-551 1351779 1352850 1353147 "ITAYLOR" 1353712 NIL ITAYLOR (NIL T) -8 NIL NIL) (-550 1340756 1345954 1347113 "ISUPS" 1350652 NIL ISUPS (NIL T) -8 NIL NIL) (-549 1339860 1340000 1340236 "ISUMP" 1340603 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-548 1335120 1339657 1339736 "ISTRING" 1339813 NIL ISTRING (NIL NIL) -8 NIL NIL) (-547 1334333 1334414 1334629 "IRURPK" 1335034 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-546 1333269 1333470 1333710 "IRSN" 1334113 T IRSN (NIL) -7 NIL NIL) (-545 1331304 1331659 1332094 "IRRF2F" 1332907 NIL IRRF2F (NIL T) -7 NIL NIL) (-544 1331051 1331089 1331165 "IRREDFFX" 1331260 NIL IRREDFFX (NIL T) -7 NIL NIL) (-543 1329666 1329925 1330224 "IROOT" 1330784 NIL IROOT (NIL T) -7 NIL NIL) (-542 1326294 1327345 1328035 "IR" 1329008 NIL IR (NIL T) -8 NIL NIL) (-541 1323907 1324402 1324968 "IR2" 1325772 NIL IR2 (NIL T T) -7 NIL NIL) (-540 1322983 1323096 1323316 "IR2F" 1323790 NIL IR2F (NIL T T) -7 NIL NIL) (-539 1322774 1322808 1322868 "IPRNTPK" 1322943 T IPRNTPK (NIL) -7 NIL NIL) (-538 1319328 1322663 1322732 "IPF" 1322737 NIL IPF (NIL NIL) -8 NIL NIL) (-537 1317645 1319253 1319310 "IPADIC" 1319315 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-536 1317144 1317202 1317391 "INVLAPLA" 1317581 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-535 1306730 1309083 1311469 "INTTR" 1314808 NIL INTTR (NIL T T) -7 NIL NIL) (-534 1303073 1303814 1304677 "INTTOOLS" 1305916 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-533 1302659 1302750 1302867 "INTSLPE" 1302976 T INTSLPE (NIL) -7 NIL NIL) (-532 1300609 1302582 1302641 "INTRVL" 1302646 NIL INTRVL (NIL T) -8 NIL NIL) (-531 1298174 1298686 1299260 "INTRF" 1300094 NIL INTRF (NIL T) -7 NIL NIL) (-530 1297581 1297678 1297819 "INTRET" 1298072 NIL INTRET (NIL T) -7 NIL NIL) (-529 1295562 1295951 1296420 "INTRAT" 1297189 NIL INTRAT (NIL T T) -7 NIL NIL) (-528 1292795 1293378 1294003 "INTPM" 1295047 NIL INTPM (NIL T T) -7 NIL NIL) (-527 1289504 1290103 1290847 "INTPAF" 1292181 NIL INTPAF (NIL T T T) -7 NIL NIL) (-526 1284747 1285693 1286728 "INTPACK" 1288489 T INTPACK (NIL) -7 NIL NIL) (-525 1281601 1284476 1284603 "INT" 1284640 T INT (NIL) -8 NIL NIL) (-524 1280853 1281005 1281213 "INTHERTR" 1281443 NIL INTHERTR (NIL T T) -7 NIL NIL) (-523 1280292 1280372 1280560 "INTHERAL" 1280767 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-522 1278138 1278581 1279038 "INTHEORY" 1279855 T INTHEORY (NIL) -7 NIL NIL) (-521 1269460 1271081 1272859 "INTG0" 1276490 NIL INTG0 (NIL T T T) -7 NIL NIL) (-520 1250033 1254823 1259633 "INTFTBL" 1264670 T INTFTBL (NIL) -8 NIL NIL) (-519 1249282 1249420 1249593 "INTFACT" 1249892 NIL INTFACT (NIL T) -7 NIL NIL) (-518 1246673 1247119 1247682 "INTEF" 1248836 NIL INTEF (NIL T T) -7 NIL NIL) (-517 1245135 1245884 1245912 "INTDOM" 1246213 T INTDOM (NIL) -9 NIL 1246420) (-516 1244504 1244678 1244920 "INTDOM-" 1244925 NIL INTDOM- (NIL T) -8 NIL NIL) (-515 1240997 1242929 1242983 "INTCAT" 1243782 NIL INTCAT (NIL T) -9 NIL 1244101) (-514 1240470 1240572 1240700 "INTBIT" 1240889 T INTBIT (NIL) -7 NIL NIL) (-513 1239145 1239299 1239612 "INTALG" 1240315 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-512 1238602 1238692 1238862 "INTAF" 1239049 NIL INTAF (NIL T T) -7 NIL NIL) (-511 1232056 1238412 1238552 "INTABL" 1238557 NIL INTABL (NIL T T T) -8 NIL NIL) (-510 1227007 1229736 1229764 "INS" 1230732 T INS (NIL) -9 NIL 1231413) (-509 1224247 1225018 1225992 "INS-" 1226065 NIL INS- (NIL T) -8 NIL NIL) (-508 1223026 1223253 1223550 "INPSIGN" 1224000 NIL INPSIGN (NIL T T) -7 NIL NIL) (-507 1222140 1222257 1222454 "INPRODPF" 1222906 NIL INPRODPF (NIL T T) -7 NIL NIL) (-506 1221030 1221147 1221384 "INPRODFF" 1222020 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-505 1220030 1220182 1220442 "INNMFACT" 1220866 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-504 1219227 1219324 1219512 "INMODGCD" 1219929 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-503 1217736 1217980 1218304 "INFSP" 1218972 NIL INFSP (NIL T T T) -7 NIL NIL) (-502 1216920 1217037 1217220 "INFPROD0" 1217616 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-501 1213931 1215089 1215580 "INFORM" 1216437 T INFORM (NIL) -8 NIL NIL) (-500 1213541 1213601 1213699 "INFORM1" 1213866 NIL INFORM1 (NIL T) -7 NIL NIL) (-499 1213064 1213153 1213267 "INFINITY" 1213447 T INFINITY (NIL) -7 NIL NIL) (-498 1211681 1211930 1212251 "INEP" 1212812 NIL INEP (NIL T T T) -7 NIL NIL) (-497 1210957 1211578 1211643 "INDE" 1211648 NIL INDE (NIL T) -8 NIL NIL) (-496 1210521 1210589 1210706 "INCRMAPS" 1210884 NIL INCRMAPS (NIL T) -7 NIL NIL) (-495 1205832 1206757 1207701 "INBFF" 1209609 NIL INBFF (NIL T) -7 NIL NIL) (-494 1202327 1205677 1205780 "IMATRIX" 1205785 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-493 1201039 1201162 1201477 "IMATQF" 1202183 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-492 1199259 1199486 1199823 "IMATLIN" 1200795 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-491 1193885 1199183 1199241 "ILIST" 1199246 NIL ILIST (NIL T NIL) -8 NIL NIL) (-490 1191838 1193745 1193858 "IIARRAY2" 1193863 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-489 1187206 1191749 1191813 "IFF" 1191818 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-488 1182245 1186494 1186682 "IFARRAY" 1187063 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-487 1181452 1182149 1182222 "IFAMON" 1182227 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-486 1181036 1181101 1181155 "IEVALAB" 1181362 NIL IEVALAB (NIL T T) -9 NIL NIL) (-485 1180711 1180779 1180939 "IEVALAB-" 1180944 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-484 1180369 1180625 1180688 "IDPO" 1180693 NIL IDPO (NIL T T) -8 NIL NIL) (-483 1179646 1180258 1180333 "IDPOAMS" 1180338 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-482 1178980 1179535 1179610 "IDPOAM" 1179615 NIL IDPOAM (NIL T T) -8 NIL NIL) (-481 1178066 1178316 1178369 "IDPC" 1178782 NIL IDPC (NIL T T) -9 NIL 1178931) (-480 1177562 1177958 1178031 "IDPAM" 1178036 NIL IDPAM (NIL T T) -8 NIL NIL) (-479 1176965 1177454 1177527 "IDPAG" 1177532 NIL IDPAG (NIL T T) -8 NIL NIL) (-478 1173220 1174068 1174963 "IDECOMP" 1176122 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-477 1166093 1167143 1168190 "IDEAL" 1172256 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-476 1165257 1165369 1165568 "ICDEN" 1165977 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-475 1164356 1164737 1164884 "ICARD" 1165130 T ICARD (NIL) -8 NIL NIL) (-474 1162428 1162741 1163144 "IBPTOOLS" 1164033 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-473 1158042 1162048 1162161 "IBITS" 1162347 NIL IBITS (NIL NIL) -8 NIL NIL) (-472 1154765 1155341 1156036 "IBATOOL" 1157459 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-471 1152545 1153006 1153539 "IBACHIN" 1154300 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-470 1150422 1152391 1152494 "IARRAY2" 1152499 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-469 1146575 1150348 1150405 "IARRAY1" 1150410 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-468 1140513 1144993 1145471 "IAN" 1146117 T IAN (NIL) -8 NIL NIL) (-467 1140024 1140081 1140254 "IALGFACT" 1140450 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-466 1139552 1139665 1139693 "HYPCAT" 1139900 T HYPCAT (NIL) -9 NIL NIL) (-465 1139090 1139207 1139393 "HYPCAT-" 1139398 NIL HYPCAT- (NIL T) -8 NIL NIL) (-464 1135770 1137101 1137142 "HOAGG" 1138123 NIL HOAGG (NIL T) -9 NIL 1138802) (-463 1134364 1134763 1135289 "HOAGG-" 1135294 NIL HOAGG- (NIL T T) -8 NIL NIL) (-462 1128194 1133805 1133971 "HEXADEC" 1134218 T HEXADEC (NIL) -8 NIL NIL) (-461 1126938 1127160 1127423 "HEUGCD" 1127971 NIL HEUGCD (NIL T) -7 NIL NIL) (-460 1126041 1126775 1126905 "HELLFDIV" 1126910 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-459 1124269 1125818 1125906 "HEAP" 1125985 NIL HEAP (NIL T) -8 NIL NIL) (-458 1118136 1124184 1124246 "HDP" 1124251 NIL HDP (NIL NIL T) -8 NIL NIL) (-457 1111848 1117773 1117924 "HDMP" 1118037 NIL HDMP (NIL NIL T) -8 NIL NIL) (-456 1111173 1111312 1111476 "HB" 1111704 T HB (NIL) -7 NIL NIL) (-455 1104670 1111019 1111123 "HASHTBL" 1111128 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-454 1102423 1104298 1104477 "HACKPI" 1104511 T HACKPI (NIL) -8 NIL NIL) (-453 1098119 1102277 1102389 "GTSET" 1102394 NIL GTSET (NIL T T T T) -8 NIL NIL) (-452 1091645 1097997 1098095 "GSTBL" 1098100 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-451 1083878 1090681 1090945 "GSERIES" 1091436 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-450 1082901 1083354 1083382 "GROUP" 1083643 T GROUP (NIL) -9 NIL 1083802) (-449 1082017 1082240 1082584 "GROUP-" 1082589 NIL GROUP- (NIL T) -8 NIL NIL) (-448 1080386 1080705 1081092 "GROEBSOL" 1081694 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-447 1079327 1079589 1079640 "GRMOD" 1080169 NIL GRMOD (NIL T T) -9 NIL 1080337) (-446 1079095 1079131 1079259 "GRMOD-" 1079264 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-445 1074421 1075449 1076449 "GRIMAGE" 1078115 T GRIMAGE (NIL) -8 NIL NIL) (-444 1072888 1073148 1073472 "GRDEF" 1074117 T GRDEF (NIL) -7 NIL NIL) (-443 1072332 1072448 1072589 "GRAY" 1072767 T GRAY (NIL) -7 NIL NIL) (-442 1071566 1071946 1071997 "GRALG" 1072150 NIL GRALG (NIL T T) -9 NIL 1072242) (-441 1071227 1071300 1071463 "GRALG-" 1071468 NIL GRALG- (NIL T T T) -8 NIL NIL) (-440 1068035 1070816 1070992 "GPOLSET" 1071134 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-439 1067391 1067448 1067705 "GOSPER" 1067972 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-438 1063150 1063829 1064355 "GMODPOL" 1067090 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-437 1062155 1062339 1062577 "GHENSEL" 1062962 NIL GHENSEL (NIL T T) -7 NIL NIL) (-436 1056221 1057064 1058090 "GENUPS" 1061239 NIL GENUPS (NIL T T) -7 NIL NIL) (-435 1055918 1055969 1056058 "GENUFACT" 1056164 NIL GENUFACT (NIL T) -7 NIL NIL) (-434 1055330 1055407 1055572 "GENPGCD" 1055836 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-433 1054804 1054839 1055052 "GENMFACT" 1055289 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-432 1053372 1053627 1053934 "GENEEZ" 1054547 NIL GENEEZ (NIL T T) -7 NIL NIL) (-431 1047246 1052985 1053146 "GDMP" 1053295 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-430 1036613 1041007 1042113 "GCNAALG" 1046229 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-429 1035035 1035907 1035935 "GCDDOM" 1036190 T GCDDOM (NIL) -9 NIL 1036347) (-428 1034505 1034632 1034847 "GCDDOM-" 1034852 NIL GCDDOM- (NIL T) -8 NIL NIL) (-427 1033177 1033362 1033666 "GB" 1034284 NIL GB (NIL T T T T) -7 NIL NIL) (-426 1021797 1024123 1026515 "GBINTERN" 1030868 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-425 1019634 1019926 1020347 "GBF" 1021472 NIL GBF (NIL T T T T) -7 NIL NIL) (-424 1018415 1018580 1018847 "GBEUCLID" 1019450 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-423 1017764 1017889 1018038 "GAUSSFAC" 1018286 T GAUSSFAC (NIL) -7 NIL NIL) (-422 1016141 1016443 1016756 "GALUTIL" 1017483 NIL GALUTIL (NIL T) -7 NIL NIL) (-421 1014458 1014732 1015055 "GALPOLYU" 1015868 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-420 1011847 1012137 1012542 "GALFACTU" 1014155 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-419 1003653 1005152 1006760 "GALFACT" 1010279 NIL GALFACT (NIL T) -7 NIL NIL) (-418 1001041 1001699 1001727 "FVFUN" 1002883 T FVFUN (NIL) -9 NIL 1003603) (-417 1000307 1000489 1000517 "FVC" 1000808 T FVC (NIL) -9 NIL 1000991) (-416 999944 1000099 1000180 "FUNCTION" 1000259 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-415 997614 998165 998654 "FT" 999475 T FT (NIL) -8 NIL NIL) (-414 996432 996915 997118 "FTEM" 997431 T FTEM (NIL) -8 NIL NIL) (-413 994697 994985 995387 "FSUPFACT" 996124 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-412 993094 993383 993715 "FST" 994385 T FST (NIL) -8 NIL NIL) (-411 992269 992375 992569 "FSRED" 992976 NIL FSRED (NIL T T) -7 NIL NIL) (-410 990948 991203 991557 "FSPRMELT" 991984 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-409 988033 988471 988970 "FSPECF" 990511 NIL FSPECF (NIL T T) -7 NIL NIL) (-408 970407 978964 979004 "FS" 982842 NIL FS (NIL T) -9 NIL 985124) (-407 959057 962047 966103 "FS-" 966400 NIL FS- (NIL T T) -8 NIL NIL) (-406 958573 958627 958803 "FSINT" 958998 NIL FSINT (NIL T T) -7 NIL NIL) (-405 956854 957566 957869 "FSERIES" 958352 NIL FSERIES (NIL T T) -8 NIL NIL) (-404 955872 955988 956218 "FSCINT" 956734 NIL FSCINT (NIL T T) -7 NIL NIL) (-403 952107 954817 954858 "FSAGG" 955228 NIL FSAGG (NIL T) -9 NIL 955487) (-402 949869 950470 951266 "FSAGG-" 951361 NIL FSAGG- (NIL T T) -8 NIL NIL) (-401 948911 949054 949281 "FSAGG2" 949722 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-400 946570 946849 947402 "FS2UPS" 948629 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-399 946156 946199 946352 "FS2" 946521 NIL FS2 (NIL T T T T) -7 NIL NIL) (-398 945016 945187 945495 "FS2EXPXP" 945981 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-397 944442 944557 944709 "FRUTIL" 944896 NIL FRUTIL (NIL T) -7 NIL NIL) (-396 935862 939941 941297 "FR" 943118 NIL FR (NIL T) -8 NIL NIL) (-395 930939 933582 933622 "FRNAALG" 935018 NIL FRNAALG (NIL T) -9 NIL 935625) (-394 926617 927688 928963 "FRNAALG-" 929713 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-393 926255 926298 926425 "FRNAAF2" 926568 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-392 924604 925096 925390 "FRMOD" 926068 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-391 922326 922995 923311 "FRIDEAL" 924395 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-390 921525 921612 921899 "FRIDEAL2" 922233 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-389 920783 921191 921232 "FRETRCT" 921237 NIL FRETRCT (NIL T) -9 NIL 921408) (-388 919895 920126 920477 "FRETRCT-" 920482 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-387 917105 918325 918384 "FRAMALG" 919266 NIL FRAMALG (NIL T T) -9 NIL 919558) (-386 915238 915694 916324 "FRAMALG-" 916547 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-385 909140 914713 914989 "FRAC" 914994 NIL FRAC (NIL T) -8 NIL NIL) (-384 908776 908833 908940 "FRAC2" 909077 NIL FRAC2 (NIL T T) -7 NIL NIL) (-383 908412 908469 908576 "FR2" 908713 NIL FR2 (NIL T T) -7 NIL NIL) (-382 903086 905999 906027 "FPS" 907146 T FPS (NIL) -9 NIL 907702) (-381 902535 902644 902808 "FPS-" 902954 NIL FPS- (NIL T) -8 NIL NIL) (-380 899984 901681 901709 "FPC" 901934 T FPC (NIL) -9 NIL 902076) (-379 899777 899817 899914 "FPC-" 899919 NIL FPC- (NIL T) -8 NIL NIL) (-378 898656 899266 899307 "FPATMAB" 899312 NIL FPATMAB (NIL T) -9 NIL 899464) (-377 896356 896832 897258 "FPARFRAC" 898293 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-376 891749 892248 892930 "FORTRAN" 895788 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-375 889421 889921 890460 "FORT" 891230 T FORT (NIL) -7 NIL NIL) (-374 887097 887659 887687 "FORTFN" 888747 T FORTFN (NIL) -9 NIL 889371) (-373 886861 886911 886939 "FORTCAT" 886998 T FORTCAT (NIL) -9 NIL 887060) (-372 884921 885404 885803 "FORMULA" 886482 T FORMULA (NIL) -8 NIL NIL) (-371 884709 884739 884808 "FORMULA1" 884885 NIL FORMULA1 (NIL T) -7 NIL NIL) (-370 884232 884284 884457 "FORDER" 884651 NIL FORDER (NIL T T T T) -7 NIL NIL) (-369 883328 883492 883685 "FOP" 884059 T FOP (NIL) -7 NIL NIL) (-368 881920 882592 882766 "FNLA" 883210 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-367 880589 880978 881006 "FNCAT" 881578 T FNCAT (NIL) -9 NIL 881871) (-366 880155 880548 880576 "FNAME" 880581 T FNAME (NIL) -8 NIL NIL) (-365 878815 879788 879816 "FMTC" 879821 T FMTC (NIL) -9 NIL 879856) (-364 875133 876340 876968 "FMONOID" 878220 NIL FMONOID (NIL T) -8 NIL NIL) (-363 874353 874876 875024 "FM" 875029 NIL FM (NIL T T) -8 NIL NIL) (-362 871777 872423 872451 "FMFUN" 873595 T FMFUN (NIL) -9 NIL 874303) (-361 871046 871227 871255 "FMC" 871545 T FMC (NIL) -9 NIL 871727) (-360 868276 869110 869163 "FMCAT" 870345 NIL FMCAT (NIL T T) -9 NIL 870839) (-359 867171 868044 868143 "FM1" 868221 NIL FM1 (NIL T T) -8 NIL NIL) (-358 864945 865361 865855 "FLOATRP" 866722 NIL FLOATRP (NIL T) -7 NIL NIL) (-357 858431 862601 863231 "FLOAT" 864335 T FLOAT (NIL) -8 NIL NIL) (-356 855869 856369 856947 "FLOATCP" 857898 NIL FLOATCP (NIL T) -7 NIL NIL) (-355 854658 855506 855546 "FLINEXP" 855551 NIL FLINEXP (NIL T) -9 NIL 855644) (-354 853813 854048 854375 "FLINEXP-" 854380 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-353 852889 853033 853257 "FLASORT" 853665 NIL FLASORT (NIL T T) -7 NIL NIL) (-352 850108 850950 851002 "FLALG" 852229 NIL FLALG (NIL T T) -9 NIL 852696) (-351 843893 847595 847636 "FLAGG" 848898 NIL FLAGG (NIL T) -9 NIL 849550) (-350 842619 842958 843448 "FLAGG-" 843453 NIL FLAGG- (NIL T T) -8 NIL NIL) (-349 841661 841804 842031 "FLAGG2" 842472 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-348 838634 839652 839711 "FINRALG" 840839 NIL FINRALG (NIL T T) -9 NIL 841347) (-347 837794 838023 838362 "FINRALG-" 838367 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-346 837201 837414 837442 "FINITE" 837638 T FINITE (NIL) -9 NIL 837745) (-345 829661 831822 831862 "FINAALG" 835529 NIL FINAALG (NIL T) -9 NIL 836982) (-344 825002 826043 827187 "FINAALG-" 828566 NIL FINAALG- (NIL T T) -8 NIL NIL) (-343 824397 824757 824860 "FILE" 824932 NIL FILE (NIL T) -8 NIL NIL) (-342 823082 823394 823448 "FILECAT" 824132 NIL FILECAT (NIL T T) -9 NIL 824348) (-341 820945 822501 822529 "FIELD" 822569 T FIELD (NIL) -9 NIL 822649) (-340 819565 819950 820461 "FIELD-" 820466 NIL FIELD- (NIL T) -8 NIL NIL) (-339 817380 818202 818548 "FGROUP" 819252 NIL FGROUP (NIL T) -8 NIL NIL) (-338 816470 816634 816854 "FGLMICPK" 817212 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-337 812272 816395 816452 "FFX" 816457 NIL FFX (NIL T NIL) -8 NIL NIL) (-336 811873 811934 812069 "FFSLPE" 812205 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-335 807866 808645 809441 "FFPOLY" 811109 NIL FFPOLY (NIL T) -7 NIL NIL) (-334 807370 807406 807615 "FFPOLY2" 807824 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-333 803191 807289 807352 "FFP" 807357 NIL FFP (NIL T NIL) -8 NIL NIL) (-332 798559 803102 803166 "FF" 803171 NIL FF (NIL NIL NIL) -8 NIL NIL) (-331 793655 797902 798092 "FFNBX" 798413 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-330 788512 792738 792996 "FFNBP" 793509 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-329 783115 787796 788007 "FFNB" 788345 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-328 781947 782145 782460 "FFINTBAS" 782912 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-327 778171 780411 780439 "FFIELDC" 781059 T FFIELDC (NIL) -9 NIL 781435) (-326 776834 777204 777701 "FFIELDC-" 777706 NIL FFIELDC- (NIL T) -8 NIL NIL) (-325 776404 776449 776573 "FFHOM" 776776 NIL FFHOM (NIL T T T) -7 NIL NIL) (-324 774102 774586 775103 "FFF" 775919 NIL FFF (NIL T) -7 NIL NIL) (-323 769690 773844 773945 "FFCGX" 774045 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-322 765292 769422 769529 "FFCGP" 769633 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-321 760445 765019 765127 "FFCG" 765228 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-320 742391 751514 751600 "FFCAT" 756765 NIL FFCAT (NIL T T T) -9 NIL 758252) (-319 737589 738636 739950 "FFCAT-" 741180 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-318 737000 737043 737278 "FFCAT2" 737540 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-317 726156 729946 731163 "FEXPR" 735855 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-316 725156 725591 725632 "FEVALAB" 725716 NIL FEVALAB (NIL T) -9 NIL 725977) (-315 724315 724525 724863 "FEVALAB-" 724868 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-314 722908 723698 723901 "FDIV" 724214 NIL FDIV (NIL T T T T) -8 NIL NIL) (-313 719975 720690 720805 "FDIVCAT" 722373 NIL FDIVCAT (NIL T T T T) -9 NIL 722810) (-312 719737 719764 719934 "FDIVCAT-" 719939 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-311 718957 719044 719321 "FDIV2" 719644 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-310 717643 717902 718191 "FCPAK1" 718688 T FCPAK1 (NIL) -7 NIL NIL) (-309 716771 717143 717284 "FCOMP" 717534 NIL FCOMP (NIL T) -8 NIL NIL) (-308 700406 703820 707381 "FC" 713230 T FC (NIL) -8 NIL NIL) (-307 693002 697048 697088 "FAXF" 698890 NIL FAXF (NIL T) -9 NIL 699581) (-306 690281 690936 691761 "FAXF-" 692226 NIL FAXF- (NIL T T) -8 NIL NIL) (-305 685381 689657 689833 "FARRAY" 690138 NIL FARRAY (NIL T) -8 NIL NIL) (-304 680772 682843 682895 "FAMR" 683907 NIL FAMR (NIL T T) -9 NIL 684367) (-303 679663 679965 680399 "FAMR-" 680404 NIL FAMR- (NIL T T T) -8 NIL NIL) (-302 678859 679585 679638 "FAMONOID" 679643 NIL FAMONOID (NIL T) -8 NIL NIL) (-301 676692 677376 677429 "FAMONC" 678370 NIL FAMONC (NIL T T) -9 NIL 678755) (-300 675384 676446 676583 "FAGROUP" 676588 NIL FAGROUP (NIL T) -8 NIL NIL) (-299 673187 673506 673908 "FACUTIL" 675065 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-298 672286 672471 672693 "FACTFUNC" 672997 NIL FACTFUNC (NIL T) -7 NIL NIL) (-297 664606 671537 671749 "EXPUPXS" 672142 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-296 662089 662629 663215 "EXPRTUBE" 664040 T EXPRTUBE (NIL) -7 NIL NIL) (-295 658283 658875 659612 "EXPRODE" 661428 NIL EXPRODE (NIL T T) -7 NIL NIL) (-294 643414 656914 657340 "EXPR" 657889 NIL EXPR (NIL T) -8 NIL NIL) (-293 637826 638413 639225 "EXPR2UPS" 642712 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-292 637462 637519 637626 "EXPR2" 637763 NIL EXPR2 (NIL T T) -7 NIL NIL) (-291 628816 636599 636894 "EXPEXPAN" 637300 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-290 628643 628773 628802 "EXIT" 628807 T EXIT (NIL) -8 NIL NIL) (-289 628270 628332 628445 "EVALCYC" 628575 NIL EVALCYC (NIL T) -7 NIL NIL) (-288 627811 627929 627970 "EVALAB" 628140 NIL EVALAB (NIL T) -9 NIL 628244) (-287 627292 627414 627635 "EVALAB-" 627640 NIL EVALAB- (NIL T T) -8 NIL NIL) (-286 624755 626067 626095 "EUCDOM" 626650 T EUCDOM (NIL) -9 NIL 627000) (-285 623160 623602 624192 "EUCDOM-" 624197 NIL EUCDOM- (NIL T) -8 NIL NIL) (-284 610738 613486 616226 "ESTOOLS" 620440 T ESTOOLS (NIL) -7 NIL NIL) (-283 610374 610431 610538 "ESTOOLS2" 610675 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-282 610125 610167 610247 "ESTOOLS1" 610326 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-281 604063 605787 605815 "ES" 608579 T ES (NIL) -9 NIL 609985) (-280 599010 600297 602114 "ES-" 602278 NIL ES- (NIL T) -8 NIL NIL) (-279 595385 596145 596925 "ESCONT" 598250 T ESCONT (NIL) -7 NIL NIL) (-278 595122 595154 595236 "ESCONT1" 595347 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-277 594797 594847 594947 "ES2" 595066 NIL ES2 (NIL T T) -7 NIL NIL) (-276 594427 594485 594594 "ES1" 594733 NIL ES1 (NIL T T) -7 NIL NIL) (-275 593643 593772 593948 "ERROR" 594271 T ERROR (NIL) -7 NIL NIL) (-274 587146 593502 593593 "EQTBL" 593598 NIL EQTBL (NIL T T) -8 NIL NIL) (-273 579583 582464 583911 "EQ" 585732 NIL -2558 (NIL T) -8 NIL NIL) (-272 579215 579272 579381 "EQ2" 579520 NIL EQ2 (NIL T T) -7 NIL NIL) (-271 574507 575553 576646 "EP" 578154 NIL EP (NIL T) -7 NIL NIL) (-270 573090 573390 573707 "ENV" 574210 T ENV (NIL) -8 NIL NIL) (-269 572250 572814 572842 "ENTIRER" 572847 T ENTIRER (NIL) -9 NIL 572892) (-268 568706 570205 570575 "EMR" 572049 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-267 567850 568035 568089 "ELTAGG" 568469 NIL ELTAGG (NIL T T) -9 NIL 568680) (-266 567569 567631 567772 "ELTAGG-" 567777 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-265 567358 567387 567441 "ELTAB" 567525 NIL ELTAB (NIL T T) -9 NIL NIL) (-264 566484 566630 566829 "ELFUTS" 567209 NIL ELFUTS (NIL T T) -7 NIL NIL) (-263 566226 566282 566310 "ELEMFUN" 566415 T ELEMFUN (NIL) -9 NIL NIL) (-262 566096 566117 566185 "ELEMFUN-" 566190 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-261 560988 564197 564238 "ELAGG" 565178 NIL ELAGG (NIL T) -9 NIL 565641) (-260 559273 559707 560370 "ELAGG-" 560375 NIL ELAGG- (NIL T T) -8 NIL NIL) (-259 557930 558210 558505 "ELABEXPR" 558998 T ELABEXPR (NIL) -8 NIL NIL) (-258 550787 552586 553413 "EFUPXS" 557206 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-257 544226 546027 546837 "EFULS" 550063 NIL EFULS (NIL T T T) -8 NIL NIL) (-256 541657 542015 542493 "EFSTRUC" 543858 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-255 530729 532294 533854 "EF" 540172 NIL EF (NIL T T) -7 NIL NIL) (-254 529830 530214 530363 "EAB" 530600 T EAB (NIL) -8 NIL NIL) (-253 529043 529789 529817 "E04UCFA" 529822 T E04UCFA (NIL) -8 NIL NIL) (-252 528256 529002 529030 "E04NAFA" 529035 T E04NAFA (NIL) -8 NIL NIL) (-251 527469 528215 528243 "E04MBFA" 528248 T E04MBFA (NIL) -8 NIL NIL) (-250 526682 527428 527456 "E04JAFA" 527461 T E04JAFA (NIL) -8 NIL NIL) (-249 525897 526641 526669 "E04GCFA" 526674 T E04GCFA (NIL) -8 NIL NIL) (-248 525112 525856 525884 "E04FDFA" 525889 T E04FDFA (NIL) -8 NIL NIL) (-247 524325 525071 525099 "E04DGFA" 525104 T E04DGFA (NIL) -8 NIL NIL) (-246 518510 519855 521217 "E04AGNT" 522983 T E04AGNT (NIL) -7 NIL NIL) (-245 517237 517717 517757 "DVARCAT" 518232 NIL DVARCAT (NIL T) -9 NIL 518430) (-244 516441 516653 516967 "DVARCAT-" 516972 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-243 509303 516243 516370 "DSMP" 516375 NIL DSMP (NIL T T T) -8 NIL NIL) (-242 504113 505248 506316 "DROPT" 508255 T DROPT (NIL) -8 NIL NIL) (-241 503778 503837 503935 "DROPT1" 504048 NIL DROPT1 (NIL T) -7 NIL NIL) (-240 498893 500019 501156 "DROPT0" 502661 T DROPT0 (NIL) -7 NIL NIL) (-239 497238 497563 497949 "DRAWPT" 498527 T DRAWPT (NIL) -7 NIL NIL) (-238 491825 492748 493827 "DRAW" 496212 NIL DRAW (NIL T) -7 NIL NIL) (-237 491458 491511 491629 "DRAWHACK" 491766 NIL DRAWHACK (NIL T) -7 NIL NIL) (-236 490189 490458 490749 "DRAWCX" 491187 T DRAWCX (NIL) -7 NIL NIL) (-235 489707 489775 489925 "DRAWCURV" 490115 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-234 480178 482137 484252 "DRAWCFUN" 487612 T DRAWCFUN (NIL) -7 NIL NIL) (-233 476992 478874 478915 "DQAGG" 479544 NIL DQAGG (NIL T) -9 NIL 479817) (-232 465499 472237 472319 "DPOLCAT" 474157 NIL DPOLCAT (NIL T T T T) -9 NIL 474701) (-231 460339 461685 463642 "DPOLCAT-" 463647 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-230 453135 460201 460298 "DPMO" 460303 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-229 445834 452916 453082 "DPMM" 453087 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-228 445254 445457 445571 "DOMAIN" 445740 T DOMAIN (NIL) -8 NIL NIL) (-227 438966 444891 445042 "DMP" 445155 NIL DMP (NIL NIL T) -8 NIL NIL) (-226 438566 438622 438766 "DLP" 438904 NIL DLP (NIL T) -7 NIL NIL) (-225 432210 437667 437894 "DLIST" 438371 NIL DLIST (NIL T) -8 NIL NIL) (-224 429057 431066 431107 "DLAGG" 431657 NIL DLAGG (NIL T) -9 NIL 431886) (-223 427767 428459 428487 "DIVRING" 428637 T DIVRING (NIL) -9 NIL 428745) (-222 426755 427008 427401 "DIVRING-" 427406 NIL DIVRING- (NIL T) -8 NIL NIL) (-221 424857 425214 425620 "DISPLAY" 426369 T DISPLAY (NIL) -7 NIL NIL) (-220 418746 424771 424834 "DIRPROD" 424839 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-219 417594 417797 418062 "DIRPROD2" 418539 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-218 407113 413118 413171 "DIRPCAT" 413579 NIL DIRPCAT (NIL NIL T) -9 NIL 414418) (-217 404431 405073 405954 "DIRPCAT-" 406299 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-216 403718 403878 404064 "DIOSP" 404265 T DIOSP (NIL) -7 NIL NIL) (-215 400421 402631 402672 "DIOPS" 403106 NIL DIOPS (NIL T) -9 NIL 403335) (-214 399970 400084 400275 "DIOPS-" 400280 NIL DIOPS- (NIL T T) -8 NIL NIL) (-213 398842 399480 399508 "DIFRING" 399695 T DIFRING (NIL) -9 NIL 399804) (-212 398488 398565 398717 "DIFRING-" 398722 NIL DIFRING- (NIL T) -8 NIL NIL) (-211 396278 397560 397600 "DIFEXT" 397959 NIL DIFEXT (NIL T) -9 NIL 398252) (-210 394564 394992 395657 "DIFEXT-" 395662 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-209 391887 394097 394138 "DIAGG" 394143 NIL DIAGG (NIL T) -9 NIL 394163) (-208 391271 391428 391680 "DIAGG-" 391685 NIL DIAGG- (NIL T T) -8 NIL NIL) (-207 386736 390230 390507 "DHMATRIX" 391040 NIL DHMATRIX (NIL T) -8 NIL NIL) (-206 382348 383257 384267 "DFSFUN" 385746 T DFSFUN (NIL) -7 NIL NIL) (-205 377134 381062 381427 "DFLOAT" 382003 T DFLOAT (NIL) -8 NIL NIL) (-204 375367 375648 376043 "DFINTTLS" 376842 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-203 372400 373402 373800 "DERHAM" 375034 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-202 370249 372175 372264 "DEQUEUE" 372344 NIL DEQUEUE (NIL T) -8 NIL NIL) (-201 369467 369600 369795 "DEGRED" 370111 NIL DEGRED (NIL T T) -7 NIL NIL) (-200 365867 366612 367464 "DEFINTRF" 368695 NIL DEFINTRF (NIL T) -7 NIL NIL) (-199 363398 363867 364465 "DEFINTEF" 365386 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-198 357228 362839 363005 "DECIMAL" 363252 T DECIMAL (NIL) -8 NIL NIL) (-197 354740 355198 355704 "DDFACT" 356772 NIL DDFACT (NIL T T) -7 NIL NIL) (-196 354336 354379 354530 "DBLRESP" 354691 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-195 352011 352345 352714 "DBASE" 354094 NIL DBASE (NIL T) -8 NIL NIL) (-194 351146 351970 351998 "D03FAFA" 352003 T D03FAFA (NIL) -8 NIL NIL) (-193 350282 351105 351133 "D03EEFA" 351138 T D03EEFA (NIL) -8 NIL NIL) (-192 348232 348698 349187 "D03AGNT" 349813 T D03AGNT (NIL) -7 NIL NIL) (-191 347550 348191 348219 "D02EJFA" 348224 T D02EJFA (NIL) -8 NIL NIL) (-190 346868 347509 347537 "D02CJFA" 347542 T D02CJFA (NIL) -8 NIL NIL) (-189 346186 346827 346855 "D02BHFA" 346860 T D02BHFA (NIL) -8 NIL NIL) (-188 345504 346145 346173 "D02BBFA" 346178 T D02BBFA (NIL) -8 NIL NIL) (-187 338702 340290 341896 "D02AGNT" 343918 T D02AGNT (NIL) -7 NIL NIL) (-186 336471 336993 337539 "D01WGTS" 338176 T D01WGTS (NIL) -7 NIL NIL) (-185 335574 336430 336458 "D01TRNS" 336463 T D01TRNS (NIL) -8 NIL NIL) (-184 334677 335533 335561 "D01GBFA" 335566 T D01GBFA (NIL) -8 NIL NIL) (-183 333780 334636 334664 "D01FCFA" 334669 T D01FCFA (NIL) -8 NIL NIL) (-182 332883 333739 333767 "D01ASFA" 333772 T D01ASFA (NIL) -8 NIL NIL) (-181 331986 332842 332870 "D01AQFA" 332875 T D01AQFA (NIL) -8 NIL NIL) (-180 331089 331945 331973 "D01APFA" 331978 T D01APFA (NIL) -8 NIL NIL) (-179 330192 331048 331076 "D01ANFA" 331081 T D01ANFA (NIL) -8 NIL NIL) (-178 329295 330151 330179 "D01AMFA" 330184 T D01AMFA (NIL) -8 NIL NIL) (-177 328398 329254 329282 "D01ALFA" 329287 T D01ALFA (NIL) -8 NIL NIL) (-176 327501 328357 328385 "D01AKFA" 328390 T D01AKFA (NIL) -8 NIL NIL) (-175 326604 327460 327488 "D01AJFA" 327493 T D01AJFA (NIL) -8 NIL NIL) (-174 319908 321457 323016 "D01AGNT" 325065 T D01AGNT (NIL) -7 NIL NIL) (-173 319245 319373 319525 "CYCLOTOM" 319776 T CYCLOTOM (NIL) -7 NIL NIL) (-172 315980 316693 317420 "CYCLES" 318538 T CYCLES (NIL) -7 NIL NIL) (-171 315292 315426 315597 "CVMP" 315841 NIL CVMP (NIL T) -7 NIL NIL) (-170 313073 313331 313706 "CTRIGMNP" 315020 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-169 312584 312773 312872 "CTORCALL" 312994 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) 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*7 *3 *4)) (-4 *4 (-996 *5 *6 *7 *3))))) +(((*1 *1 *2) + (-12 + (-5 *2 + (-592 + (-2 + (|:| -3390 + (-2 (|:| |xinit| (-205)) (|:| |xend| (-205)) + (|:| |fn| (-1173 (-294 (-205)))) + (|:| |yinit| (-592 (-205))) (|:| |intvals| (-592 (-205))) + (|:| |g| (-294 (-205))) (|:| |abserr| (-205)) + (|:| |relerr| (-205)))) + (|:| -2348 + (-2 (|:| |stiffness| (-357)) (|:| |stability| (-357)) + (|:| |expense| (-357)) (|:| |accuracy| (-357)) + (|:| |intermediateResults| (-357))))))) + (-5 *1 (-745))))) (((*1 *1 *1 *2) (-12 (-4 *1 (-46 *2 *3)) (-4 *2 (-977)) (-4 *3 (-734)) (-4 *2 (-341)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-525)) (-5 *1 (-205)))) ((*1 *1 *1 *1) - (-3316 (-12 (-5 *1 (-273 *2)) (-4 *2 (-341)) (-4 *2 (-1127))) + (-3204 (-12 (-5 *1 (-273 *2)) (-4 *2 (-341)) (-4 *2 (-1127))) (-12 (-5 *1 (-273 *2)) (-4 *2 (-450)) (-4 *2 (-1127))))) ((*1 *1 *1 *1) (-4 *1 (-341))) ((*1 *1 *1 *2) (-12 (-5 *2 (-525)) (-5 *1 (-357)))) @@ -569,50 +748,67 @@ ((*1 *1 *1 *2) (-12 (-5 *1 (-1194 *2 *3)) (-4 *2 (-341)) (-4 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(-5 *1 (-1091))))) +(((*1 *2 *3) + (-12 (-5 *3 (-632 (-385 (-887 (-525))))) + (-5 *2 + (-592 + (-2 (|:| |radval| (-294 (-525))) (|:| |radmult| (-525)) + (|:| |radvect| (-592 (-632 (-294 (-525)))))))) + (-5 *1 (-962))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-385 *2)) (-5 *4 (-1 *2 *2)) (-4 *2 (-1149 *5)) + (-5 *1 (-670 *5 *2)) (-4 *5 (-341))))) +(((*1 *2 *3 *4 *4) + (-12 (-5 *4 (-1091)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-644 *3 *5 *6 *7)) + (-4 *3 (-567 (-501))) (-4 *5 (-1127)) (-4 *6 (-1127)) + (-4 *7 (-1127)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-1091)) (-5 *2 (-1 *6 *5)) (-5 *1 (-649 *3 *5 *6)) + (-4 *3 (-567 (-501))) (-4 *5 (-1127)) (-4 *6 (-1127))))) +(((*1 *2 *2) + (-12 (-5 *2 (-878 *3)) (-4 *3 (-13 (-341) (-1113) (-934))) + (-5 *1 (-163 *3))))) (((*1 *2 *1) - (-12 (-5 *2 (-592 (-2 (|:| |k| (-1091)) (|:| |c| (-1193 *3))))) - (-5 *1 (-1193 *3)) (-4 *3 (-977)))) + (-12 (-4 *1 (-1188 *3 *4)) (-4 *3 (-789)) (-4 *4 (-977)) + (-5 *2 (-108)))) ((*1 *2 *1) - (-12 (-5 *2 (-592 (-2 (|:| |k| *3) (|:| |c| (-1195 *3 *4))))) - (-5 *1 (-1195 *3 *4)) (-4 *3 (-789)) (-4 *4 (-977))))) -(((*1 *2 *3) (-12 (-5 *3 (-357)) (-5 *2 (-205)) (-5 *1 (-284))))) + (-12 (-5 *2 (-108)) (-5 *1 (-1194 *3 *4)) (-4 *3 (-977)) + (-4 *4 (-785))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-713)) (-5 *3 (-878 *4)) (-4 *1 (-1052 *4)) + (-4 *4 (-977)))) + ((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-713)) (-5 *4 (-878 (-205))) (-5 *2 (-1178)) + (-5 *1 (-1175))))) (((*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 -3494 ((-1074) $ (-1091))) (-15 -2746 ((-1178) $)) - (-15 -2591 ((-1178) $))))))) + (-10 -8 (-15 -3360 ((-1074) $ (-1091))) (-15 -2714 ((-1178) $)) + (-15 -2039 ((-1178) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-273 *2)) (-4 *2 (-21)) (-4 *2 (-1127)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-273 *2)) (-4 *2 (-21)) (-4 *2 (-1127)))) ((*1 *1 *1 *1) @@ -632,84 +828,65 @@ ((*1 *2 *2 *2) (-12 (-5 *2 (-878 (-205))) (-5 *1 (-1124)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1171 *2)) (-4 *2 (-1127)) (-4 *2 (-21)))) ((*1 *1 *1) (-12 (-4 *1 (-1171 *2)) (-4 *2 (-1127)) (-4 *2 (-21))))) -(((*1 *1) - (-12 (-4 *1 (-382)) (-1809 (|has| *1 (-6 -4246))) - (-1809 (|has| *1 (-6 -4238))))) - ((*1 *2 *1) (-12 (-4 *1 (-403 *2)) (-4 *2 (-1020)) (-4 *2 (-789)))) - ((*1 *2 *1) (-12 (-4 *1 (-772 *2)) (-4 *2 (-789)))) - ((*1 *1 *1 *1) (-4 *1 (-789))) ((*1 *1) (-5 *1 (-1038)))) -(((*1 *1 *2 *2) (-12 (-5 *1 (-812 *2)) (-4 *2 (-1127)))) - ((*1 *1 *2 *2 *2) (-12 (-5 *1 (-814 *2)) (-4 *2 (-1127)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1052 *3)) (-4 *3 (-977)) (-5 *2 (-592 (-878 *3))))) - ((*1 *1 *2) - (-12 (-5 *2 (-592 (-878 *3))) (-4 *3 (-977)) (-4 *1 (-1052 *3)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-592 (-592 *3))) (-4 *1 (-1052 *3)) (-4 *3 (-977)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-592 (-878 *3))) (-4 *1 (-1052 *3)) (-4 *3 (-977))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |var| (-1091)) (|:| |fn| (-294 (-205))) - (|:| -3157 (-1015 (-782 (-205)))) (|:| |abserr| (-205)) - (|:| |relerr| (-205)))) +(((*1 *2 *3 *4 *5 *4 *4 *4) + (-12 (-4 *6 (-789)) (-5 *5 (-592 (-592 *6))) (-5 *2 - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| "There are singularities at both end points") - (|:| |notEvaluated| "End point continuity not yet evaluated"))) - (-5 *1 (-174))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-1178)) (-5 *1 (-1174)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-1178)) (-5 *1 (-1175))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 - (|:| |endPointContinuity| - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| - "There are singularities at both end points") - (|:| 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(-12 (-5 *1 (-364 *2)) (-4 *2 (-1020)))) ((*1 *1 *2 *1) (-12 (-14 *3 (-592 (-1091))) (-4 *4 (-160)) - (-4 *6 (-218 (-3674 *3) (-713))) + (-4 *6 (-218 (-3552 *3) (-713))) (-14 *7 - (-1 (-108) (-2 (|:| -3703 *5) (|:| -1474 *6)) - (-2 (|:| -3703 *5) (|:| -1474 *6)))) + (-1 (-108) (-2 (|:| -3640 *5) (|:| -1990 *6)) + (-2 (|:| -3640 *5) (|:| -1990 *6)))) (-5 *1 (-438 *3 *4 *5 *6 *7 *2)) (-4 *5 (-789)) (-4 *2 (-884 *4 *6 (-800 *3))))) ((*1 *1 *1 *2) @@ -4400,116 +5101,25 @@ (-12 (-4 *1 (-1188 *3 *2)) (-4 *3 (-789)) (-4 *2 (-977)))) ((*1 *1 *1 *2) (-12 (-5 *1 (-1194 *2 *3)) (-4 *2 (-977)) (-4 *3 (-785))))) -(((*1 *2 *1) (-12 (-4 *1 (-927 *2)) (-4 *2 (-1127))))) -(((*1 *2 *3 *4 *5 *5 *5 *5 *4 *6) - (-12 (-5 *3 (-1173 (-357))) (-5 *4 (-525)) (-5 *5 (-357)) - (-5 *6 (-1 (-1178) (-1173 (-357)) (-1173 (-357)) (-357))) - (-5 *2 (-1178)) (-5 *1 (-730))))) -(((*1 *1 *2 *1) (-12 (-4 *1 (-102 *2)) (-4 *2 (-1127)))) - ((*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 (-1127)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *3 (-525)) (-4 *1 (-261 *2)) (-4 *2 (-1127)))) - ((*1 *1 *2) - (-12 - (-5 *2 - (-2 - (|:| -3511 - (-2 (|:| |var| (-1091)) (|:| |fn| (-294 (-205))) - (|:| -3157 (-1015 (-782 (-205)))) (|:| |abserr| (-205)) - (|:| |relerr| (-205)))) - (|:| -3631 - (-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| (-1072 (-205))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -3157 - (-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 (-1020)))) - ((*1 *1 *2) - (-12 - (-5 *2 - (-2 - (|:| -3511 - (-2 (|:| |xinit| (-205)) (|:| |xend| (-205)) - (|:| |fn| (-1173 (-294 (-205)))) (|:| |yinit| (-592 (-205))) - (|:| |intvals| (-592 (-205))) (|:| |g| (-294 (-205))) - (|:| |abserr| (-205)) (|:| |relerr| (-205)))) - (|:| -3631 - (-2 (|:| |stiffness| (-357)) (|:| |stability| (-357)) - (|:| |expense| (-357)) (|:| |accuracy| (-357)) - (|:| |intermediateResults| (-357)))))) - (-5 *1 (-745)))) - ((*1 *2 *3 *4) - (-12 (-5 *2 (-1178)) (-5 *1 (-1105 *3 *4)) (-4 *3 (-1020)) - (-4 *4 (-1020))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-592 (-592 (-592 *4)))) (-5 *3 (-592 *4)) (-4 *4 (-789)) - (-5 *1 (-1099 *4))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-517)) (-5 *2 (-592 (-713))) (-5 *1 (-903 *4 *3)) - (-4 *3 (-1149 *4))))) -(((*1 *1 *1 *1) (-5 *1 (-798))) ((*1 *1 *1) (-5 *1 (-798))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1087 (-525))) (-5 *3 (-525)) (-4 *1 (-804 *4))))) -(((*1 *1 *1 *1) (-5 *1 (-798)))) -(((*1 *1 *1) - (-12 (-5 *1 (-550 *2)) (-4 *2 (-37 (-385 (-525)))) (-4 *2 (-977))))) -(((*1 *2 *3 *3 *3 *4 *4 *3) - (-12 (-5 *3 (-525)) (-5 *4 (-632 (-205))) (-5 *2 (-966)) - (-5 *1 (-698))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-991 *2 *3 *4)) (-4 *2 (-977)) (-4 *3 (-735)) - (-4 *4 (-789)))) - ((*1 *2 *2 *1) - (-12 (-4 *1 (-1121 *3 *4 *5 *2)) (-4 *3 (-517)) (-4 *4 (-735)) - (-4 *5 (-789)) (-4 *2 (-991 *3 *4 *5))))) -(((*1 *2 *3 *4 *5 *3) - (-12 (-5 *4 (-1 *7 *7)) - (-5 *5 (-1 (-3 (-2 (|:| -3515 *6) (|:| |coeff| *6)) "failed") *6)) - (-4 *6 (-341)) (-4 *7 (-1149 *6)) - (-5 *2 - (-3 (-2 (|:| |answer| (-385 *7)) (|:| |a0| *6)) - (-2 (|:| -3515 (-385 *7)) (|:| |coeff| (-385 *7))) "failed")) - (-5 *1 (-535 *6 *7)) (-5 *3 (-385 *7))))) -(((*1 *1) (-4 *1 (-23))) - ((*1 *1) (-12 (-4 *1 (-447 *2 *3)) (-4 *2 (-160)) (-4 *3 (-23)))) - ((*1 *1) (-5 *1 (-501))) - ((*1 *1) (-12 (-5 *1 (-827 *2)) (-4 *2 (-1020))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| -3986 (-632 (-385 (-887 *4)))) - (|:| |vec| (-592 (-385 (-887 *4)))) (|:| -2052 (-713)) - (|:| |rows| (-592 (-525))) (|:| |cols| (-592 (-525))))) - (-4 *4 (-13 (-286) (-138))) (-4 *5 (-13 (-789) (-567 (-1091)))) - (-4 *6 (-735)) - (-5 *2 - (-2 (|:| |partsol| (-1173 (-385 (-887 *4)))) - (|:| -2261 (-592 (-1173 (-385 (-887 *4))))))) - (-5 *1 (-859 *4 *5 *6 *7)) (-4 *7 (-884 *4 *6 *5))))) -(((*1 *1 *1 *1 *1) (-4 *1 (-510)))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-108)) (-5 *1 (-1056 *3 *4)) (-4 *3 (-13 (-1020) (-33))) + (-4 *4 (-13 (-1020) (-33)))))) +(((*1 *1) (-12 (-4 *1 (-442 *2 *3)) (-4 *2 (-160)) (-4 *3 (-23)))) + ((*1 *1) (-5 *1 (-501))) ((*1 *1) (-4 *1 (-665))) + ((*1 *1) (-4 *1 (-669))) + ((*1 *1) (-12 (-5 *1 (-827 *2)) (-4 *2 (-1020)))) + ((*1 *1) (-12 (-5 *1 (-828 *2)) (-4 *2 (-789))))) +(((*1 *2) + (-12 (-5 *2 (-632 (-845 *3))) (-5 *1 (-329 *3 *4)) (-14 *3 (-856)) + (-14 *4 (-856)))) + ((*1 *2) + (-12 (-5 *2 (-632 *3)) (-5 *1 (-330 *3 *4)) (-4 *3 (-327)) + (-14 *4 + (-3 (-1087 *3) + (-1173 (-592 (-2 (|:| -3310 *3) (|:| -3640 (-1038))))))))) + ((*1 *2) + (-12 (-5 *2 (-632 *3)) (-5 *1 (-331 *3 *4)) (-4 *3 (-327)) + (-14 *4 (-856))))) (((*1 *2 *1) (-12 (-5 *2 (-525)) (-5 *1 (-797)))) ((*1 *2 *1) (-12 (-5 *2 (-1024)) (-5 *1 (-899)))) ((*1 *2 *1) (-12 (-5 *2 (-1074)) (-5 *1 (-922)))) @@ -4517,35 +5127,101 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-1020) (-33))) (-5 *1 (-1056 *2 *3)) (-4 *3 (-13 (-1020) (-33)))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-916 *2)) (-4 *2 (-1113))))) -(((*1 *2 *3 *2) (-12 (-5 *3 (-713)) (-5 *1 (-795 *2)) (-4 *2 (-160)))) - ((*1 *2 *3 *3 *2) - (-12 (-5 *3 (-713)) (-5 *1 (-795 *2)) (-4 *2 (-160))))) -(((*1 *2 *1) - (-12 (-4 *3 (-977)) (-4 *4 (-735)) (-4 *5 (-789)) (-5 *2 (-592 *1)) - (-4 *1 (-991 *3 *4 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-593 *3)) (-4 *3 (-1020))))) -(((*1 *2) - (-12 (-5 *2 (-385 (-887 *3))) (-5 *1 (-430 *3 *4 *5 *6)) - (-4 *3 (-517)) (-4 *3 (-160)) (-14 *4 (-856)) - (-14 *5 (-592 (-1091))) (-14 *6 (-1173 (-632 *3)))))) (((*1 *2 *2 *3) + (-12 (-5 *3 (-713)) (-4 *4 (-341)) (-5 *1 (-831 *2 *4)) + (-4 *2 (-1149 *4))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-762)) (-14 *5 (-1091)) (-5 *2 (-592 (-1146 *5 *4))) + (-5 *1 (-1034 *4 *5)) (-5 *3 (-1146 *5 *4))))) +(((*1 *2 *3 *3 *4) + (-12 (-5 *3 (-205)) (-5 *4 (-592 (-294 (-205)))) (-5 *2 (-108)) + (-5 *1 (-192))))) +(((*1 *1 *2 *1) (-12 (-5 *2 (-104)) (-5 *1 (-1007))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1020)) (-4 *5 (-1020)) + (-4 *6 (-1020)) (-5 *2 (-1 *6 *5)) (-5 *1 (-627 *4 *5 *6))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-429)) (-4 *6 (-735)) (-4 *7 (-789)) + (-4 *3 (-991 *5 *6 *7)) + (-5 *2 (-592 (-2 (|:| |val| *3) (|:| -1820 *4)))) + (-5 *1 (-997 *5 *6 *7 *3 *4)) (-4 *4 (-996 *5 *6 *7 *3))))) +(((*1 *1) (-4 *1 (-23))) + ((*1 *1) (-12 (-4 *1 (-447 *2 *3)) (-4 *2 (-160)) (-4 *3 (-23)))) + ((*1 *1) (-5 *1 (-501))) + ((*1 *1) (-12 (-5 *1 (-827 *2)) (-4 *2 (-1020))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-357)) (-5 *2 (-1178)) (-5 *1 (-1175))))) +(((*1 *2 *1) (-12 (-5 *2 - (-2 (|:| |partsol| (-1173 (-385 (-887 *4)))) - (|:| -2261 (-592 (-1173 (-385 (-887 *4))))))) - (-5 *3 (-592 *7)) (-4 *4 (-13 (-286) (-138))) - (-4 *7 (-884 *4 *6 *5)) (-4 *5 (-13 (-789) (-567 (-1091)))) - (-4 *6 (-735)) (-5 *1 (-859 *4 *5 *6 *7))))) -(((*1 *2 *1) - (-12 (-4 *3 (-341)) (-4 *4 (-1149 *3)) (-4 *5 (-1149 (-385 *4))) - (-5 *2 (-1173 *6)) (-5 *1 (-314 *3 *4 *5 *6)) - (-4 *6 (-320 *3 *4 *5))))) + (-592 + (-2 + (|:| -3390 + (-2 (|:| |var| (-1091)) (|:| |fn| (-294 (-205))) + (|:| -2971 (-1015 (-782 (-205)))) (|:| |abserr| (-205)) + (|:| |relerr| (-205)))) + (|:| -2348 + (-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| (-1072 (-205))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2971 + (-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 *2 *1) + (-12 (-4 *1 (-558 *3 *4)) (-4 *3 (-1020)) (-4 *4 (-1127)) + (-5 *2 (-592 *4))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |xinit| (-205)) (|:| |xend| (-205)) + (|:| |fn| (-1173 (-294 (-205)))) (|:| |yinit| (-592 (-205))) + (|:| |intvals| (-592 (-205))) (|:| |g| (-294 (-205))) + (|:| |abserr| (-205)) (|:| |relerr| (-205)))) + (-5 *2 + (-2 (|:| |stiffnessFactor| (-357)) (|:| |stabilityFactor| (-357)))) + (-5 *1 (-187))))) (((*1 *1 *1 *2 *1) (-12 (-4 *1 (-121 *2)) (-4 *2 (-1020))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-856)) (-5 *2 (-1087 *3)) (-5 *1 (-1102 *3)) - (-4 *3 (-341))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-286)) (-5 *2 (-108))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1 *3 *3 (-525))) (-4 *3 (-977)) (-5 *1 (-94 *3)))) + ((*1 *1 *2 *2) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-977)) (-5 *1 (-94 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-977)) (-5 *1 (-94 *3))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-713)) (-5 *1 (-1080 *3 *4)) (-14 *3 (-856)) + (-4 *4 (-977))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-205)) (-5 *1 (-206)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-157 (-205))) (-5 *1 (-206)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-13 (-789) (-517))) (-5 *1 (-409 *3 *2)) + (-4 *2 (-408 *3)))) + ((*1 *1 *1 *1) (-4 *1 (-1055)))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-1173 (-1173 (-525)))) (-5 *3 (-856)) (-5 *1 (-443))))) +(((*1 *2 *2) (-12 (-5 *2 (-366)) (-5 *1 (-414)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-366)) (-5 *1 (-414))))) +(((*1 *2 *3 *4 *4 *4 *4) + (-12 (-5 *4 (-205)) + (-5 *2 + (-2 (|:| |brans| (-592 (-592 (-878 *4)))) + (|:| |xValues| (-1015 *4)) (|:| |yValues| (-1015 *4)))) + (-5 *1 (-144)) (-5 *3 (-592 (-592 (-878 *4))))))) (((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| (-1074))) (-5 *2 (-108)) (-5 *1 (-1096)))) ((*1 *2 *1 *3) @@ -4554,351 +5230,661 @@ (-12 (-5 *3 (|[\|\|]| (-205))) (-5 *2 (-108)) (-5 *1 (-1096)))) ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| (-525))) (-5 *2 (-108)) (-5 *1 (-1096))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-205)) (-5 *4 (-525)) (-5 *2 (-966)) (-5 *1 (-701))))) +(((*1 *1 *1 *1 *2) + (-12 (-4 *1 (-991 *3 *4 *2)) (-4 *3 (-977)) (-4 *4 (-735)) + (-4 *2 (-789)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-991 *2 *3 *4)) (-4 *2 (-977)) (-4 *3 (-735)) + (-4 *4 (-789))))) +(((*1 *2 *1) + (-12 (-5 *2 (-385 (-887 *3))) (-5 *1 (-430 *3 *4 *5 *6)) + (-4 *3 (-517)) (-4 *3 (-160)) (-14 *4 (-856)) + (-14 *5 (-592 (-1091))) (-14 *6 (-1173 (-632 *3)))))) +(((*1 *2) (-12 (-5 *2 (-108)) (-5 *1 (-128))))) +(((*1 *2 *1 *3) + (-12 (-5 *2 (-592 (-1074))) (-5 *1 (-989)) (-5 *3 (-1074))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-592 (-800 *5))) (-14 *5 (-592 (-1091))) (-4 *6 (-429)) + (-5 *2 + (-2 (|:| |dpolys| (-592 (-227 *5 *6))) + (|:| |coords| (-592 (-525))))) + (-5 *1 (-448 *5 *6 *7)) (-5 *3 (-592 (-227 *5 *6))) (-4 *7 (-429))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-592 (-51))) (-5 *1 (-827 *3)) (-4 *3 (-1020))))) +(((*1 *1 *1 *1) (-5 *1 (-798)))) +(((*1 *2 *1) + (-12 (-4 *1 (-1041 *3 *4 *2 *5)) (-4 *4 (-977)) (-4 *5 (-218 *3 *4)) + (-4 *2 (-218 *3 *4))))) +(((*1 *2 *1 *3 *4 *4 *5) + (-12 (-5 *3 (-878 (-205))) (-5 *4 (-809)) (-5 *5 (-856)) + (-5 *2 (-1178)) (-5 *1 (-445)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-878 (-205))) (-5 *2 (-1178)) (-5 *1 (-445)))) + ((*1 *2 *1 *3 *4 *4 *5) + (-12 (-5 *3 (-592 (-878 (-205)))) (-5 *4 (-809)) (-5 *5 (-856)) + (-5 *2 (-1178)) (-5 *1 (-445))))) (((*1 *2 *3) - (|partial| -12 (-4 *4 (-13 (-517) (-138))) - (-5 *2 (-2 (|:| -3670 *3) (|:| -3680 *3))) 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+ (-4 *3 (-977)) (-4 *2 (-734)))) + ((*1 *1 *1 *2 *3 *1) + (-12 (-5 *2 (-713)) (-5 *1 (-1087 *3)) (-4 *3 (-977)))) + ((*1 *1 *1 *2 *3 *1) + (-12 (-5 *2 (-904)) (-4 (-904) (-126)) (-5 *1 (-1093 *3)) + (-4 *3 (-517)) (-4 *3 (-977)))) + ((*1 *1 *1 *2 *3 *1) + (-12 (-5 *2 (-713)) (-5 *1 (-1146 *4 *3)) (-14 *4 (-1091)) + (-4 *3 (-977))))) (((*1 *2 *3) - (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1020)) (-4 *6 (-1020)) - (-5 *2 (-1 *6 *4 *5)) (-5 *1 (-627 *4 *5 *6)) (-4 *4 (-1020))))) -(((*1 *1 *1) - (-12 (-5 *1 (-550 *2)) (-4 *2 (-37 (-385 (-525)))) (-4 *2 (-977))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-789) (-517))) (-5 *1 (-255 *3 *2)) - (-4 *2 (-13 (-408 *3) (-934)))))) + (-12 (-4 *2 (-341)) (-4 *2 (-787)) (-5 *1 (-880 *2 *3)) + (-4 *3 (-1149 *2))))) (((*1 *2 *3) (-12 (-4 *4 (-1020)) (-4 *5 (-13 (-567 (-827 *4)) (-160))) (-5 *2 (-827 *4)) (-5 *1 (-158 *4 *5 *3)) (-4 *3 (-154 *5)))) @@ -8649,9 +8589,9 @@ (-12 (-5 *2 (-887 *3)) (-4 *3 (-977)) (-4 *1 (-991 *3 *4 *5)) (-4 *5 (-567 (-1091))) (-4 *4 (-735)) (-4 *5 (-789)))) ((*1 *1 *2) - (-3316 + (-3204 (-12 (-5 *2 (-887 (-525))) (-4 *1 (-991 *3 *4 *5)) - (-12 (-1809 (-4 *3 (-37 (-385 (-525))))) (-4 *3 (-37 (-525))) + (-12 (-1796 (-4 *3 (-37 (-385 (-525))))) (-4 *3 (-37 (-525))) (-4 *5 (-567 (-1091)))) (-4 *3 (-977)) (-4 *4 (-735)) (-4 *5 (-789))) (-12 (-5 *2 (-887 (-525))) (-4 *1 (-991 *3 *4 *5)) @@ -8662,7 +8602,7 @@ (-4 *3 (-37 (-385 (-525)))) (-4 *5 (-567 (-1091))) (-4 *3 (-977)) (-4 *4 (-735)) (-4 *5 (-789)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-592 *7)) (|:| -1839 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-592 *7)) (|:| -1820 *8))) (-4 *7 (-991 *4 *5 *6)) (-4 *8 (-996 *4 *5 *6 *7)) (-4 *4 (-429)) (-4 *5 (-735)) (-4 *6 (-789)) (-5 *2 (-1074)) (-5 *1 (-994 *4 *5 *6 *7 *8)))) @@ -8687,7 +8627,7 @@ (-12 (-5 *2 (-592 *1)) (-4 *1 (-1023 *3 *4 *5 *6 *7)) (-4 *3 (-1020)) (-4 *4 (-1020)) (-4 *5 (-1020)) (-4 *6 (-1020)) (-4 *7 (-1020)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-592 *7)) (|:| -1839 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-592 *7)) (|:| -1820 *8))) (-4 *7 (-991 *4 *5 *6)) (-4 *8 (-1029 *4 *5 *6 *7)) (-4 *4 (-429)) (-4 *5 (-735)) (-4 *6 (-789)) (-5 *2 (-1074)) (-5 *1 (-1061 *4 *5 *6 *7 *8)))) @@ -8722,115 +8662,131 @@ (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-294 (-525))) (|:| -3855 (-294 (-357))) + (-3 (|:| I (-294 (-525))) (|:| -3837 (-294 (-357))) (|:| CF (-294 (-157 (-357)))) (|:| |switch| (-1090)))) (-5 *1 (-1090))))) -(((*1 *2 *3 *4 *5 *4 *4 *4) - (-12 (-4 *6 (-789)) (-5 *5 (-592 (-592 *6))) - (-5 *2 - (-2 (|:| |f1| (-592 *6)) (|:| |f2| (-592 *5)) (|:| |f3| *5) - (|:| |f4| (-592 *5)))) - (-5 *1 (-1099 *6)) (-5 *3 (-592 *6)) (-5 *4 (-592 *5))))) -(((*1 *2 *3 *3 *4 *4 *5 *4 *5 *4 *4 *5 *4) - (-12 (-5 *3 (-1074)) (-5 *4 (-525)) (-5 *5 (-632 (-157 (-205)))) - (-5 *2 (-966)) (-5 *1 (-697))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-108)) (-4 *5 (-13 (-341) (-787))) - (-5 *2 (-592 (-2 (|:| -1968 (-592 *3)) (|:| -1248 *5)))) - (-5 *1 (-167 *5 *3)) (-4 *3 (-1149 (-157 *5))))) - ((*1 *2 *3 *3) - (-12 (-4 *4 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(-12 (-5 *2 (-856)) (-5 *1 (-242))))) -(((*1 *2 *3) - (-12 (-5 *3 (-632 (-294 (-205)))) (-5 *2 (-357)) (-5 *1 (-187))))) + (-12 (-5 *2 (-592 (-592 (-713)))) (-5 *1 (-839 *3)) (-4 *3 (-1020))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-713)) (-4 *1 (-1149 *4)) (-4 *4 (-977)) + (-5 *2 (-1173 *4))))) +(((*1 *1 *1) + (-12 (-5 *1 (-550 *2)) (-4 *2 (-37 (-385 (-525)))) (-4 *2 (-977))))) +(((*1 *2 *1) (-12 (-4 *1 (-367)) (-5 *2 (-108))))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-1093 (-385 (-525)))) (-5 *2 (-385 (-525))) + (-5 *1 (-172))))) (((*1 *1 *1) (-12 (-4 *1 (-46 *2 *3)) (-4 *2 (-977)) (-4 *3 (-734)))) ((*1 *1 *1) (-12 (-5 *1 (-49 *2 *3)) (-4 *2 (-977)) (-14 *3 (-592 (-1091))))) @@ -10118,10 +10335,10 @@ ((*1 *1 *1) (-12 (-4 *1 (-360 *2 *3)) (-4 *2 (-977)) (-4 *3 (-1020)))) ((*1 *1 *1) (-12 (-14 *2 (-592 (-1091))) (-4 *3 (-160)) - (-4 *5 (-218 (-3674 *2) (-713))) + (-4 *5 (-218 (-3552 *2) (-713))) (-14 *6 - (-1 (-108) (-2 (|:| -3703 *4) (|:| -1474 *5)) - (-2 (|:| -3703 *4) (|:| -1474 *5)))) + (-1 (-108) (-2 (|:| -3640 *4) (|:| -1990 *5)) + (-2 (|:| -3640 *4) (|:| -1990 *5)))) (-5 *1 (-438 *2 *3 *4 *5 *6 *7)) (-4 *4 (-789)) (-4 *7 (-884 *3 *5 (-800 *2))))) ((*1 *1 *1) (-12 (-4 *1 (-481 *2 *3)) (-4 *2 (-1020)) (-4 *3 (-789)))) @@ -10136,121 +10353,139 @@ (-12 (-4 *1 (-991 *3 *4 *2)) (-4 *3 (-977)) (-4 *4 (-735)) (-4 *2 (-789)))) ((*1 *1 *1) (-12 (-5 *1 (-1194 *2 *3)) (-4 *2 (-977)) (-4 *3 (-785))))) -(((*1 *1) (-5 *1 (-1005)))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-827 *4)) (-5 *3 (-1 (-108) *5)) (-4 *4 (-1020)) - (-4 *5 (-1127)) (-5 *1 (-825 *4 *5)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-827 *4)) (-5 *3 (-592 (-1 (-108) *5))) (-4 *4 (-1020)) - (-4 *5 (-1127)) (-5 *1 (-825 *4 *5)))) - ((*1 *2 *2 *3 *4) - (-12 (-5 *2 (-827 *5)) (-5 *3 (-592 (-1091))) - (-5 *4 (-1 (-108) (-592 *6))) (-4 *5 (-1020)) (-4 *6 (-1127)) - (-5 *1 (-825 *5 *6)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1 (-108) *5)) (-4 *5 (-1127)) (-4 *4 (-789)) - (-5 *1 (-872 *4 *2 *5)) (-4 *2 (-408 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 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+(((*1 *2 *3) (-12 (-5 *3 (-1091)) (-5 *2 (-1178)) (-5 *1 (-1094))))) +(((*1 *2 *1) (-12 (-4 *1 (-1014 *2)) (-4 *2 (-1127))))) +(((*1 *2 *2) (-12 (-5 *2 (-713)) (-5 *1 (-422 *3)) (-4 *3 (-977)))) + ((*1 *2) (-12 (-5 *2 (-713)) (-5 *1 (-422 *3)) (-4 *3 (-977))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-713)) (-4 *1 (-1149 *3)) (-4 *3 (-977)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-856)) (-4 *1 (-1151 *3 *4)) (-4 *3 (-977)) + (-4 *4 (-734)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-385 (-525))) (-4 *1 (-1154 *3)) (-4 *3 (-977))))) +(((*1 *2 *1) + (-12 (-4 *2 (-651 *3)) (-5 *1 (-769 *2 *3)) (-4 *3 (-977))))) +(((*1 *2 *3) + (-12 (-5 *3 (-592 (-592 (-878 (-205))))) + (-5 *2 (-592 (-1015 (-205)))) (-5 *1 (-863))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-592 (-294 (-205)))) (|:| -3347 (-592 (-205))))) - (-5 *2 (-357)) (-5 *1 (-246)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1173 (-294 (-205)))) (-5 *2 (-357)) (-5 *1 (-284))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-1087 *1)) (-4 *1 (-429)))) - ((*1 *2 *2 *2) - (-12 (-5 *2 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(-366)) (|:| |fp| (-62 -3855)))) (-5 *2 (-966)) - (-5 *1 (-691))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1173 (-294 (-205)))) (-5 *4 (-592 (-1091))) - (-5 *2 (-632 (-294 (-205)))) (-5 *1 (-187)))) + (-2 (|:| |var| (-1091)) (|:| |fn| (-294 (-205))) + (|:| -2971 (-1015 (-782 (-205)))) (|:| |abserr| (-205)) + (|:| |relerr| (-205)))) + (-5 *2 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1072 (-205))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2971 + (-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 *3 *3 *3) + (-12 (-5 *2 (-1091)) (-5 *3 (-108)) (-5 *1 (-827 *4)) + (-4 *4 (-1020))))) +(((*1 *2 *3 *3) (-12 (-5 *3 (-525)) (-5 *2 (-108)) (-5 *1 (-514))))) +(((*1 *2 *3 *3 *3) + (-12 (-5 *3 (-1074)) (-4 *4 (-429)) (-4 *5 (-735)) (-4 *6 (-789)) + (-4 *7 (-991 *4 *5 *6)) (-5 *2 (-1178)) + (-5 *1 (-997 *4 *5 *6 *7 *8)) (-4 *8 (-996 *4 *5 *6 *7)))) + ((*1 *2 *3 *3 *3) + (-12 (-5 *3 (-1074)) (-4 *4 (-429)) (-4 *5 (-735)) (-4 *6 (-789)) + (-4 *7 (-991 *4 *5 *6)) (-5 *2 (-1178)) + (-5 *1 (-1028 *4 *5 *6 *7 *8)) (-4 *8 (-996 *4 *5 *6 *7))))) +(((*1 *2) (-12 (-5 *2 (-592 (-1091))) (-5 *1 (-100))))) +(((*1 *2 *1) + (-12 (-4 *1 (-313 *3 *4 *5 *6)) (-4 *3 (-341)) (-4 *4 (-1149 *3)) + (-4 *5 (-1149 (-385 *4))) (-4 *6 (-320 *3 *4 *5)) + (-5 *2 + (-2 (|:| -3417 (-391 *4 (-385 *4) *5 *6)) (|:| |principalPart| *6))))) ((*1 *2 *3 *4) - 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(-592 (-1091))) (-5 *2 (-1178)) (-5 *1 (-1094)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-1091)) (-5 *4 (-592 (-1091))) (-5 *2 (-1178)) - (-5 *1 (-1094)))) - ((*1 *2 *3 *4 *1) - (-12 (-5 *3 (-1091)) (-5 *4 (-592 (-1091))) (-5 *2 (-1178)) - (-5 *1 (-1094))))) + (-12 (-5 *2 (-1072 (-525))) (-5 *1 (-1076 *4)) (-4 *4 (-977)) + (-5 *3 (-525))))) (((*1 *2 *3 *3) - (-12 (-5 *2 (-1087 *3)) (-5 *1 (-849 *3)) (-4 *3 (-286))))) -(((*1 *2) - (-12 (-5 *2 (-1178)) (-5 *1 (-1105 *3 *4)) (-4 *3 (-1020)) - (-4 *4 (-1020))))) -(((*1 *1 *1) (-12 (-4 *1 (-403 *2)) (-4 *2 (-1020)) (-4 *2 (-346))))) + (-12 (-4 *4 (-517)) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2991 *4))) + (-5 *1 (-903 *4 *3)) (-4 *3 (-1149 *4))))) (((*1 *2 *2) - (-12 (-5 *2 (-878 *3)) (-4 *3 (-13 (-341) (-1113) (-934))) - (-5 *1 (-163 *3))))) -(((*1 *2 *3 *3) - (-12 (|has| *2 (-6 (-4257 "*"))) (-4 *5 (-351 *2)) (-4 *6 (-351 *2)) - (-4 *2 (-977)) (-5 *1 (-99 *2 *3 *4 *5 *6)) (-4 *3 (-1149 *2)) - (-4 *4 (-630 *2 *5 *6))))) -(((*1 *2 *1 *1) - (-12 (-4 *1 (-909 *3 *4 *5 *6)) (-4 *3 (-977)) (-4 *4 (-735)) - (-4 *5 (-789)) (-4 *6 (-991 *3 *4 *5)) (-4 *3 (-517)) - (-5 *2 (-108))))) -(((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-542 *3)) (-4 *3 (-341))))) -(((*1 *2 *3 *4 *3 *4 *4 *4) - (-12 (-5 *3 (-632 (-205))) (-5 *4 (-525)) (-5 *2 (-966)) - (-5 *1 (-699))))) -(((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-412))))) -(((*1 *2) - (-12 (-4 *3 (-517)) (-5 *2 (-592 (-632 *3))) (-5 *1 (-42 *3 *4)) - (-4 *4 (-395 *3))))) + (-12 (-5 *2 (-592 (-457 *3 *4))) (-14 *3 (-592 (-1091))) + (-4 *4 (-429)) (-5 *1 (-580 *3 *4))))) (((*1 *2 *1) (-12 (-4 *1 (-46 *2 *3)) (-4 *3 (-734)) (-4 *2 (-977)))) ((*1 *2 *1) (-12 (-4 *2 (-977)) (-5 *1 (-49 *2 *3)) (-14 *3 (-592 (-1091))))) @@ -10259,10 +10494,10 @@ (-4 *3 (-13 (-977) (-789))) (-14 *4 (-592 (-1091))))) ((*1 *2 *1) (-12 (-4 *1 (-360 *2 *3)) (-4 *3 (-1020)) (-4 *2 (-977)))) ((*1 *2 *1) - (-12 (-14 *3 (-592 (-1091))) (-4 *5 (-218 (-3674 *3) (-713))) + (-12 (-14 *3 (-592 (-1091))) (-4 *5 (-218 (-3552 *3) (-713))) (-14 *6 - (-1 (-108) (-2 (|:| -3703 *4) (|:| -1474 *5)) - (-2 (|:| -3703 *4) (|:| -1474 *5)))) + (-1 (-108) (-2 (|:| -3640 *4) (|:| -1990 *5)) + (-2 (|:| -3640 *4) (|:| -1990 *5)))) (-4 *2 (-160)) (-5 *1 (-438 *3 *2 *4 *5 *6 *7)) (-4 *4 (-789)) (-4 *7 (-884 *2 *5 (-800 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-481 *2 *3)) (-4 *3 (-789)) (-4 *2 (-1020)))) @@ -10279,74 +10514,63 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-991 *3 *4 *2)) (-4 *3 (-977)) (-4 *4 (-735)) (-4 *2 (-789))))) -(((*1 *2 *2) (-12 (-5 *2 (-205)) (-5 *1 (-206)))) - ((*1 *2 *2) (-12 (-5 *2 (-157 (-205))) (-5 *1 (-206)))) +(((*1 *2) + (-12 (-5 *2 (-856)) (-5 *1 (-419 *3)) (-4 *3 (-1149 (-525))))) ((*1 *2 *2) + (-12 (-5 *2 (-856)) (-5 *1 (-419 *3)) (-4 *3 (-1149 (-525)))))) +(((*1 *2) (-12 (-5 *2 (-525)) (-5 *1 (-861))))) +(((*1 *2 *2 *3 *4 *4) + (-12 (-5 *4 (-525)) (-4 *3 (-160)) (-4 *5 (-351 *3)) + (-4 *6 (-351 *3)) (-5 *1 (-631 *3 *5 *6 *2)) + (-4 *2 (-630 *3 *5 *6))))) +(((*1 *2 *1 *2 *3) + (|partial| -12 (-5 *2 (-1074)) 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(-12 (-5 *2 (-317 (-1276 'X) (-1276 '-3367) (-641))) (-5 *1 (-87 *3)) (-14 *3 (-1091)))) ((*1 *2 *1) (-12 (-5 *2 (-936 2)) (-5 *1 (-103)))) ((*1 *2 *1) (-12 (-5 *2 (-385 (-525))) (-5 *1 (-103)))) @@ -16688,8 +16551,8 @@ (-12 (-5 *2 (-592 *3)) (-4 *3 (-13 (-789) - (-10 -8 (-15 -3494 ((-1074) $ (-1091))) (-15 -2746 ((-1178) $)) - (-15 -2591 ((-1178) $))))) + (-10 -8 (-15 -3360 ((-1074) $ (-1091))) (-15 -2714 ((-1178) $)) + (-15 -2039 ((-1178) $))))) (-5 *1 (-195 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-936 10)) (-5 *1 (-198)))) ((*1 *2 *1) (-12 (-5 *2 (-385 (-525))) (-5 *1 (-198)))) @@ -16730,14 +16593,14 @@ ((*1 *1 *2) (-12 (-4 *1 (-352 *2 *3)) (-4 *2 (-789)) (-4 *3 (-160)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1095)) (|:| -4090 (-592 (-308))))) + (-5 *2 (-2 (|:| |localSymbols| (-1095)) (|:| -3480 (-592 (-308))))) (-4 *1 (-361)))) ((*1 *1 *2) (-12 (-5 *2 (-308)) (-4 *1 (-361)))) ((*1 *1 *2) (-12 (-5 *2 (-592 (-308))) (-4 *1 (-361)))) ((*1 *1 *2) (-12 (-5 *2 (-632 (-641))) (-4 *1 (-361)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1095)) (|:| -4090 (-592 (-308))))) + (-5 *2 (-2 (|:| |localSymbols| (-1095)) (|:| -3480 (-592 (-308))))) (-4 *1 (-362)))) ((*1 *1 *2) (-12 (-5 *2 (-308)) (-4 *1 (-362)))) ((*1 *1 *2) (-12 (-5 *2 (-592 (-308))) (-4 *1 (-362)))) @@ -16747,71 +16610,71 @@ ((*1 *1 *2) (-12 (-5 *2 (-798)) (-5 *1 (-372)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1095)) (|:| -4090 (-592 (-308))))) + (-5 *2 (-2 (|:| |localSymbols| (-1095)) (|:| -3480 (-592 (-308))))) (-4 *1 (-374)))) ((*1 *1 *2) (-12 (-5 *2 (-308)) (-4 *1 (-374)))) ((*1 *1 *2) (-12 (-5 *2 (-592 (-308))) (-4 *1 (-374)))) ((*1 *1 *2) (-12 (-5 *2 (-273 (-294 (-157 (-357))))) (-5 *1 (-376 *3 *4 *5 *6)) - (-14 *3 (-1091)) (-14 *4 (-3 (|:| |fst| (-412)) (|:| -3348 "void"))) + (-14 *3 (-1091)) (-14 *4 (-3 (|:| |fst| (-412)) (|:| -1219 "void"))) (-14 *5 (-592 (-1091))) (-14 *6 (-1095)))) ((*1 *1 *2) (-12 (-5 *2 (-273 (-294 (-357)))) (-5 *1 (-376 *3 *4 *5 *6)) - (-14 *3 (-1091)) 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(|:| -1219 "void"))) (-14 *5 (-592 (-1091))) (-14 *6 (-1095)))) ((*1 *1 *2) (-12 (-5 *2 (-592 (-308))) (-5 *1 (-376 *3 *4 *5 *6)) - (-14 *3 (-1091)) (-14 *4 (-3 (|:| |fst| (-412)) (|:| -3348 "void"))) + (-14 *3 (-1091)) (-14 *4 (-3 (|:| |fst| (-412)) (|:| -1219 "void"))) (-14 *5 (-592 (-1091))) (-14 *6 (-1095)))) ((*1 *1 *2) (-12 (-5 *2 (-308)) (-5 *1 (-376 *3 *4 *5 *6)) (-14 *3 (-1091)) - (-14 *4 (-3 (|:| |fst| (-412)) (|:| -3348 "void"))) + (-14 *4 (-3 (|:| |fst| (-412)) (|:| -1219 "void"))) (-14 *5 (-592 (-1091))) (-14 *6 (-1095)))) ((*1 *1 *2) (-12 (-5 *2 (-309 *4)) (-4 *4 (-13 (-789) (-21))) @@ -16839,14 +16702,14 @@ ((*1 *2 *1) (-12 (-5 *2 (-798)) (-5 *1 (-415)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1095)) (|:| -4090 (-592 (-308))))) + (-5 *2 (-2 (|:| |localSymbols| (-1095)) (|:| -3480 (-592 (-308))))) (-4 *1 (-417)))) ((*1 *1 *2) (-12 (-5 *2 (-308)) (-4 *1 (-417)))) ((*1 *1 *2) (-12 (-5 *2 (-592 (-308))) (-4 *1 (-417)))) ((*1 *1 *2) (-12 (-5 *2 (-1173 (-641))) (-4 *1 (-417)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1095)) (|:| -4090 (-592 (-308))))) + (-5 *2 (-2 (|:| |localSymbols| (-1095)) (|:| -3480 (-592 (-308))))) (-4 *1 (-418)))) ((*1 *1 *2) (-12 (-5 *2 (-308)) (-4 *1 (-418)))) ((*1 *1 *2) (-12 (-5 *2 (-592 (-308))) (-4 *1 (-418)))) @@ -16913,24 +16776,24 @@ ((*1 *1 *2) (-12 (-4 *3 (-977)) (-5 *1 (-655 *3 *2)) (-4 *2 (-1149 *3)))) ((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| -3703 *3) (|:| -1474 *4))) + (-12 (-5 *2 (-2 (|:| -3640 *3) (|:| -1990 *4))) (-5 *1 (-656 *3 *4 *5)) (-4 *3 (-789)) (-4 *4 (-1020)) (-14 *5 - (-1 (-108) (-2 (|:| -3703 *3) (|:| -1474 *4)) - (-2 (|:| -3703 *3) (|:| -1474 *4)))))) + (-1 (-108) (-2 (|:| -3640 *3) (|:| -1990 *4)) + (-2 (|:| -3640 *3) (|:| -1990 *4)))))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| -3703 *3) (|:| -1474 *4))) (-4 *3 (-789)) + (-12 (-5 *2 (-2 (|:| -3640 *3) (|:| -1990 *4))) (-4 *3 (-789)) (-4 *4 (-1020)) (-14 *5 - (-1 (-108) (-2 (|:| -3703 *3) (|:| -1474 *4)) - (-2 (|:| -3703 *3) (|:| -1474 *4)))) + (-1 (-108) (-2 (|:| -3640 *3) (|:| -1990 *4)) + (-2 (|:| -3640 *3) (|:| -1990 *4)))) (-5 *1 (-656 *3 *4 *5)))) ((*1 *2 *1) (-12 (-4 *2 (-160)) (-5 *1 (-658 *2 *3 *4 *5 *6)) (-4 *3 (-23)) (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-592 (-2 (|:| -1631 *3) (|:| -3205 *4)))) (-4 *3 (-977)) + (-12 (-5 *2 (-592 (-2 (|:| -2593 *3) (|:| -4144 *4)))) (-4 *3 (-977)) (-4 *4 (-669)) (-5 *1 (-678 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-525)) (-4 *1 (-706)))) ((*1 *1 *2) @@ -16939,25 +16802,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1091)) (|:| |fn| (-294 (-205))) - (|:| -3157 (-1015 (-782 (-205)))) (|:| |abserr| (-205)) + (|:| -2971 (-1015 (-782 (-205)))) (|:| |abserr| (-205)) (|:| |relerr| (-205)))) (|:| |mdnia| (-2 (|:| |fn| (-294 (-205))) - (|:| -3157 (-592 (-1015 (-782 (-205))))) + (|:| -2971 (-592 (-1015 (-782 (-205))))) (|:| |abserr| (-205)) (|:| |relerr| (-205)))))) (-5 *1 (-711)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-294 (-205))) - (|:| -3157 (-592 (-1015 (-782 (-205))))) (|:| |abserr| (-205)) + (|:| -2971 (-592 (-1015 (-782 (-205))))) (|:| |abserr| (-205)) (|:| |relerr| (-205)))) (-5 *1 (-711)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1091)) (|:| |fn| (-294 (-205))) - (|:| -3157 (-1015 (-782 (-205)))) (|:| |abserr| (-205)) + (|:| -2971 (-1015 (-782 (-205)))) (|:| |abserr| (-205)) (|:| |relerr| (-205)))) (-5 *1 (-711)))) ((*1 *2 *1) (-12 (-5 *2 (-798)) (-5 *1 (-711)))) @@ -16983,23 +16846,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-294 (-205))) (|:| -3347 (-592 (-205))) + (-2 (|:| |fn| (-294 (-205))) (|:| -3265 (-592 (-205))) (|:| |lb| (-592 (-782 (-205)))) (|:| |cf| (-592 (-294 (-205)))) (|:| |ub| (-592 (-782 (-205)))))) (|:| |lsa| (-2 (|:| |lfn| (-592 (-294 (-205)))) - (|:| -3347 (-592 (-205))))))) + (|:| -3265 (-592 (-205))))))) (-5 *1 (-780)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-592 (-294 (-205)))) (|:| -3347 (-592 (-205))))) + (-2 (|:| |lfn| (-592 (-294 (-205)))) (|:| -3265 (-592 (-205))))) (-5 *1 (-780)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-294 (-205))) (|:| -3347 (-592 (-205))) + (-2 (|:| |fn| (-294 (-205))) (|:| -3265 (-592 (-205))) (|:| |lb| (-592 (-782 (-205)))) (|:| |cf| (-592 (-294 (-205)))) (|:| |ub| (-592 (-782 (-205)))))) (-5 *1 (-780)))) @@ -17158,14 +17021,10 @@ (-12 (-5 *2 (-610 *3 *4)) (-4 *3 (-789)) (-4 *4 (-160)) (-5 *1 (-1191 *3 *4)))) ((*1 *1 *2) (-12 (-5 *1 (-1194 *3 *2)) (-4 *3 (-977)) (-4 *2 (-785))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-1 *7 *7)) - (-5 *5 - (-1 (-2 (|:| |ans| *6) (|:| -3680 *6) (|:| |sol?| (-108))) (-525) - *6)) - (-4 *6 (-341)) (-4 *7 (-1149 *6)) - (-5 *2 (-2 (|:| |answer| (-542 (-385 *7))) (|:| |a0| *6))) - (-5 *1 (-535 *6 *7)) (-5 *3 (-385 *7))))) +(((*1 *2 *1) + (-12 (-4 *1 (-909 *3 *4 *5 *6)) (-4 *3 (-977)) (-4 *4 (-735)) + (-4 *5 (-789)) (-4 *6 (-991 *3 *4 *5)) (-4 *3 (-517)) + (-5 *2 (-108))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-780)) (-5 *4 (-989)) (-5 *2 (-966)) (-5 *1 (-779)))) ((*1 *2 *3) (-12 (-5 *3 (-780)) (-5 *2 (-966)) (-5 *1 (-779)))) @@ -17182,60 +17041,28 @@ ((*1 *2 *3 *4) (-12 (-5 *3 (-592 (-294 (-357)))) (-5 *4 (-592 (-357))) (-5 *2 (-966)) (-5 *1 (-779))))) -(((*1 *2 *2 *1) - (-12 (-5 *2 (-1195 *3 *4)) (-4 *1 (-352 *3 *4)) (-4 *3 (-789)) - (-4 *4 (-160)))) - ((*1 *1 *1 *1) (|partial| -12 (-5 *1 (-364 *2)) (-4 *2 (-1020)))) - ((*1 *1 *1 *2) (|partial| -12 (-5 *1 (-761 *2)) (-4 *2 (-789)))) - ((*1 *1 *1 *1) (|partial| -12 (-5 *1 (-761 *2)) (-4 *2 (-789)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1188 *2 *3)) (-4 *2 (-789)) (-4 *3 (-977)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-761 *3)) (-4 *1 (-1188 *3 *4)) (-4 *3 (-789)) - (-4 *4 (-977)))) - ((*1 *1 *1 *2) - (-12 (-4 *1 (-1188 *2 *3)) (-4 *2 (-789)) (-4 *3 (-977))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-789) (-429))) (-5 *1 (-1119 *3 *2)) - (-4 *2 (-13 (-408 *3) (-1113)))))) -(((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-827 *3)) (-4 *3 (-1020))))) -(((*1 *2 *3 *4 *5 *3 *6 *3) - (-12 (-5 *3 (-525)) (-5 *4 (-205)) (-5 *5 (-157 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(-3864 . 96647) (-3865 . 96564) (-3866 . 96505) (-3867 . 96347) + (-3868 . 96294) (-3869 . 96184) (-3870 . 90857) (-3871 . 90784) + (-3872 . 90713) (-3873 . 90644) (-3874 . 89573) (-3875 . 89421) + (-3876 . 89302) (-3877 . 88956) (-3878 . 88860) (-3879 . 88573) + (-3880 . 88402) (-3881 . 88126) (-3882 . 87960) (-3883 . 87793) + (-3884 . 87663) (-3885 . 87614) (-3886 . 87282) (-3887 . 87213) + (-3888 . 86971) (-3889 . 86457) (-3890 . 86383) (-3891 . 86265) + (-3892 . 86072) (-3893 . 85826) (-3894 . 85389) (-3895 . 84998) + (-3896 . 84752) (-3897 . 84631) (-3898 . 84506) (-3899 . 84165) + (-3900 . 83407) (-3901 . 83224) (-3902 . 83115) (-3903 . 82871) + (-3904 . 82695) (-3905 . 82558) (-3906 . 82424) (-3907 . 82287) + (-3908 . 82214) (-3909 . 82148) (-3910 . 82004) (-3911 . 81892) + (-3912 . 81818) (-3913 . 81704) (-3914 . 81601) (-3915 . 80978) + (-3916 . 80876) (-3917 . 80756) (-3918 . 80152) (-3919 . 79876) + (-3920 . 79765) (-3921 . 79568) (-3922 . 79454) (-3923 . 79403) + (-3924 . 79301) (-3925 . 79157) (-3926 . 79004) (-3927 . 78882) + (-3928 . 78805) (-3929 . 78534) (-3930 . 78431) (-3931 . 78350) + (-3932 . 76775) (-3933 . 76731) (-3934 . 76660) (-3935 . 76589) + (-3936 . 76181) (-3937 . 76108) (-3938 . 75633) (-3939 . 75316) + (-3940 . 75244) (-3941 . 75157) (-3942 . 75077) (-3943 . 75007) + (-3944 . 74833) (-3945 . 74692) (-3946 . 74513) (-3947 . 74443) + (-3948 . 74391) (-3949 . 74276) (-3950 . 74171) (-3951 . 73924) + (-3952 . 73731) (-3953 . 73607) (-3954 . 73477) (-3955 . 73397) + (-3956 . 73273) (-3957 . 73182) (-3958 . 72765) (-3959 . 72613) + (-3960 . 72506) (-3961 . 72233) (-3962 . 72177) (-3963 . 72106) + (-3964 . 71879) (-3965 . 71531) (-3966 . 71329) (-3967 . 71214) + (-3968 . 70559) (-3969 . 70450) (-3970 . 70376) (-3971 . 70261) + (-3972 . 70071) (-3973 . 69445) (-3974 . 69055) (-3975 . 68881) + (-3976 . 68308) (-3977 . 68064) (-3978 . 67763) (-3979 . 67568) + (-3980 . 67469) (-3981 . 67284) (-3982 . 67142) (-3983 . 67047) + (-3984 . 66944) 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50287) (-4046 . 50191) (-4047 . 50038) + (-4048 . 49951) (-4049 . 49749) (-4050 . 49583) (-4051 . 49373) + (-4052 . 49307) (-4053 . 49028) (-4054 . 48938) (-4055 . 48668) + (-4056 . 48600) (-4057 . 48482) (-4058 . 48358) (-4059 . 48254) + (-4060 . 47970) (-4061 . 47811) (-4062 . 47704) (-4063 . 47264) + (-4064 . 47190) (-4065 . 46805) (-4066 . 46675) (-4067 . 46535) + (-4068 . 46086) (-4069 . 46016) (-4070 . 45929) (-4071 . 44150) + (-4072 . 43130) (-4073 . 43043) (-4074 . 42797) (-4075 . 42702) + (-4076 . 42161) (-4077 . 42108) (-4078 . 41970) (-4079 . 41776) + (-4080 . 41708) (-4081 . 41606) (-4082 . 41548) (-4083 . 41389) + (-4084 . 41290) (-4085 . 41106) (-4086 . 41023) (-4087 . 40971) + (-4088 . 40581) (-4089 . 40211) (-4090 . 39818) (-4091 . 39747) + (-4092 . 39640) (-4093 . 39590) (-4094 . 39209) (-4095 . 39107) + (-4096 . 38991) (-4097 . 38821) (-4098 . 38715) (-4099 . 38620) + (-4100 . 38099) (-4101 . 37886) (-4102 . 37680) (-4103 . 37573) + (-4104 . 36389) (-4105 . 35119) 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19863) (-4167 . 19745) + (-4168 . 19492) (-4169 . 19387) (-4170 . 19293) (-4171 . 19216) + (-4172 . 19129) (-4173 . 18961) (-4174 . 18880) (-4175 . 18567) + (-4176 . 18421) (-4177 . 18232) (-4178 . 18180) (-4179 . 17470) + (-4180 . 17082) (-4181 . 16871) (-4182 . 16771) (-4183 . 16664) + (-4184 . 16567) (-4185 . 16184) (-4186 . 16107) (-4187 . 15885) + (-4188 . 15787) (-4189 . 15600) (-4190 . 15315) (-4191 . 15196) + (-4192 . 15111) (-4193 . 14944) (-4194 . 14860) (-4195 . 14530) + (-4196 . 14163) (-4197 . 13157) (-4198 . 12914) (-4199 . 12727) + (-4200 . 12612) (-4201 . 12070) (-4202 . 11961) (-4203 . 11800) + (-4204 . 11722) (-4205 . 11615) (-4206 . 11453) (-4207 . 11359) + (-4208 . 11307) (-4209 . 11219) (-4210 . 11001) (-4211 . 4002) + (-4212 . 3792) (-4213 . 3505) (-4214 . 3188) (-4215 . 3025) + (-4216 . 2799) (-4217 . 2631) (-4218 . 2536) (-4219 . 2032) + (-4220 . 1979) (-4221 . 1775) (-4222 . 1694) (-4223 . 1541) + (-4224 . 1283) (-4225 . 1184) (-4226 . 1050) (-4227 . 977) + (-4228 . 949) (-4229 . 822) (-4230 . 609) (-4231 . 463) (-4232 . 397) + (-4233 . 207) (-4234 . 108) (-4235 . 30))
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