diff options
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/algebra/browse.daase | 758 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1126 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1297 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8308 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 27396 |
5 files changed, 19441 insertions, 19444 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index e27af808..cb82cb8b 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2241087 . 3421035922) +(2241087 . 3422100676) (-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) (-1336 . T)) +((-4256 . T) (-4255 . T) (-1355 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4252 . T) (-4250 . T) (-4249 . T) ((-4257 "*") . T) (-4248 . T) (-4253 . T) (-4247 . T) (-1336 . T)) +((-4252 . T) (-4250 . T) (-4249 . T) ((-4257 "*") . T) (-4248 . T) (-4253 . T) (-4247 . T) (-1355 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -3832) +(-31 R -3855) ((|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|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-1336 . T)) +((-1355 . T)) NIL (-34) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\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| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4255 . T) (-4256 . T) (-1336 . T)) +((-4255 . T) (-4256 . T) (-1355 . T)) NIL (-36 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#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 -3832 UP UPUP -2714) +(-39 -3855 UP UPUP -3694) ((|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))) (-3275 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-3275 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-3275 (-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))) (-3275 (|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 -3832) +((|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) ((|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)) -((-3275 (-12 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3420) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2542) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3420) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2542) (|devaluate| |#2|))))))) (-3275 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-3275 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (-3275 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3275 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3420) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2542) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) +((-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))))) (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -140,7 +140,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-53 |Base| R -3832) +(-53 |Base| R -3855) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -150,7 +150,7 @@ NIL NIL (-55 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|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) (-1336 . T)) +((-4255 . T) (-4256 . T) (-1355 . 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)) -((-3275 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3275 (-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)))) (-3275 (|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))))) +((-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))))) (-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))) (-3275 (-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 -3798) +((-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) ((|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 -3798) +(-60 -3823) ((|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 -3798) +(-61 -3823) ((|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 -3798) +(-62 -3823) ((|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 -3798) +(-63 -3823) ((|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 -3798) +(-64 -3823) ((|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 -3798) +(-65 -3823) ((|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 -3798) +(-66 -3823) ((|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 -3798) +(-67 -3823) ((|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 -3798) +(-68 -3823) ((|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 -3798) +(-69 -3823) ((|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 -3798) +(-70 -3823) ((|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 -3798) +(-71 -3823) ((|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 -3798) +(-72 -3823) ((|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 -3798) +(-75 -3823) ((|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 -3798) +(-76 -3823) ((|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 -3798) +(-77 -3823) ((|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 -3798) +(-78 -3823) ((|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 -3798) +(-79 -3823) ((|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 -3798) +(-80 -3823) ((|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 -3798) +(-81 -3823) ((|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 -3798) +(-82 -3823) ((|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 -3798) +(-83 -3823) ((|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 -3798) +(-84 -3823) ((|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 -3798) +(-85 -3823) ((|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 -3798) +(-86 -3823) ((|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 -3798) +(-87 -3823) ((|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))) (-3275 (-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))) (-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))))) (-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))) (-3275 (-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))) (-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))))) (-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) (-1336 . T)) +((-4256 . T) (-1355 . 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))) (-3275 (|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)))) (-3275 (-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))) (-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))))) (-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 -3832 UP) +(-111 -3855 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))) (-3275 (|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)))) (-3275 (-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))) (-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))))) (-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."))) -((-1336 . T)) +((-1355 . 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))) (-3275 (-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))) (-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))))) (-118 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-119) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4256 . T) (-4255 . T) (-1336 . T)) +((-4256 . T) (-4255 . T) (-1355 . T)) NIL (-120 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#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| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4255 . T) (-4256 . T) (-1336 . T)) +((-4255 . T) (-4256 . T) (-1355 . T)) NIL (-122 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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))) (-3275 (-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))) (-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))))) (-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))) (-3275 (-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))) (-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))))) (-124) ((|constructor| (NIL "ByteArray provides datatype for fix-sized buffer of bytes."))) ((-4256 . T) (-4255 . T)) -((-3275 (-12 (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (-12 (|HasCategory| (-125) (QUOTE (-1020))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125)))))) (-3275 (-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)))) (-3275 (|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))))) +((-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))))) (-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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4257 "*") . T)) NIL -(-129 |minix| -3476 S T$) +(-129 |minix| -3540 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-130 |minix| -3476 R) +(-130 |minix| -3540 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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)) -((-3275 (-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))))) +((-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))))) (-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 -3832 UP UPUP) +(-139 -3855 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."))) -((-1336 . T)) +((-1355 . 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 -3832) +(-147 R -3855) ((|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 -3275 (|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)) (-1378 . T) (-1336 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-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)) 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 -3275 (|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)) (-1378 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) -((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327))) (-3275 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3275 (-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))) (-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| 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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))) (-3316 (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-341)))) (-3316 (-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))))) (-3316 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136)))) (-3316 (-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|) $) "\\spad{constructorName c} returns the name of the constructor"))) NIL NIL -(-170 R -3832) +(-170 R -3855) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -712,19 +712,19 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|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 -3832 UP UPUP R) +(-196 -3855 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 -3832 FP) +(-197 -3855 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))) (-3275 (|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)))) (-3275 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (|HasCategory| (-525) (QUOTE (-136))))) -(-199 R -3832) +((|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) ((|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))) (-3275 (-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))) (-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))))) (-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 -3832) +(-204 R -3855) ((|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}."))) -((-1371 . T) (-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-1391 . 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))) (-3275 (-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))) (-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))))) (-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) (-1336 . T)) +((-4256 . T) (-1355 . 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) (-1336 . T)) +((-4256 . T) (-1355 . 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 -3476 R) +(-217 S -3540 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 -3476 R) +(-218 -3540 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) (-1336 . T)) +((-4249 |has| |#2| (-977)) (-4250 |has| |#2| (-977)) (-4252 |has| |#2| (-6 -4252)) ((-4257 "*") |has| |#2| (-160)) (-4255 . T) (-1355 . T)) NIL -(-219 -3476 A B) +(-219 -3540 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."))) -((-1336 . T)) +((-1355 . 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)) -((-3275 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3275 (-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)))) (-3275 (|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))))) +((-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))))) (-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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(-3316 (-12 (|HasCategory| |#3| (QUOTE (-213))) (|HasCategory| |#3| (QUOTE (-977)))) (|HasCategory| |#3| (QUOTE (-669))) (-12 (|HasCategory| |#3| (QUOTE (-977))) (|HasCategory| |#3| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-977))) (|HasCategory| |#3| (LIST (QUOTE -835) (QUOTE (-1091)))))) (-3316 (|HasCategory| |#3| (QUOTE (-977))) (-12 (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (LIST (QUOTE -968) (QUOTE (-525)))))) (-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)))) (-3316 (|HasAttribute| |#3| (QUOTE -4252)) (-12 (|HasCategory| |#3| (QUOTE (-213))) (|HasCategory| |#3| (QUOTE (-977)))) (-12 (|HasCategory| |#3| (QUOTE (-977))) (|HasCategory| |#3| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-977))) (|HasCategory| |#3| (LIST (QUOTE -835) (QUOTE (-1091)))))) (|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) (-1336 . T)) +((-4255 . T) (-4256 . T) (-1355 . 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))) (-3275 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3275 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3275 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3275 (|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))) (-3275 (|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)))) (-3275 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|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))))) (-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 -3832) +(-255 R -3855) ((|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 -3832) +(-256 R -3855) ((|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) (-1336 . T)) +((-4256 . T) (-1355 . 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| -1964 -2025 |exactQuo|) +(-268 S R |Mod| -2787 -2727 |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 -3832 S) +(-276 -3855 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 -3832) +(-277 E -3855) ((|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 -3832) +(-289 -3855) ((|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))) (-3275 (|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)))) (-3275 (|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))) (-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)))))) (-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 -3275 (-3828 (|has| |#1| (-977)) (|has| |#1| (-588 (-525)))) (-12 (|has| |#1| (-517)) (-3275 (-3828 (|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))) -((-3275 (|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))) (-3275 (|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)))) (-3275 (|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)))))) (-3316 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-977)))) (-3316 (-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 -3855) ((|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))) (-3275 (|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))) (-3275 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3275 (|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 -1271) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3275 (-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 -2824) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2383) (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))) (-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|))))))) (-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)) -((-3275 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3275 (-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)))) (-3275 (|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 -3832) +((-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) ((|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 -3832) +(-307 -3855) ((|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 -3832 UP UPUP R) +(-312 S -3855 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 -3832 UP UPUP R) +(-313 -3855 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 -3832 UP UPUP R) +(-314 -3855 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 -3832 UP UPUP) +(-319 S -3855 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 -3832 UP UPUP) +(-320 -3855 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)) -((-3275 (|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)))) +((-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)))) (-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)) -((-3275 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3316 (|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)) -((-3275 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3316 (|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 -3832) +(-328 R UP -3855) ((|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)) -((-3275 (|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)))) +((-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)))) (-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)) -((-3275 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3316 (|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)) -((-3275 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3316 (|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)) -((-3275 (|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)))) +((-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)))) (-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)) -((-3275 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) -(-334 -3832 GF) +((-3316 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +(-334 -3855 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 -3832 FP FPP) +(-336 -3855 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)) -((-3275 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3316 (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4255 . T) (-1336 . T)) +((-4255 . T) (-1355 . T)) NIL (-352 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-1371 . T) (-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-4238 . T) (-4246 . T) (-1391 . 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}."))) -((-1336 . T)) +((-1355 . 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.}"))) -((-1336 . T)) +((-1355 . 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 -3832 UP UPUP R) +(-370 -3855 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."))) -((-1336 . T)) +((-1355 . 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.}"))) -((-1336 . T)) +((-1355 . 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 -3798 |returnType| -3520 |symbols|) +(-376 -3823 |returnType| -2199 |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 -3832 UP) +(-377 -3855 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-378 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-1336 . T)) +((-1355 . T)) NIL (-379 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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\"."))) -((-1371 . T) (-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-1391 . 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))) (-3275 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-953))) (|HasCategory| |#1| (QUOTE (-762))) (-3275 (|HasCategory| |#1| (QUOTE (-762))) (|HasCategory| |#1| (QUOTE (-789)))) (-3275 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-1067))) (-3275 (-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))))) (-3275 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770))))) (-3275 (|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)))) (-3275 (-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))) (-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))))) (-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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1492,11 +1492,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-391 R -3832 UP A) +(-391 R -3855 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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 -3832 UP A |ibasis|) +(-392 R -3855 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))) (-3275 (|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))) (-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)))) (-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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4255 . T) (-4245 . T) (-4256 . T) (-1336 . T)) +((-4255 . T) (-4245 . T) (-4256 . T) (-1355 . T)) NIL -(-404 R -3832) +(-404 R -3855) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1552,7 +1552,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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 -3832) +(-406 R -3855) ((|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 -3275 (|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)) (-1336 . T)) +((-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)) NIL -(-409 R -3832) +(-409 R -3855) ((|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 -3832) +(-410 R -3855) ((|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 -3832) +(-411 R -3855) ((|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 -3832 UP) +(-413 R -3855 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}."))) -((-1336 . T)) +((-1355 . 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.}"))) -((-1336 . T)) +((-1355 . 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 -3832) +(-420 R UP -3855) ((|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))) (-3275 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3275 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3275 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3275 (|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))) (-3275 (|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)))) (-3275 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) +((|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))))) (-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| -3832 R) +(-448 |lv| -3855 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 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3420) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2542) (|devaluate| |#2|)))))) (-3275 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3275 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-789))) (-3275 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#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 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#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|)))))) (-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))))) (-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 . 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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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-1336 . T)) +((-1355 . T)) NIL (-465 S) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) @@ -1796,7 +1796,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-467 -3832 UP |AlExt| |AlPol|) +(-467 -3855 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)) -((-3275 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3275 (-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)))) (-3275 (|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))))) +((-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))))) (-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))) (-3275 (-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))) (-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))))) (-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 -3832) +(-472 R UP -3855) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1836,7 +1836,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-477 -3832 |Expon| |VarSet| |DPoly|) +(-477 -3855 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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)) -((-3275 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3275 (-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)))) (-3275 (|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))))) +((-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))))) (-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)) -((-3275 (|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)))) +((-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)))) (-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))) (-3275 (-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))) (-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))))) (-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)) -((-3275 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3275 (-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)))) (-3275 (|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))))) +((-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))))) (-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))) (-3275 (-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))) (-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))))) (-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 -3832 |Par|) +(-498 K -3855 |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 -3832 |Par|) +(-503 K -3855 |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 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3420) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2542) (|devaluate| |#2|)))))) (-3275 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3275 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (-3275 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) -(-512 R -3832) +((-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) ((|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 -3832 UP UPUP R) +(-513 R0 -3855 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."))) -((-1371 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-1391 . 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 -3832) +(-518 R -3855) ((|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 -3832 L) +(-521 R -3855 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 -3832 UP UPUP R) +(-523 -3855 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 -3832 UP) +(-524 -3855 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 -3832 L) +(-527 R -3855 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 -3832) +(-528 R -3855) ((|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 -3832 UP) +(-529 -3855 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 -3832) +(-531 -3855) ((|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."))) -((-1371 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-1391 . 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 -3832) +(-534 R -3855) ((|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 -3832 UP) +(-535 -3855 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 -3832) +(-536 R -3855) ((|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 -3832) +(-540 R -3855) ((|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 -3832) +(-541 E -3855) ((|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 -3832) +(-542 -3855) ((|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)) -((-3275 (-12 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (-3275 (|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)))) (-3275 (|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))))) +((-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))))) (-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))) (-3275 (|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 -1271) (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))) (-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)))))) (-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 -3832 FG) +(-554 R -3855 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)) -((-3275 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3275 (-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)))) (-3275 (|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))))) +((-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))))) (-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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-1336 . T)) +((-1355 . T)) NIL (-559) ((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes.")) (|coerce| (($ (|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 -3275 (-3828 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4250 . T) (-4249 . T)) -((-3275 (|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|)))) (-3275 (-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 -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|)))) (-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 (|:| -3420 (-1074)) (|:| -2542 |#1|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3420) (QUOTE (-1074))) (LIST (QUOTE |:|) (QUOTE -2542) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 |#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 (|:| -3420 (-1074)) (|:| -2542 |#1|)) (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|)) (LIST (QUOTE -566) (QUOTE (-798))))) +((-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))))) (-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) (-1336 . T)) +((-4256 . T) (-1355 . 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-568 -3832 UP) +(-568 -3855 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 -3832) +(-572 R -3855) ((|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 -3832) +(-579 R -3855) ((|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| -3832) +(-580 |lv| -3855) ((|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 (|:| -3420 (-1074)) (|:| -2542 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3420) (QUOTE (-1074))) (LIST (QUOTE |:|) (QUOTE -2542) (QUOTE (-51))))))) (-3275 (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 (-51))) (QUOTE (-1020))) (|HasCategory| (-51) (QUOTE (-1020)))) (-3275 (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-1074) (QUOTE (-789))) (-3275 (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 (-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 (|:| -3420 (-1074)) (|:| -2542 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 (-51))) (LIST (QUOTE -566) (QUOTE (-798))))) +((-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))))) (-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 -3275 (-3828 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4250 . T) (-4249 . T)) -((-3275 (|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|)))) (-3275 (-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 -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|)))) (-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 -((-1830 (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-341)))) +((-1809 (|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)) -((-3275 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3275 (-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)))) (-3275 (|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))))) +((-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))))) (-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|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4255 . T) (-4256 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3275 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-594 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#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})}."))) -((-1336 . T)) +((-1355 . T)) NIL -(-598 R -3832 L) +(-598 R -3855 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 -3832 UP) +(-603 -3855 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 -1759) +(-604 A -3257) ((|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) (-1336 . T)) +((-4256 . T) (-4255 . T) (-1355 . T)) NIL -(-613 -3832) +(-613 -3855) ((|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 -3832 |Row| |Col| M) +(-614 -3855 |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)))) (-3275 (-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))) (-3275 (|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)))) (-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)))) (-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)]}."))) -((-1336 . T)) +((-1355 . 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 -((-3275 (-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))) (-3275 (-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))))) +((-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))))) (-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) (-1336 . T)) +((-4255 . T) (-4256 . T) (-1355 . 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)) -((-3275 (-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))) (-3275 (-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))))) +((-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))))) (-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 -3832 FLAF FLAS) +(-634 S -3855 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)) (-1378 . 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))) (-3275 (|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))))) (-3275 (|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)))) (-3275 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-341))) (-12 (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (QUOTE (-844))))) (-3275 (-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))) (-3275 (|HasCategory| (-641) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-641) (QUOTE (-341)))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844))) (-3275 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-341)))) (-3275 (-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)))) (-3275 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-136)))) (-3275 (-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)) (-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))))) (-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) (-1336 . T)) +((-4256 . T) (-1355 . 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 -3832 PG) +(-640 OV E -3855 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}"))) -((-1371 . T) (-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-1391 . 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 -2096 I) +(-649 S -2004 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| -1964 -2025 |exactQuo|) +(-654 R |Mod| -2787 -2727 |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))) (-3275 (|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))))) (-3275 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3275 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3275 (|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))) (-3275 (|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)))) (-3275 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|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))))) (-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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4250 |has| |#1| (-160)) (-4249 |has| |#1| (-160)) (-4252 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138)))) -(-658 R |Mod| -1964 -2025 |exactQuo|) +(-658 R |Mod| -2787 -2727 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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 -3832) +(-661 -3855) ((|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 -3832 UP) +(-670 -3855 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))) (-3275 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3275 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3275 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3275 (|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))) (-3275 (|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)))) (-3275 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) +((|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))))) (-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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2646,7 +2646,7 @@ NIL ((-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-789)))) (-679 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4245 . T) (-4256 . T) (-1336 . T)) +((-4245 . T) (-4256 . T) (-1355 . T)) NIL (-680 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|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 -3832) +(-708 -3855) ((|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 -3832) +(-709 P -3855) ((|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 -3832) +(-710 UP -3855) ((|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 -3832) +(-714 R -3855) ((|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 -3832 |ExtF| |SUEx| |ExtP| |n|) +(-719 -3855 |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))) (-3275 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3275 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3275 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3275 (|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))))) (-1809 (|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)))) (-1809 (|HasCategory| |#1| (LIST (QUOTE -925) (QUOTE (-525))))))) (-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))))) (-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))) (-3275 (|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))))) (-3275 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3275 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3275 (|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)))) (-3275 (|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)))) (-3275 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|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))))) (-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) (-1336 . T)) +((-4256 . T) (-4255 . T) (-1355 . 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4249 . T) (-4250 . T) (-4252 . T)) NIL -(-740 -3275 R OS S) +(-740 -3316 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-741 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|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|))) (-3275 (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3275 (|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|))) (-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))))) (-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 -3832 L) +(-743 R -3855 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 -3832) +(-744 R -3855) ((|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 -3832) +(-746 R -3855) ((|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 -3832 UP UPUP R) +(-748 -3855 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 -3832 UP L LQ) +(-749 -3855 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 -3832 UP L LQ) +(-751 -3855 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 -3832 UP) +(-752 -3855 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 -3832 L UP A LO) +(-753 -3855 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 -3832 UP) +(-754 -3855 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 -3832 LO) +(-755 -3855 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 -3832 LODO) +(-756 -3855 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))))) (-3316 (|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))) (-3275 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3275 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3275 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3275 (|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))) (-3275 (|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)))) (-3275 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|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))))) (-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) (-1336 . T)) +((-4255 . T) (-4245 . T) (-4256 . T) (-1355 . 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))) (-3275 (|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))) (-3275 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) +((|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)))) (-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))) (-3275 (|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))) (-3275 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) +((|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)))) (-783) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-784 -3476 S) +(-784 -3540 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| -3054) +(-793 R |sigma| -1752) ((|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| -3054) +(-794 |x| R |sigma| -1752) ((|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))) (-3275 (|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)))) (-3275 (-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))) (-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))))) (-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))) (-3275 (|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)))) (-3275 (-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))) (-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))))) (-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)))) (-3275 (-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)))) (-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)))))) (-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 (-1830 (|HasCategory| |#2| (QUOTE (-977)))) (-1830 (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1091)))))) (-12 (|HasCategory| |#2| (QUOTE (-977))) (-1830 (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1091)))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1091))))) +((-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))))) (-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 -2096) +(-825 R -2004) ((|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 -3832) +(-831 UP -3855) ((|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))) (-3275 (-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))) (-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))))) (-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)) -((-3275 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-789)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-789)))) +((-3316 (|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 -3832 UP UPUP R) +(-846 R0 -3855 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 -3832) +(-853 -3855) ((|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 -3832 P) +(-857 -3855 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-858 |xx| -3832) +(-858 |xx| -3855) ((|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 -3832) +(-864 R -3855) ((|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 -3832) +(-867 S R -3855) ((|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 -3832 -2096) +(-872 R -3855 -2004) ((|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 -2096) +(-873 -2004) ((|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)) -((-3275 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3275 (-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)))) (-3275 (|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))))) +((-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))))) (-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 -3832) +(-885 E V R P -3855) ((|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))) (-3275 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3275 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3275 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3275 (|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))) (-3275 (|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)))) (-3275 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) -(-888 E V R P -3832) +((|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) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-429)))) @@ -3499,12 +3499,12 @@ NIL (-892 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4256 . T) (-4255 . T)) -((-3275 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3275 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3275 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-3316 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3316 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-893) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -3832) +(-894 -3855) ((|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 @@ -3519,11 +3519,11 @@ 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))) (-3275 (|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)))) (-3275 (|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))) (-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))) (-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)))) -((-3275 (-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)))) (-3275 (-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)))) (-3275 (-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)))) (-3275 (-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)))) (-3275 (-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))))) +((-3316 (-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)))) (-3316 (-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)))) (-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 (-735))) (|HasCategory| |#2| (QUOTE (-735))))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-3316 (-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)))) (-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))))) (-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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3538,7 +3538,7 @@ NIL NIL (-902 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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) (-1336 . T)) +((-4255 . T) (-4256 . T) (-1355 . 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) (-1336 . T)) +((-4255 . T) (-1355 . 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) (-1336 . T)) +((-4256 . T) (-4255 . T) (-1355 . 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 -3832) +(-918 K R UP -3855) ((|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}."))) -((-1336 . T) (-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-1355 . 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) (-1336 . T)) +((-4255 . T) (-4256 . T) (-1355 . 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))) (-3275 (|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))) (-3275 (|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))) (-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))))) (-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))) (-3275 (-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))) (-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))))) (-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 -3832 UP UPUP |radicnd| |n|) +(-935 -3855 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))) (-3275 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-3275 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-3275 (-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))) (-3275 (|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))) (-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))))) (-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))) (-3275 (|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)))) (-3275 (-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))) (-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))))) (-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}."))) -((-1336 . T)) +((-1355 . 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 -3832) +(-945 R -3855) ((|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 -3832) +(-946 R -3855) ((|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 -3832 UP) +(-947 -3855 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 -3832 UP) +(-948 -3855 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)) -((-3275 (|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 -3832 L) +((-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) ((|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 -3832 |Expon| |VarSet| |FPol| |LFPol|) +(-965 -3855 |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 (|:| -3420 (-1091)) (|:| -2542 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3420) (QUOTE (-1091))) (LIST (QUOTE |:|) (QUOTE -2542) (QUOTE (-51))))))) (-3275 (|HasCategory| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (QUOTE (-1020))) (|HasCategory| (-51) (QUOTE (-1020)))) (-3275 (|HasCategory| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (QUOTE (-1020))) (|HasCategory| (-1091) (QUOTE (-789))) (|HasCategory| (-51) (QUOTE (-1020))) (-3275 (|HasCategory| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (LIST (QUOTE -566) (QUOTE (-798))))) +((-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))))) (-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| -3832) +(-978 |xx| -3855) ((|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) (-1336 . T) (-4250 . T) (-4249 . T)) +((-4255 . T) (-1355 . 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)) -((-3275 (-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)))) (-3275 (|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|))))) +((-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|))))) (-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 (|:| -3420 (-1091)) (|:| -2542 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3420) (QUOTE (-1091))) (LIST (QUOTE |:|) (QUOTE -2542) (QUOTE (-51))))))) (-3275 (|HasCategory| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (QUOTE (-1020))) (|HasCategory| (-51) (QUOTE (-1020)))) (-3275 (|HasCategory| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (QUOTE (-1020))) (|HasCategory| (-1091) (QUOTE (-789))) (|HasCategory| (-51) (QUOTE (-1020))) (-3275 (|HasCategory| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (LIST (QUOTE -566) (QUOTE (-798))))) +((-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))))) (-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) (-1336 . T)) +((-4256 . T) (-4255 . T) (-1355 . 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 -3832) +(-999 |Base| R -3855) ((|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 -3832) +(-1000 |Base| R -3855) ((|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))) (-3275 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3275 (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-327)))) (-3275 (-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))))) (-3275 (|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))) (-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))))) (-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."))) -((-1336 . T)) +((-1355 . 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| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-1336 . T)) +((-1355 . T)) NIL (-1017 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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) (-1336 . T)) +((-4245 . T) (-1355 . 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)) -((-3275 (-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))))) +((-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))))) (-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) (-1336 . T)) +((-4256 . T) (-4255 . T) (-1355 . 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))))) (-3316 (|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 -3832) +(-1035 R -3855) ((|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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4255 . T) (-4256 . T) (-1336 . T)) +((-4255 . T) (-4256 . T) (-1355 . T)) NIL (-1040 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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."))) -((-1336 . T) (-4255 . T) (-4249 . T) (-4250 . T) (-4252 . T)) +((-1355 . 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))) (-3275 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3275 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3275 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3275 (|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))) (-3275 (|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)))) (-3275 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|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))))) (-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))) (-3275 (|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))) (-3316 (|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) (-1336 . T)) +((-4256 . T) (-4255 . T) (-1355 . T)) NIL -(-1046 UP -3832) +(-1046 UP -3855) ((|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))) (-3275 (|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))) (-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))))) (-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)))) (-3275 (-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))) (-3275 (|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)))) (-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)))) (-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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4256 . T) (-4255 . T) (-1336 . T)) +((-4256 . T) (-4255 . T) (-1355 . T)) NIL (-1061 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4183,19 +4183,19 @@ NIL (-1063 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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))) (-3275 (-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))) (-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))))) (-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})}."))) -((-1336 . T)) +((-1355 . 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 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3420) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2542) (|devaluate| |#2|)))))) (-3275 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3275 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-789))) (-3275 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#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 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#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|)))))) (-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))))) (-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))) (-3275 (-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))) (-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))))) (-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) (-1336 . T)) +((-4256 . T) (-4255 . T) (-1355 . T)) NIL (-1074) NIL ((-4256 . T) (-4255 . T)) -((-3275 (-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))))) +((-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))))) (-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 (|:| -3420 (-1074)) (|:| -2542 |#1|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3420) (QUOTE (-1074))) (LIST (QUOTE |:|) (QUOTE -2542) (|devaluate| |#1|)))))) (-3275 (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-1020)))) (-3275 (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|)) (QUOTE (-1020))) (|HasCategory| (-1074) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-3275 (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|)) (LIST (QUOTE -566) (QUOTE (-798))))) +((-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))))) (-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 "*") -3275 (-3828 (|has| |#1| (-341)) (|has| (-1089 |#1| |#2| |#3|) (-762))) (|has| |#1| (-160)) (-3828 (|has| |#1| (-341)) (|has| (-1089 |#1| |#2| |#3|) (-844)))) (-4248 -3275 (-3828 (|has| |#1| (-341)) (|has| (-1089 |#1| |#2| |#3|) (-762))) (|has| |#1| (-517)) (-3828 (|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)))) (-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))))) (-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))) (-3275 (|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))) (-3275 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3275 (|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 -1271) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3275 (-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 -2824) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2383) (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))) (-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|))))))) (-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))) (-3275 (|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 -1271) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasCategory| |#1| (QUOTE (-341))) (-3275 (-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 -2824) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2383) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|devaluate| |#1|))))))) +((|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|))))))) (-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))) (-3275 (|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)))) (-3275 (|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))) (-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))) (-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 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3420) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2542) (|devaluate| |#2|)))))) (-3275 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3275 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (-3275 (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3420 |#1|) (|:| -2542 |#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|)))))) (-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))))) (-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) (-1336 . T)) +((-4256 . T) (-1355 . 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4256 . T) (-4255 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3275 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3316 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-1115 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4396,7 +4396,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1117 R -3832) +(-1117 R -3855) ((|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 -3832) +(-1119 R -3855) ((|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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4256 . T) (-4255 . T) (-1336 . T)) +((-4256 . T) (-4255 . T) (-1355 . T)) NIL (-1122 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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))) (-3275 (|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))) (-3316 (|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 -3832) +(-1126 -3855) ((|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."))) -((-1336 . T)) +((-1355 . 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)))))) (-3316 (-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)))) (-3316 (-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))) (-3275 (|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))))) (-3275 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3275 (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3275 (|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)))) (-3275 (|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)))) (-3275 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) +((|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))))) (-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 -1271) (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 -1278) (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))) (-3275 (|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))) (-3275 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3275 (|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 -1271) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3275 (-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 -2824) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2383) (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))) (-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)))))) (-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))) (-3275 (|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))) (-3275 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3275 (|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 -1271) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3275 (-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 -2824) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2383) (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))) (-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|))))))) (-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))) (-3275 (|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))) (-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)))) (-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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-1336 . T)) +((-1355 . T)) NIL (-1162 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) @@ -4583,7 +4583,7 @@ NIL (-1163 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 -2383) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2824) (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 -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)))) (-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))) (-3275 (|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 -1271) (LIST (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasCategory| |#1| (QUOTE (-341))) (-3275 (-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 -2824) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (LIST (QUOTE -2383) (LIST (LIST (QUOTE -592) (QUOTE (-1091))) (|devaluate| |#1|))))))) +((|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|))))))) (-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 -3832 UP L UTS) +(-1167 -3855 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."))) -((-1336 . T)) +((-1355 . 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4256 . T) (-4255 . T) (-1336 . T)) +((-4256 . T) (-4255 . T) (-1355 . T)) NIL (-1172 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4623,7 +4623,7 @@ NIL (-1173 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4256 . T) (-4255 . T)) -((-3275 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3275 (-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)))) (-3275 (|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))))) +((-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))))) (-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 -3832) +(-1182 K R UP -3855) ((|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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4248 |has| |#2| (-6 -4248)) (-4250 . T) (-4249 . T) (-4252 . T)) NIL -(-1189 S -3832) +(-1189 S -3855) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138)))) -(-1190 -3832) +(-1190 -3855) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4247 . T) (-4253 . T) (-4248 . T) ((-4257 "*") . T) (-4249 . T) (-4250 . T) (-4252 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 1a02dcf1..b77c6994 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,14 +1,14 @@ -(143277 . 3421035927) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) #0#) |has| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (-288 (-2 (|:| -3420 |#1|) (|:| -2542 |#2|))))) +(143277 . 3422100682) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) #0#) |has| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (-288 (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))))) (((|#2| |#2|) . T)) ((((-525)) . T)) -((($ $) -3275 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) ((|#2| |#2|) . T) ((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525))))) +((($ $) -3316 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) ((|#2| |#2|) . T) ((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2|) . T)) -((($) -3275 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) ((|#2|) . T) (((-385 (-525))) |has| |#2| (-37 (-385 (-525))))) +((($) -3316 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) ((|#2|) . T) (((-385 (-525))) |has| |#2| (-37 (-385 (-525))))) (|has| |#1| (-844)) ((((-798)) . T)) ((((-798)) . T)) @@ -23,28 +23,28 @@ ((((-205)) . T) (((-798)) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1|) . T)) -(-3275 (|has| |#1| (-21)) (|has| |#1| (-787))) -((($ $) . T) ((#0=(-385 (-525)) #0#) -3275 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1| |#1|) . T)) -(-3275 (|has| |#1| (-762)) (|has| |#1| (-789))) +(-3316 (|has| |#1| (-21)) (|has| |#1| (-787))) +((($ $) . T) ((#0=(-385 (-525)) #0#) -3316 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1| |#1|) . T)) +(-3316 (|has| |#1| (-762)) (|has| |#1| (-789))) ((((-385 (-525))) |has| |#1| (-968 (-385 (-525)))) (((-525)) |has| |#1| (-968 (-525))) ((|#1|) . T)) ((((-798)) . T)) ((((-798)) . T)) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-787)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1| |#2| |#3|) . T)) (((|#4|) . T)) -((($) . T) (((-385 (-525))) -3275 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) . T) (((-385 (-525))) -3316 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) ((((-798)) . T)) ((((-798)) |has| |#1| (-1020))) (((|#1|) . T) ((|#2|) . T)) (((|#1|) . T) (((-525)) |has| |#1| (-968 (-525))) (((-385 (-525))) |has| |#1| (-968 (-385 (-525))))) -(-3275 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) -(-3275 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) -(((|#2| (-458 (-3594 |#1|) (-713))) . T)) +(-3316 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-3316 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(((|#2| (-458 (-3674 |#1|) (-713))) . T)) (((|#1| (-497 (-1091))) . T)) (((#0=(-805 |#1|) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) (|has| |#4| (-346)) (|has| |#3| (-346)) (((|#1|) . T)) @@ -54,10 +54,10 @@ (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-517)) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) ((($) . T)) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) ((((-501)) |has| |#1| (-567 (-501)))) ((($) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T)) ((($) . T)) @@ -66,59 +66,59 @@ ((((-798)) . T)) ((((-798)) . T)) ((((-385 (-525))) . T) (($) . T)) -((((-385 (-525))) -3275 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (((-1165 |#1| |#2| |#3|)) |has| |#1| (-341)) (($) . T) ((|#1|) . T)) +((((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (((-1165 |#1| |#2| |#3|)) |has| |#1| (-341)) (($) . T) ((|#1|) . T)) ((((-798)) . 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T)) (((|#1|) . T)) ((((-385 (-525))) |has| |#1| (-968 (-385 (-525)))) (((-525)) |has| |#1| (-968 (-525))) ((|#1|) . T)) (((|#1|) . T) (((-525)) |has| |#1| (-588 (-525)))) -(((|#2|) . T) (((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -3420 (-1074)) (|:| -2542 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) (|has| |#1| (-517)) (|has| |#1| (-517)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) -(-3275 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-3316 (|has| |#1| (-789)) (|has| |#1| (-1020))) (((|#1|) . T)) (|has| |#1| (-517)) (|has| |#1| (-517)) @@ -218,11 +218,11 @@ (((|#2|) . T) (($) . 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) (((-205)) . T) (((-357)) . T) (((-827 (-357))) . T)) ((((-798)) . T)) -(-3275 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) +(-3316 (|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)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) +((((-798)) -3316 (|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|) $) |has| #0# (-265 #0# #0#))) @@ -273,7 +273,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1067)) -((((-2 (|:| -3420 (-1074)) (|:| -2542 |#1|))) . T)) +((((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) (|has| (-1159 |#1| |#2| |#3| |#4|) (-136)) (|has| (-1159 |#1| |#2| |#3| |#4|) (-138)) (|has| |#1| (-136)) @@ -290,20 +290,20 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-977))) ((((-798)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) #0#) |has| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (-288 (-2 (|:| -3420 |#1|) (|:| -2542 |#2|))))) +(((|#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|))))) (((|#1|) . 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T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($ $) -3316 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) ((($) . T)) ((($) . T)) ((($) . T)) -((($) -3275 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3316 (|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)) -(-3275 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) +(-3316 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) (((|#1|) . T)) ((((-525) |#1|) . T)) (((|#2|) |has| |#2| (-160))) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) -(-3275 (|has| |#1| (-21)) (|has| |#1| (-787))) +(-3316 (|has| |#1| (-21)) (|has| |#1| (-787))) ((((-798)) |has| |#1| (-1020))) -(-3275 (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)) (|has| |#1| (-1032))) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3316 (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)) (|has| |#1| (-1032))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-327))) ((((-845 |#1|)) . T)) ((((-385 |#2|) |#3|) . T)) (|has| |#1| (-15 * (|#1| (-525) |#1|))) @@ -335,7 +335,7 @@ (((|#1|) . T)) ((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) |has| |#1| (-517))) (|has| |#1| (-341)) -(-3275 (-12 (|has| (-1165 |#1| |#2| |#3|) (-213)) (|has| |#1| (-341))) (|has| |#1| (-15 * (|#1| (-525) |#1|)))) +(-3316 (-12 (|has| (-1165 |#1| |#2| |#3|) (-213)) (|has| |#1| (-341))) (|has| |#1| (-15 * (|#1| (-525) |#1|)))) (|has| |#1| (-15 * (|#1| (-385 (-525)) |#1|))) (|has| |#1| (-341)) ((((-525)) . T)) @@ -347,31 +347,31 @@ (((|#1|) . T)) ((((-525) |#1|) . T)) (((|#2|) . T)) -(-3275 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) -(-3275 (|has| |#2| (-735)) (|has| |#2| (-787))) -(-3275 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3316 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-3316 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3316 (|has| |#2| (-735)) (|has| |#2| (-787))) (((|#1|) . 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T) (($) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341)))) (((|#3|) |has| |#3| (-977))) -((($) -3275 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3316 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (|has| |#1| (-1020)) (((|#2| (-761 |#1|)) . T)) (((|#1|) . T)) @@ -383,37 +383,37 @@ ((((-135)) . T)) (((|#3|) |has| |#3| (-1020)) (((-525)) -12 (|has| |#3| (-968 (-525))) (|has| |#3| (-1020))) (((-385 (-525))) -12 (|has| |#3| (-968 (-385 (-525)))) (|has| |#3| (-1020)))) ((((-798)) . T)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) (((|#1|) . 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T)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) (|has| |#1| (-346)) (|has| |#1| (-346)) (|has| |#1| (-346)) ((((-798)) . T)) (((|#1|) . T)) -(-3275 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-3316 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) (|has| |#1| (-346)) -(-3275 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((((-525)) . T)) ((((-525)) . T)) -(-3275 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-3316 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) ((((-798)) . T)) ((((-798)) . T)) (-12 (|has| |#2| (-213)) (|has| |#2| (-977))) @@ -422,10 +422,10 @@ ((((-525) |#4|) . T)) ((((-525) |#3|) . T)) (((|#1|) . T) (((-525)) |has| |#1| (-588 (-525)))) -(-3275 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3316 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((((-1159 |#1| |#2| |#3| |#4|)) . T)) ((((-385 (-525))) . T) (((-525)) . T)) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) @@ -454,38 +454,38 @@ ((($) . T)) ((($ $) . T) ((#0=(-1091) $) . T) ((#0# |#1|) . 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T)) ((((-525) (-125)) . T)) ((((-798)) . T)) @@ -660,22 +660,22 @@ (|has| |#1| (-1020)) (((|#2|) . T)) ((((-501)) |has| |#2| (-567 (-501))) (((-827 (-357))) |has| |#2| (-567 (-827 (-357)))) (((-827 (-525))) |has| |#2| (-567 (-827 (-525))))) -(((|#4|) -3275 (|has| |#4| (-160)) (|has| |#4| (-341)))) -(((|#3|) -3275 (|has| |#3| (-160)) (|has| |#3| (-341)))) +(((|#4|) -3316 (|has| |#4| (-160)) (|has| |#4| (-341)))) +(((|#3|) -3316 (|has| |#3| (-160)) (|has| |#3| (-341)))) ((((-798)) . T)) (((|#1|) . T)) -(-3275 (|has| |#2| (-429)) (|has| |#2| (-844))) -(-3275 (|has| |#1| (-429)) (|has| |#1| (-844))) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-844))) +(-3316 (|has| |#2| (-429)) (|has| |#2| (-844))) +(-3316 (|has| |#1| (-429)) (|has| |#1| (-844))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-844))) ((($ $) . T) ((#0=(-1091) $) |has| |#1| (-213)) ((#0# |#1|) |has| |#1| (-213)) ((#1=(-760 (-1091)) |#1|) . T) ((#1# $) . T)) -(-3275 (|has| |#1| (-429)) (|has| |#1| (-844))) +(-3316 (|has| |#1| (-429)) (|has| |#1| (-844))) ((((-525) |#2|) . T)) ((((-798)) . T)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) -((($) -3275 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-977))) ((|#3|) -3275 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-977)))) +((($) -3316 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-977))) ((|#3|) -3316 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-977)))) ((((-525) |#1|) . T)) (|has| (-385 |#2|) (-138)) (|has| (-385 |#2|) (-136)) @@ -688,22 +688,22 @@ (|has| |#1| (-517)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) ((((-798)) . T)) -((((-2 (|:| -3420 (-1074)) (|:| -2542 |#1|))) . T)) +((((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) (|has| |#1| (-37 (-385 (-525)))) -((((-366) (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|))) . T)) +((((-366) (-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#2| (-1067)) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) (((|#1|) . T)) ((((-366) (-1074)) . T)) (|has| |#1| (-517)) ((((-112 |#1|)) . T)) ((((-125)) . T)) ((((-525) |#1|) . T)) -(-3275 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3316 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (((|#2|) . T)) ((((-798)) . T)) ((((-761 |#1|)) . T)) @@ -716,7 +716,7 @@ (((|#1|) |has| |#1| (-160))) ((((-798)) . T)) ((((-501)) |has| |#1| (-567 (-501)))) -(-3275 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-3316 (|has| |#1| (-789)) (|has| |#1| (-1020))) (((|#2|) |has| |#2| (-288 |#2|))) (((#0=(-525) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -726,7 +726,7 @@ (((#0=(-525) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) ((($) . T) (((-525)) . T) (((-385 (-525))) . T)) (|has| |#2| (-346)) -(-3275 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-3316 (|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))) -3275 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) . T) (((-385 (-525))) -3316 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) ((((-501)) |has| |#1| (-567 (-501)))) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) ((($ $) . T)) ((($ $) . T)) ((((-798)) . T)) @@ -749,12 +749,12 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -3275 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-385 (-525))) . T) (((-525)) . T)) ((((-525) (-135)) . T)) ((((-135)) . T)) (((|#1|) . T)) -(-3275 (|has| |#1| (-21)) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) +(-3316 (|has| |#1| (-21)) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) ((((-108)) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) ((((-108)) . T)) @@ -762,38 +762,38 @@ ((((-501)) |has| |#1| (-567 (-501))) (((-205)) . #0=(|has| |#1| (-953))) (((-357)) . #0#)) ((((-798)) . T)) (|has| |#1| (-762)) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (|has| |#1| (-789)) -(-3275 (|has| |#1| (-160)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-160)) (|has| |#1| (-517))) (|has| |#1| (-517)) (|has| |#1| (-844)) (((|#1|) . T)) (|has| |#1| (-1020)) ((((-798)) . T)) -(-3275 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3275 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3275 (|has| |#1| (-160)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-160)) (|has| |#1| (-517))) ((((-798)) . T)) ((((-798)) . T)) ((((-798)) . T)) (((|#1| (-1173 |#1|) (-1173 |#1|)) . T)) ((((-525) (-135)) . T)) ((($) . T)) -(-3275 (|has| |#4| (-160)) (|has| |#4| (-787)) (|has| |#4| (-977))) -(-3275 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-977))) +(-3316 (|has| |#4| (-160)) (|has| |#4| (-787)) (|has| |#4| (-977))) +(-3316 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-977))) ((((-798)) . T)) (|has| |#1| (-1020)) (((|#1| (-904)) . T)) (((|#1| |#1|) . T)) ((($) . T)) -(-3275 (|has| |#2| (-735)) (|has| |#2| (-787))) -(-3275 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3316 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3316 (|has| |#2| (-735)) (|has| |#2| (-787))) (-12 (|has| |#1| (-450)) (|has| |#2| (-450))) -(-3275 (|has| |#2| (-160)) (|has| |#2| (-669)) (|has| |#2| (-787)) (|has| |#2| (-977))) -(-3275 (-12 (|has| |#1| (-450)) (|has| |#2| (-450))) (-12 (|has| |#1| (-669)) (|has| |#2| (-669)))) +(-3316 (|has| |#2| (-160)) (|has| |#2| (-669)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3316 (-12 (|has| |#1| (-450)) (|has| |#2| (-450))) (-12 (|has| |#1| (-669)) (|has| |#2| (-669)))) (((|#1|) . T)) (|has| |#2| (-735)) -(-3275 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3316 (|has| |#2| (-735)) (|has| |#2| (-787))) (((|#1| |#2|) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (|has| |#2| (-787)) @@ -808,7 +808,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-385 (-525))) . T) (($) . T)) -((($) . T) (((-385 (-525))) -3275 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) +((($) . T) (((-385 (-525))) -3316 (|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))) -3275 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3275 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1165 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) -(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3275 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3275 (|has| |#1| (-341)) (|has| |#1| (-517)))) +((((-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)))) ((((-798)) . T)) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2|) . T)) @@ -830,30 +830,30 @@ (((|#1|) . T)) (((|#1|) |has| |#1| (-160))) ((((-385 (-525))) . T) (((-525)) . T)) -((($ $) -3275 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) -((($) -3275 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($ $) -3316 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($) -3316 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) ((((-135)) . T)) (((|#1|) . T)) ((((-135)) . T)) -((($) -3275 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((|#2|) -3275 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977)))) +((($) -3316 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((|#2|) -3316 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977)))) ((((-135)) . T)) (((|#1| |#2| |#3|) . T)) -(-3275 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) +(-3316 (|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)))) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-977)) (|has| |#1| (-1032))) +(-3316 (|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| $) |has| |#1| (-265 |#1| |#1|))) (((|#1| (-385 (-525))) . T)) (((|#1|) . T)) ((((-1091)) . T)) (|has| |#1| (-517)) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-517)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) @@ -864,7 +864,7 @@ (|has| |#1| (-138)) (|has| |#1| (-136)) (|has| |#4| (-787)) -(((|#2| (-220 (-3594 |#1|) (-713)) (-800 |#1|)) . T)) +(((|#2| (-220 (-3674 |#1|) (-713)) (-800 |#1|)) . T)) (|has| |#3| (-787)) (((|#1| (-497 |#3|) |#3|) . T)) (|has| |#1| (-138)) @@ -878,21 +878,21 @@ (|has| |#1| (-136)) ((((-385 (-525))) |has| |#2| (-341)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) -(-3275 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) -(-3275 (|has| |#1| (-327)) (|has| |#1| (-346))) +(-3316 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-3316 (|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 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) -(-3275 (|has| |#3| (-735)) (|has| |#3| (-787))) -(-3275 (|has| |#3| (-735)) (|has| |#3| (-787))) +(((|#2|) . T) (((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +(-3316 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-3316 (|has| |#3| (-735)) (|has| |#3| (-787))) ((((-798)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) . T) (($) . T)) ((((-641)) . T)) -(-3275 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3316 (|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 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) ((($ $) . 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 (|:| -3420 |#1|) (|:| -2542 |#2|))) |has| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (-288 (-2 (|:| -3420 |#1|) (|:| -2542 |#2|))))) -(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020))) (((-2 (|:| -3420 (-1074)) (|:| -2542 |#1|))) |has| (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|)) (-288 (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|))))) +(((|#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|))))) ((((-798)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -937,10 +937,10 @@ ((($ $) . T) ((#0=(-800 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-770)) (|has| |#1| (-1020)) -(((|#2| |#2|) -3275 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977))) (($ $) |has| |#2| (-160))) -(((|#2|) -3275 (|has| |#2| (-160)) (|has| |#2| (-341)))) -((((-525) (-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -3275 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977))) (($) |has| |#2| (-160))) +(((|#2| |#2|) -3316 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977))) (($ $) |has| |#2| (-160))) +(((|#2|) -3316 (|has| |#2| (-160)) (|has| |#2| (-341)))) +((((-525) (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -3316 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977))) (($) |has| |#2| (-160))) ((((-713)) . T)) ((((-525)) . T)) (|has| |#1| (-517)) @@ -953,29 +953,29 @@ ((((-112 |#1|)) . T)) (((|#1|) . 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T)) -(-3275 (|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))) +(-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))) (-12 (|has| |#3| (-213)) (|has| |#3| (-977))) (|has| |#2| (-1067)) -(((#0=(-51)) . T) (((-2 (|:| -3420 (-1091)) (|:| -2542 #0#))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -3511 (-1091)) (|:| -3631 #0#))) . T)) (((|#1| |#2|) . T)) -(-3275 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-977))) +(-3316 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-977))) (((|#1| (-525) (-1005)) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1| (-385 (-525)) (-1005)) . T)) -((($) -3275 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327)) (|has| |#1| (-517))) (((-385 (-525))) -3275 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) -3316 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327)) (|has| |#1| (-517))) (((-385 (-525))) -3316 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) ((((-525) |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) @@ -983,37 +983,37 @@ (-12 (|has| |#1| (-346)) (|has| |#2| (-346))) ((((-798)) . T)) ((((-1091) |#1|) |has| |#1| (-486 (-1091) |#1|)) ((|#1| |#1|) |has| |#1| (-288 |#1|))) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-346))) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-346))) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) (((|#1|) . 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T)) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) #0#) |has| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (-288 (-2 (|:| -3420 |#1|) (|:| -2542 |#2|))))) +(((|#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|))))) (|has| |#1| (-517)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) ((((-798)) . T)) (((|#1| |#2|) . T)) -(-3275 (|has| |#2| (-429)) (|has| |#2| (-844))) -(-3275 (|has| |#1| (-789)) (|has| |#1| (-1020))) -(-3275 (|has| |#1| (-429)) (|has| |#1| (-844))) +(-3316 (|has| |#2| (-429)) (|has| |#2| (-844))) +(-3316 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-3316 (|has| |#1| (-429)) (|has| |#1| (-844))) ((((-385 (-525))) . T) (((-525)) . T)) ((((-525)) . T)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3275 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3316 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) ((($) . T)) ((((-798)) . T)) (((|#1|) . T)) ((((-805 |#1|)) . T) (($) . T) (((-385 (-525))) . T)) ((((-798)) . T)) -(((|#3| |#3|) -3275 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-977))) (($ $) |has| |#3| (-160))) +(((|#3| |#3|) -3316 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-977))) (($ $) |has| |#3| (-160))) (|has| |#1| (-953)) ((((-798)) . T)) -(((|#3|) -3275 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-977))) (($) |has| |#3| (-160))) +(((|#3|) -3316 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-977))) (($) |has| |#3| (-160))) ((((-525) (-108)) . T)) (((|#1|) |has| |#1| (-288 |#1|))) (|has| |#1| (-346)) @@ -1021,31 +1021,31 @@ (|has| |#1| (-346)) ((((-1091) $) |has| |#1| (-486 (-1091) $)) (($ $) |has| |#1| (-288 $)) ((|#1| |#1|) |has| |#1| (-288 |#1|)) (((-1091) |#1|) |has| |#1| (-486 (-1091) |#1|))) ((((-1091)) |has| |#1| (-835 (-1091)))) -(-3275 (-12 (|has| |#1| (-213)) (|has| |#1| (-341))) (|has| |#1| (-327))) +(-3316 (-12 (|has| |#1| (-213)) (|has| |#1| (-341))) (|has| |#1| (-327))) ((((-366) (-1038)) . T)) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-366) |#1|) . T)) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-1020)) ((((-798)) . T)) ((((-798)) . T)) ((((-845 |#1|)) . T)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3275 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) -((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) -3275 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3316 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) +((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) -3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844)))) (((|#1| |#2|) . T)) ((($) . T)) (((|#1| |#1|) . T)) (((#0=(-805 |#1|)) |has| #0# (-288 #0#))) (((|#1| |#2|) . T)) -(-3275 (|has| |#2| (-735)) (|has| |#2| (-787))) -(-3275 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3316 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3316 (|has| |#2| (-735)) (|has| |#2| (-787))) (-12 (|has| |#1| (-735)) (|has| |#2| (-735))) (((|#1|) . T)) (-12 (|has| |#1| (-735)) (|has| |#2| (-735))) -(-3275 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3316 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) (|has| |#1| (-1113)) (((#0=(-525) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) ((((-385 (-525))) . T) (($) . T)) @@ -1056,8 +1056,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-385 (-525)) #0#) . T)) (|has| |#1| (-341)) ((((-525)) . T) (((-385 (-525))) . T) (($) . T)) -((($ $) . T) ((#0=(-385 (-525)) #0#) -3275 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1| |#1|) . T)) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((($ $) . T) ((#0=(-385 (-525)) #0#) -3316 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1| |#1|) . T)) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#1|) . T) (($) . T) (((-385 (-525))) . T)) ((((-798)) . T)) ((((-798)) . T)) @@ -1072,14 +1072,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-787)) (|has| |#1| (-787)) -((($) . T) (((-385 (-525))) -3275 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) -(-3275 (|has| |#1| (-160)) (|has| |#1| (-517))) -(((#0=(-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) #0#) |has| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (-288 (-2 (|:| -3420 (-1091)) (|:| -2542 (-51)))))) +((($) . 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)))))) ((($) . T)) (|has| |#2| (-789)) ((($) . T)) (((|#2|) |has| |#2| (-1020))) -((((-798)) -3275 (|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)) -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)) (|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 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T) ((|#1| |#2|) . T)) +((((-525) (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T) ((|#1| |#2|) . T)) ((((-385 (-525))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) ((((-798)) . T)) ((((-845 |#1|)) . T)) (|has| |#1| (-341)) @@ -1115,31 +1115,31 @@ ((($) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-160))) -((((-525) (-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T) ((|#1| |#2|) . T)) +((((-525) (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) ((($) |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)) -(-3275 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) -(((#0=(-385 (-525)) #0#) -3275 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($ $) -3275 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1| |#1|) . T)) +(-3316 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(((#0=(-385 (-525)) #0#) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($ $) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1| |#1|) . T)) ((((-385 (-525))) |has| |#1| (-968 (-525))) (((-525)) |has| |#1| (-968 (-525))) (((-1091)) |has| |#1| (-968 (-1091))) ((|#1|) . T)) ((((-525) |#2|) . T)) ((((-385 (-525))) |has| |#1| (-968 (-385 (-525)))) (((-525)) |has| |#1| (-968 (-525))) ((|#1|) . T)) ((((-525)) |has| |#1| (-821 (-525))) (((-357)) |has| |#1| (-821 (-357)))) -((((-385 (-525))) -3275 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3275 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1|) . T)) +((((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1|) . T)) (((|#1|) . T)) ((((-592 |#4|)) . T) (((-798)) . T)) ((((-501)) |has| |#4| (-567 (-501)))) @@ -1152,17 +1152,17 @@ (((|#1|) . T)) (((|#2|) . T)) ((((-1091)) |has| (-385 |#2|) (-835 (-1091)))) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) #0#) |has| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (-288 (-2 (|:| -3420 |#1|) (|:| -2542 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) #0#) |has| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (-288 (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-798)) -3275 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-566 (-798))) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-669)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-977)) (|has| |#3| (-1020))) (((-1173 |#3|)) . T)) +((((-798)) -3316 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-566 (-798))) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-669)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-977)) (|has| |#3| (-1020))) (((-1173 |#3|)) . T)) ((((-525) |#2|) . T)) -(-3275 (|has| |#1| (-789)) (|has| |#1| (-1020))) -(((|#2| |#2|) -3275 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977))) (($ $) |has| |#2| (-160))) +(-3316 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(((|#2| |#2|) -3316 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977))) (($ $) |has| |#2| (-160))) ((((-798)) . T)) ((((-798)) . T)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T) ((|#2|) . T)) ((((-798)) . T)) ((((-798)) . T)) ((((-1074) (-1091) (-525) (-205) (-798)) . T)) @@ -1197,8 +1197,8 @@ (|has| |#1| (-37 (-385 (-525)))) ((((-798)) . T)) ((((-501)) |has| |#1| (-567 (-501)))) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) -(((|#2|) -3275 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977))) (($) |has| |#2| (-160))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +(((|#2|) -3316 (|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)) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3316 (|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 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#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) (($) . T) (((-385 (-525))) . T)) -((((-2 (|:| -3420 (-1074)) (|:| -2542 |#1|))) . T)) +((((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) ((((-525) |#2|) . T)) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#2|) . T)) ((((-525) |#3|) . T)) (((|#2|) . T)) @@ -1269,7 +1269,7 @@ (((|#3|) -12 (|has| |#3| (-288 |#3|)) (|has| |#3| (-1020)))) (((|#2|) . T)) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) #0#) |has| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (-288 (-2 (|:| -3420 |#1|) (|:| -2542 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) #0#) |has| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (-288 (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))))) (((|#2| |#2|) . T)) (|has| |#2| (-341)) (((|#2|) . T) (((-525)) |has| |#2| (-968 (-525))) (((-385 (-525))) |has| |#2| (-968 (-385 (-525))))) @@ -1299,19 +1299,19 @@ (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1| |#2|) . T)) ((((-525) (-135)) . T)) -(((#0=(-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) #0#) |has| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (-288 (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) -((($) -3275 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +(((#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)))) +((($) -3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (|has| |#1| (-789)) (((|#2| (-713) (-1005)) . T)) (((|#1| |#2|) . T)) -(-3275 (|has| |#1| (-160)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-160)) (|has| |#1| (-517))) (|has| |#1| (-733)) (((|#1|) |has| |#1| (-160))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-3275 (|has| |#1| (-138)) (-12 (|has| |#1| (-341)) (|has| |#2| (-138)))) -(-3275 (|has| |#1| (-136)) (-12 (|has| |#1| (-341)) (|has| |#2| (-136)))) +(-3316 (|has| |#1| (-138)) (-12 (|has| |#1| (-341)) (|has| |#2| (-138)))) +(-3316 (|has| |#1| (-136)) (-12 (|has| |#1| (-341)) (|has| |#2| (-136)))) (((|#4|) . T)) (|has| |#1| (-136)) ((((-1074) |#1|) . T)) @@ -1324,10 +1324,10 @@ (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#3|) . T)) ((((-1165 |#1| |#2| |#3|)) |has| |#1| (-341))) -(-3275 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-3316 (|has| |#1| (-789)) (|has| |#1| (-1020))) (((|#1|) . T)) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020))) (((-892 |#1|)) . T)) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020))) (((-892 |#1|)) . T)) (|has| |#1| (-787)) (|has| |#1| (-787)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) @@ -1340,8 +1340,8 @@ ((($) . T)) ((((-366) (-1074)) . T)) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) -((((-798)) -3275 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-566 (-798))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (((-1173 |#2|)) . T)) -(((#0=(-51)) . T) (((-2 (|:| -3420 (-1074)) (|:| -2542 #0#))) . T)) +((((-798)) -3316 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-566 (-798))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (((-1173 |#2|)) . T)) +(((#0=(-51)) . T) (((-2 (|:| -3511 (-1074)) (|:| -3631 #0#))) . T)) (((|#1|) . T)) ((((-798)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) @@ -1349,7 +1349,7 @@ (|has| |#2| (-136)) (|has| |#2| (-138)) (|has| |#1| (-450)) -(-3275 (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) +(-3316 (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) (|has| |#1| (-341)) ((((-798)) . T)) (|has| |#1| (-37 (-385 (-525)))) @@ -1358,8 +1358,8 @@ (|has| |#1| (-787)) (|has| |#1| (-787)) ((((-798)) . T)) -((((-385 (-525))) -3275 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3275 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1165 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) -(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3275 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3275 (|has| |#1| (-341)) (|has| |#1| (-517)))) +((((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -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))) (($) -3316 (|has| |#1| (-341)) (|has| |#1| (-517)))) ((($) |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 (-3594 |#1|) (-713)) (-800 |#1|)) . T)) +(((|#2| (-458 (-3674 |#1|) (-713)) (-800 |#1|)) . T)) ((((-385 (-525))) . #0=(|has| |#2| (-341))) (($) . #0#)) (((|#1| (-497 (-1091)) (-1091)) . T)) (((|#1|) . T)) @@ -1387,16 +1387,16 @@ (|has| |#1| (-138)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3420 (-1074)) (|:| -2542 |#1|))) . T)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) -((((-2 (|:| -3420 (-1091)) (|:| -2542 (-51)))) . T)) +(((|#1|) . T) (((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))) . T)) ((((-1089 |#1| |#2| |#3|)) |has| |#1| (-341))) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) ((((-1091) (-51)) . T)) ((($ $) . T)) (((|#1| (-525)) . T)) ((((-845 |#1|)) . T)) -(((|#1|) -3275 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977))) (($) -3275 (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)))) +(((|#1|) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977))) (($) -3316 (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)))) (((|#1|) . T) (((-525)) |has| |#1| (-968 (-525))) (((-385 (-525))) |has| |#1| (-968 (-385 (-525))))) (|has| |#1| (-789)) (|has| |#1| (-789)) @@ -1411,13 +1411,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1020)))) (((|#1|) |has| |#1| (-160))) (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1020)))) -(((|#3|) -3275 (|has| |#3| (-160)) (|has| |#3| (-341)))) +(((|#3|) -3316 (|has| |#3| (-160)) (|has| |#3| (-341)))) (|has| |#2| (-789)) (|has| |#1| (-789)) -(-3275 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-844))) +(-3316 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-844))) ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) ((((-525) |#2|) . T)) -(((|#2|) -3275 (|has| |#2| (-160)) (|has| |#2| (-341)))) +(((|#2|) -3316 (|has| |#2| (-160)) (|has| |#2| (-341)))) (|has| |#1| (-327)) (((|#3| |#3|) -12 (|has| |#3| (-288 |#3|)) (|has| |#3| (-1020)))) ((($) . T) (((-385 (-525))) . T)) @@ -1425,7 +1425,7 @@ (|has| |#1| (-762)) (|has| |#1| (-762)) (((|#1|) . T)) -(-3275 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3316 (|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)))) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-37 (-385 (-525)))) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) ((((-1091)) |has| |#1| (-835 (-1091))) (((-1005)) . T)) (((|#1|) . T)) (|has| |#1| (-787)) -(((#0=(-2 (|:| -3420 (-1074)) (|:| -2542 (-51))) #0#) |has| (-2 (|:| -3420 (-1074)) (|:| -2542 (-51))) (-288 (-2 (|:| -3420 (-1074)) (|:| -2542 (-51)))))) +(((#0=(-2 (|:| -3511 (-1074)) (|:| -3631 (-51))) #0#) |has| (-2 (|:| -3511 (-1074)) (|:| -3631 (-51))) (-288 (-2 (|:| -3511 (-1074)) (|:| -3631 (-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))) -(-3275 (|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))) +(-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))) (((|#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 (|:| -3420 (-1074)) (|:| -2542 |#1|)) #0#) |has| (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|)) (-288 (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|))))) -(-3275 (|has| |#2| (-429)) (|has| |#2| (-844))) -(-3275 (|has| |#1| (-429)) (|has| |#1| (-844))) +(((|#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|) . T) (($) . T)) (((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) (((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(((|#3|) -3275 (|has| |#3| (-160)) (|has| |#3| (-341)))) +(((|#3|) -3316 (|has| |#3| (-160)) (|has| |#3| (-341)))) (|has| |#1| (-789)) (|has| |#1| (-517)) ((((-538 |#1|)) . T)) ((($) . T)) (((|#2|) . T)) -(-3275 (-12 (|has| |#1| (-341)) (|has| |#2| (-762))) (-12 (|has| |#1| (-341)) (|has| |#2| (-789)))) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (-12 (|has| |#1| (-341)) (|has| |#2| (-762))) (-12 (|has| |#1| (-341)) (|has| |#2| (-789)))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) ((((-845 |#1|)) . T)) (((|#1| (-469 |#1| |#3|) (-469 |#1| |#2|)) . T)) (((|#1| |#4| |#5|) . T)) (((|#1| (-713)) . 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T)) +((((-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))) . T)) ((((-385 |#2|)) . T) (((-385 (-525))) . T) (($) . 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)) (($) -3275 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3316 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) ((((-798)) . T)) ((((-798)) . T)) ((((-798)) . T)) (((|#2|) . T)) -(-3275 (|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))) -(-3275 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-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))) ((((-385 (-525))) |has| |#1| (-968 (-385 (-525)))) (((-525)) |has| |#1| (-968 (-525))) ((|#1|) . T)) (|has| |#1| (-1113)) (|has| |#1| (-1113)) -(-3275 (|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))) +(-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))) (|has| |#1| (-1113)) (|has| |#1| (-1113)) (((|#3| |#3|) . T)) @@ -1537,43 +1537,43 @@ (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) ((((-1074) (-51)) . T)) (|has| |#1| (-1020)) -(-3275 (|has| |#2| (-762)) (|has| |#2| (-789))) +(-3316 (|has| |#2| (-762)) (|has| |#2| (-789))) (((|#1|) . T)) -((($) -3275 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -3275 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . 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T)) -(-3275 (|has| |#1| (-429)) (|has| |#1| (-844))) +(-3316 (|has| |#1| (-429)) (|has| |#1| (-844))) (|has| |#2| (-844)) (|has| |#1| (-341)) (((|#2|) |has| |#2| (-1020))) -(-3275 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((($) . T) ((|#2|) . T)) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-844))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-844))) (|has| |#1| (-844)) (|has| |#1| (-844)) ((((-501)) . T) (((-385 (-1087 (-525)))) . T) (((-205)) . T) (((-357)) . T)) ((((-357)) . T) (((-205)) . T) (((-798)) . T)) (|has| |#1| (-844)) -(-3275 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-3316 (|has| |#1| (-789)) (|has| |#1| (-1020))) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) ((($ $) . T)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) ((($ $) . T)) ((((-525) (-108)) . T)) ((($) . T)) (((|#1|) . T)) ((((-525)) . T)) ((((-108)) . T)) -(-3275 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|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 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) ((((-798)) . T)) (|has| |#1| (-1020)) ((((-1074) |#1|) . T)) @@ -1615,18 +1615,18 @@ (((|#1|) . T)) ((((-525)) . T)) ((((-798)) . T)) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-327))) +(-3316 (|has| |#1| (-136)) (|has| |#1| (-327))) (|has| |#1| (-138)) ((((-798)) . T)) (((|#3|) . T)) -(-3275 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-977))) +(-3316 (|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))) -3275 (-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 $)) . T) ((|#1|) . T) (((-525)) |has| |#1| (-968 (-525))) (((-385 (-525))) -3316 (-12 (|has| |#1| (-517)) (|has| |#1| (-968 (-525)))) (|has| |#1| (-968 (-385 (-525))))) (((-385 (-887 |#1|))) |has| |#1| (-517)) (((-887 |#1|)) |has| |#1| (-977)) (((-1091)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-713)) . T)) -((($) -3275 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3275 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) +((($) -3316 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3316 (|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)) . 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T)) -(-3275 (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +(-3316 (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#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))) -(-3275 (|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))) +(-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))) (((|#2|) |has| |#2| (-160))) (((|#1|) |has| |#1| (-160))) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) -((((-2 (|:| -3420 (-1074)) (|:| -2542 |#1|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) ((((-798)) . T)) (|has| |#3| (-787)) ((((-798)) . T)) ((((-1158 |#2| |#3| |#4|) (-297 |#2| |#3| |#4|)) . T)) ((((-798)) . T)) -(((|#1| |#1|) -3275 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977)))) +(((|#1| |#1|) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977)))) (((|#1|) . T)) ((((-525)) . T)) ((((-525)) . T)) -(((|#1|) -3275 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977)))) +(((|#1|) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977)))) (((|#2|) |has| |#2| (-341))) ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-341))) (|has| |#1| (-789)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3420 (-1091)) (|:| -2542 (-51)))) |has| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (-288 (-2 (|:| -3420 (-1091)) (|:| -2542 (-51)))))) -(-3275 (|has| |#1| (-429)) (|has| |#1| (-844))) +((((-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))) |has| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (-288 (-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))))) +(-3316 (|has| |#1| (-429)) (|has| |#1| (-844))) (((|#2|) . T) (((-525)) |has| |#2| (-588 (-525)))) ((((-798)) . T)) ((((-798)) . T)) @@ -1724,18 +1724,18 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (((|#1|) . T)) -(-3275 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3316 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) (((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) . T) (($ $) . T)) ((((-798)) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (|has| |#1| (-341)) (|has| |#1| (-341)) (|has| (-385 |#2|) (-213)) (|has| |#1| (-844)) (((|#2|) |has| |#2| (-977))) -(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) |has| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (-288 (-2 (|:| -3420 |#1|) (|:| -2542 |#2|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) |has| (-2 (|:| -3511 |#1|) (|:| -3631 |#2|)) (-288 (-2 (|:| -3511 |#1|) (|:| -3631 |#2|))))) (|has| |#1| (-341)) (((|#1|) |has| |#1| (-160))) (((|#1| |#1|) . T)) @@ -1760,7 +1760,7 @@ (((|#1| (-385 (-525)) (-1005)) . T)) (((|#1| (-713) (-1005)) . T)) (((#0=(-385 |#2|) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-525)) -3275 (|has| (-385 (-525)) (-968 (-525))) (|has| |#1| (-968 (-525)))) (((-385 (-525))) . T)) +(((|#1|) . T) (((-525)) -3316 (|has| (-385 (-525)) (-968 (-525))) (|has| |#1| (-968 (-525)))) (((-385 (-525))) . T)) (((|#1| (-556 |#1| |#3|) (-556 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) @@ -1779,24 +1779,24 @@ ((((-641)) . T)) (((|#2|) |has| |#2| (-160))) (|has| |#2| (-787)) -((((-108)) |has| |#1| (-1020)) (((-798)) -3275 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020)))) +((((-108)) |has| |#1| (-1020)) (((-798)) -3316 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3420 (-1074)) (|:| -2542 (-51)))) . T)) +((((-2 (|:| -3511 (-1074)) (|:| -3631 (-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 (|:| -3420 |#1|) (|:| -2542 |#2|))) |has| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (-288 (-2 (|:| -3420 |#1|) (|:| -2542 |#2|))))) +(((|#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|))))) ((((-357)) . T)) ((((-641)) . T)) ((((-385 (-525))) . #0=(|has| |#2| (-341))) (($) . #0#)) (((|#1|) |has| |#1| (-160))) ((((-385 (-887 |#1|))) . T)) (((|#2| |#2|) . T)) -(-3275 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) -(-3275 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3316 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (((|#2|) . T)) (|has| |#2| (-789)) (((|#3|) |has| |#3| (-977))) @@ -1806,14 +1806,14 @@ (|has| |#1| (-789)) ((((-1091)) |has| |#2| (-835 (-1091)))) ((((-798)) . T)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) ((((-385 (-525))) . T) (($) . T)) (|has| |#1| (-450)) (|has| |#1| (-346)) (|has| |#1| (-346)) (|has| |#1| (-346)) (|has| |#1| (-341)) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-977)) (|has| |#1| (-1032))) +(-3316 (|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 (|:| -3420 (-1074)) (|:| -2542 |#1|))) . T)) +((((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-138)) (|has| |#1| (-136)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) |has| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (-288 (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)))) ((|#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|) . 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 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) ((($ $) . T) (((-565 $) $) . T)) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) ((($) . T) (((-1159 |#1| |#2| |#3| |#4|)) . T) (((-385 (-525))) . T)) -((($) -3275 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-517))) +((($) -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))) (|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)) -(-3275 (|has| |#2| (-429)) (|has| |#2| (-844))) +(-3316 (|has| |#2| (-429)) (|has| |#2| (-844))) (((|#1|) . T)) (|has| |#1| (-789)) (|has| |#1| (-789)) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3316 (|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)) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|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)) -(-3275 (-12 (|has| (-1165 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) -(-3275 (-12 (|has| (-1165 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) +(-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))) (|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))) -(-3275 (|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))) +(-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))) ((((-525)) . T)) (((|#1| $) |has| |#1| (-265 |#1| |#1|))) ((((-385 (-525))) . T) (($) . T) (((-385 |#1|)) . T) ((|#1|) . T)) ((((-798)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -3275 (|has| |#1| (-269)) (|has| |#1| (-341))) ((#0=(-385 (-525)) #0#) |has| |#1| (-341))) -((((-2 (|:| -3420 (-1091)) (|:| -2542 (-51)))) . T)) +(((|#1| |#1|) . T) (($ $) -3316 (|has| |#1| (-269)) (|has| |#1| (-341))) ((#0=(-385 (-525)) #0#) |has| |#1| (-341))) +((((-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))) . T)) ((($) . T)) ((((-525) |#1|) . T)) ((((-1091)) |has| (-385 |#2|) (-835 (-1091)))) -(((|#1|) . T) (($) -3275 (|has| |#1| (-269)) (|has| |#1| (-341))) (((-385 (-525))) |has| |#1| (-341))) +(((|#1|) . T) (($) -3316 (|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)))) -(-3275 (|has| |#4| (-735)) (|has| |#4| (-787))) -(-3275 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-3316 (|has| |#4| (-735)) (|has| |#4| (-787))) +(-3316 (|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) (($) . T)) -(-3275 (|has| |#1| (-429)) (|has| |#1| (-1131))) +(-3316 (|has| |#1| (-429)) (|has| |#1| (-1131))) ((($) . 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)))) -((($) -3275 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -3275 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) -3316 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -3316 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) ((((-525)) . T)) (|has| |#1| (-37 (-385 (-525)))) -((((-2 (|:| -3420 (-1074)) (|:| -2542 (-51)))) |has| (-2 (|:| -3420 (-1074)) (|:| -2542 (-51))) (-288 (-2 (|:| -3420 (-1074)) (|:| -2542 (-51)))))) +((((-2 (|:| -3511 (-1074)) (|:| -3631 (-51)))) |has| (-2 (|:| -3511 (-1074)) (|:| -3631 (-51))) (-288 (-2 (|:| -3511 (-1074)) (|:| -3631 (-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)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (|has| |#1| (-1113)) (((|#1|) . 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T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-845 |#1|)) . T)) ((($) . 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 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-787)) -(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020))) (((-2 (|:| -3420 (-1074)) (|:| -2542 |#1|))) |has| (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|)) (-288 (-2 (|:| -3420 (-1074)) (|:| -2542 |#1|))))) +(((|#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|))))) (|has| |#1| (-1020)) (|has| |#1| (-341)) (|has| |#1| (-789)) @@ -2003,16 +2003,16 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-385 (-525))) . T)) -((($) -3275 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3275 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) +((($) -3316 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) (|has| |#1| (-136)) (|has| |#1| (-138)) -(-3275 (-12 (|has| (-1089 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) -(-3275 (-12 (|has| (-1089 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) +(-3316 (-12 (|has| (-1089 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) +(-3316 (-12 (|has| (-1089 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-138)) (|has| |#1| (-136)) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) ((((-1165 |#1| |#2| |#3|)) |has| |#1| (-341))) (|has| |#1| (-787)) (((|#1| |#2|) . T)) @@ -2035,9 +2035,9 @@ ((((-798)) . T)) ((((-798)) . T)) ((((-501)) |has| |#1| (-567 (-501)))) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) ((((-1091) |#1|) |has| |#1| (-486 (-1091) |#1|)) ((|#1| |#1|) |has| |#1| (-288 |#1|))) -(((|#1|) -3275 (|has| |#1| (-160)) (|has| |#1| (-341)))) +(((|#1|) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)))) ((((-294 |#1|)) . T)) (((|#2|) |has| |#2| (-341))) (((|#2|) . T)) @@ -2058,14 +2058,14 @@ (|has| |#1| (-136)) (|has| |#1| (-138)) ((($ $) . T)) -(-3275 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020))) +(-3316 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020))) (|has| |#1| (-517)) (((|#2|) . T)) ((((-525)) . T)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) +(-3316 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) ((((-538 |#1|)) . T)) ((($) . T)) (((|#1| (-57 |#1|) (-57 |#1|)) . T)) @@ -2090,12 +2090,12 @@ (((|#1| |#2|) . T)) ((((-1091) |#1|) . T)) (((|#4|) . T)) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3316 (|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)) -(-3275 (|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))) +(-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))) (((#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)) -(-3275 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-3316 (|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)) -(-3275 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3316 (|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)) ((($) . T)) (|has| |#1| (-341)) -(-3275 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327)) (|has| |#1| (-517))) (|has| |#1| (-341)) ((($) . T) ((#0=(-1158 |#2| |#3| |#4|)) . T) (((-385 (-525))) |has| #0# (-37 (-385 (-525))))) (((|#1| |#2|) . T)) ((((-1089 |#1| |#2| |#3|)) |has| |#1| (-341))) -(-3275 (-12 (|has| |#1| (-286)) (|has| |#1| (-844))) (|has| |#1| (-341)) (|has| |#1| (-327))) -(-3275 (|has| |#1| (-835 (-1091))) (|has| |#1| (-977))) +(-3316 (-12 (|has| |#1| (-286)) (|has| |#1| (-844))) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3316 (|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|) -3275 (|has| |#2| (-6 (-4257 "*"))) (|has| |#2| (-160)))) -(-3275 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) -(-3275 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(((|#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))) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#1| (-844)) (((|#2|) |has| |#2| (-160))) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#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 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) -((((-2 (|:| -3420 (-1074)) (|:| -2542 (-51)))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3511 (-1074)) (|:| -3631 (-51)))) . T)) (((|#1|) . T)) ((((-798)) . T)) (((|#1| |#2|) . T)) (((|#1| (-385 (-525))) . T)) (((|#1|) . T)) -(-3275 (|has| |#1| (-269)) (|has| |#1| (-341))) +(-3316 (|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 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#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 (|:| -3420 (-1074)) (|:| -2542 |#1|))) . T)) +((((-2 (|:| -3511 (-1074)) (|:| -3631 |#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) (($) . T)) -(-3275 (|has| |#4| (-160)) (|has| |#4| (-669)) (|has| |#4| (-787)) (|has| |#4| (-977))) -(-3275 (|has| |#3| (-160)) (|has| |#3| (-669)) (|has| |#3| (-787)) (|has| |#3| (-977))) +(-3316 (|has| |#4| (-160)) (|has| |#4| (-669)) (|has| |#4| (-787)) (|has| |#4| (-977))) +(-3316 (|has| |#3| (-160)) (|has| |#3| (-669)) (|has| |#3| (-787)) (|has| |#3| (-977))) ((((-1091) (-51)) . T)) -(-3275 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3275 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) -(-3275 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3316 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3316 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-787)) (|has| |#2| (-977))) (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#2|) . T)) @@ -2250,12 +2250,12 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (|has| |#1| (-762)) (((#0=(-845 |#1|) #0#) . T) (($ $) . T) ((#1=(-385 (-525)) #1#) . T)) ((((-385 |#2|)) . T)) (|has| |#1| (-787)) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) . T) ((#1=(-525) #1#) . T) (($ $) . T)) ((((-845 |#1|)) . T) (($) . 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)) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-346))) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-346))) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-346))) -((((-2 (|:| -3420 (-1091)) (|:| -2542 (-51)))) . T)) -(((#0=(-51)) . T) (((-2 (|:| -3420 (-1091)) (|:| -2542 #0#))) . 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)) (|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# $) . T) (($ $) . T)) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-327))) (((#0=(-385 (-525)) #0#) . T) ((#1=(-641) #1#) . T) (($ $) . T)) ((((-294 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) |has| |#1| (-341))) (|has| |#1| (-1020)) (((|#1|) . T)) -(((|#1|) -3275 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) -(((|#1|) -3275 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) +(((|#1|) -3316 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) +(((|#1|) -3316 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) (((|#2|) . T)) ((((-385 (-525))) . T) (((-641)) . T) (($) . T)) (((|#3| |#3|) . T)) @@ -2302,7 +2302,7 @@ (((|#2|) . T)) (((|#1|) . T)) ((((-525)) . T)) -(-3275 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (((|#2|) . T) (((-525)) |has| |#2| (-588 (-525)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2339,7 +2339,7 @@ (|has| |#2| (-953)) ((($) . T)) (|has| |#1| (-844)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2347,24 +2347,24 @@ ((($) . T)) (|has| |#1| (-341)) ((((-845 |#1|)) . T)) -((($) -3275 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3316 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) -(-3275 (|has| |#1| (-346)) (|has| |#1| (-789))) +(-3316 (|has| |#1| (-346)) (|has| |#1| (-789))) (((|#1|) . T)) ((((-798)) . T)) ((((-1091)) -12 (|has| |#1| (-15 * (|#1| (-385 (-525)) |#1|))) (|has| |#1| (-835 (-1091))))) ((((-385 |#2|) |#3|) . T)) ((($) . T) (((-385 (-525))) . T)) ((((-713) |#1|) . T)) -(((|#2| (-220 (-3594 |#1|) (-713))) . T)) +(((|#2| (-220 (-3674 |#1|) (-713))) . T)) (((|#1| (-497 |#3|)) . T)) ((((-385 (-525))) . T)) -(-3275 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((((-798)) . T)) -(((#0=(-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) #0#) |has| (-2 (|:| -3420 (-1091)) (|:| -2542 (-51))) (-288 (-2 (|:| -3420 (-1091)) (|:| -2542 (-51)))))) +(((#0=(-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) #0#) |has| (-2 (|:| -3511 (-1091)) (|:| -3631 (-51))) (-288 (-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))))) (|has| |#1| (-844)) (|has| |#2| (-341)) -(-3275 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3316 (|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)))) -(-3275 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3316 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-37 (-385 (-525)))) (-12 (|has| |#1| (-510)) (|has| |#1| (-770))) ((((-798)) . T)) -((((-1091)) -3275 (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-835 (-1091)))) (-12 (|has| |#1| (-341)) (|has| |#2| (-835 (-1091)))))) +((((-1091)) -3316 (-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 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#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)) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-341)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|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)) -(-3275 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3316 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) (((|#2|) . T)) (((|#2|) . T)) -(-3275 (|has| |#2| (-160)) (|has| |#2| (-669)) (|has| |#2| (-787)) (|has| |#2| (-977))) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) -((((-2 (|:| -3420 (-1074)) (|:| -2542 |#1|))) . T)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#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)) (|has| |#1| (-37 (-385 (-525)))) (((|#1| |#2|) . T)) (|has| |#1| (-37 (-385 (-525)))) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) ((((-1074) |#1|) . T)) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3316 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) ((((-538 |#1|)) . T)) ((($) . T)) @@ -2450,7 +2450,7 @@ (|has| |#1| (-517)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-327))) +(-3316 (|has| |#1| (-136)) (|has| |#1| (-327))) (|has| |#1| (-138)) ((((-798)) . T)) ((($) . T)) @@ -2475,7 +2475,7 @@ (|has| |#1| (-733)) (|has| |#1| (-733)) ((((-501)) |has| |#1| (-567 (-501)))) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) +((((-798)) -3316 (|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)) -(-3275 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-3316 (|has| |#2| (-735)) (|has| |#2| (-787))) ((((-157 (-357))) . T) (((-205)) . T) (((-357)) . T)) ((((-798)) . T)) ((((-798)) . T)) @@ -2508,9 +2508,9 @@ (((|#1|) . T) (($) . T) (((-385 (-525))) . T)) (|has| |#1| (-341)) (|has| |#1| (-341)) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) -(-3275 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +(-3316 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1091))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020))) (|has| |#1| (-1067)) ((((-525) |#1|) . T)) (((|#1|) . T)) @@ -2528,8 +2528,8 @@ (((|#1|) . T)) (|has| |#1| (-517)) ((((-385 |#2|)) . T) (((-385 (-525))) . T) (($) . T)) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|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|))))) -(-3275 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-3316 (|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 (|:| -3420 (-1074)) (|:| -2542 (-51)))) . T)) +((((-2 (|:| -3511 (-1074)) (|:| -3631 (-51)))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) ((((-798)) . T)) ((((-798)) . T)) -(-3275 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-3316 (|has| |#3| (-735)) (|has| |#3| (-787))) ((((-798)) . T)) ((((-798)) . T)) (((|#1|) . T)) @@ -2562,8 +2562,8 @@ ((((-525)) . T)) (((|#3|) . T)) ((((-798)) . T)) -(-3275 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) -(-3275 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) +(-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))) (((#0=(-538 |#1|) #0#) . T) (($ $) . T) ((#1=(-385 (-525)) #1#) . T)) ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) (((|#1|) |has| |#1| (-160))) @@ -2576,7 +2576,7 @@ (((|#1|) . T)) ((((-798)) |has| |#1| (-566 (-798)))) ((((-273 |#3|)) . T)) -(((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525)))) ((|#2| |#2|) . T) (($ $) -3275 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) +(((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525)))) ((|#2| |#2|) . T) (($ $) -3316 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . 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) (($) . T)) -((($ $) -3275 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) -((($ $) -3275 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($ $) -3316 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($ $) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) (((|#2|) . T)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) . T) (($) -3275 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) . T) (($) -3316 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) (((|#2|) . T) ((|#6|) . T)) -((($ $) -3275 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($ $) -3316 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) ((((-798)) . T)) -((($) -3275 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) -((($) -3275 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3316 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3316 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (|has| |#2| (-844)) (|has| |#1| (-844)) -((($) -3275 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3316 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1|) . T)) -((((-2 (|:| -3420 (-1074)) (|:| -2542 |#1|))) . T)) +((((-2 (|:| -3511 (-1074)) (|:| -3631 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) @@ -2611,10 +2611,10 @@ (((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) (((#0=(-385 (-525)) #0#) . T)) ((((-385 (-525))) . T)) -(-3275 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3316 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) (((|#1|) . T)) (((|#1|) . T)) -(-3275 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3316 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((((-501)) . T)) ((((-798)) . T)) ((((-1091)) |has| |#2| (-835 (-1091))) (((-1005)) . T)) @@ -2628,12 +2628,12 @@ ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) ((((-1091)) |has| |#1| (-835 (-1091)))) ((((-845 |#1|)) . T) (((-385 (-525))) . T) (($) . T)) -((($) . T) (((-385 (-525))) -3275 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) -(((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525)))) ((|#1| |#1|) . T) (($ $) -3275 (|has| |#1| (-160)) (|has| |#1| (-517)))) +((($) . 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))) . T)) (((|#1|) . T) (((-385 (-525))) . T) (((-525)) . T) (($) . T)) (((|#2|) |has| |#2| (-977)) (((-525)) -12 (|has| |#2| (-588 (-525))) (|has| |#2| (-977)))) -((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T) (($) -3275 (|has| |#1| (-160)) (|has| |#1| (-517)))) +((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T) (($) -3316 (|has| |#1| (-160)) (|has| |#1| (-517)))) (|has| |#1| (-517)) (((|#1|) |has| |#1| (-341))) ((((-525)) . T)) @@ -2652,8 +2652,8 @@ ((((-798)) . T)) (|has| |#2| (-762)) (|has| |#2| (-762)) -((((-385 (-525))) -3275 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#2|) |has| |#1| (-341)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-385 (-525))) -3275 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) . T)) +((((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#2|) |has| |#1| (-341)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-385 (-525))) -3316 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1|) . T) (((-525)) |has| |#1| (-968 (-525))) (((-385 (-525))) |has| |#1| (-968 (-385 (-525))))) ((((-525)) |has| |#1| (-821 (-525))) (((-357)) |has| |#1| (-821 (-357)))) @@ -2679,12 +2679,12 @@ (((|#2| (-713)) . T)) ((((-1091)) . T)) ((((-805 |#1|)) . 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T)) +((((-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))) . T)) ((((-501)) |has| |#2| (-567 (-501))) (((-827 (-357))) |has| |#2| (-567 (-827 (-357)))) (((-827 (-525))) |has| |#2| (-567 (-827 (-525))))) ((((-798)) . T)) ((((-798)) . T)) @@ -2743,11 +2743,11 @@ ((((-385 |#2|) |#3|) . T)) (((|#1|) . T)) (|has| |#1| (-1020)) -(((|#2| (-458 (-3594 |#1|) (-713))) . T)) +(((|#2| (-458 (-3674 |#1|) (-713))) . T)) ((((-525) |#1|) . T)) (((|#2| |#2|) . T)) (((|#1| (-497 (-1091))) . T)) -(-3275 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3316 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((((-525)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -2757,9 +2757,9 @@ ((($) . T) (((-385 (-525))) . T)) ((($) . T)) ((($) . T)) -(-3275 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-3316 (|has| |#1| (-789)) (|has| |#1| (-1020))) (((|#1|) . 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T)) -(-3275 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) -(-3275 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-126)) (|has| |#2| (-126))) (-12 (|has| |#1| (-735)) (|has| |#2| (-735)))) +(-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)))) ((((-1165 |#1| |#2| |#3|)) |has| |#1| (-341))) ((($) . T) (((-805 |#1|)) . T) (((-385 (-525))) . T)) ((((-1165 |#1| |#2| |#3|)) |has| |#1| (-341))) @@ -2951,15 +2951,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-385 |#2|)) . T)) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-327))) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-327))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) ((((-501)) |has| |#1| (-567 (-501)))) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) ((((-501)) |has| |#1| (-567 (-501)))) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) ((((-501)) |has| |#1| (-567 (-501)))) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#1|) . T)) (((|#2| |#2|) . T) ((#0=(-385 (-525)) #0#) . T) (($ $) . T)) ((((-525)) . T)) @@ -2988,32 +2988,32 @@ ((((-1165 |#1| |#2| |#3|)) |has| |#1| (-341))) ((((-1091)) . T) (((-798)) . T)) (|has| |#1| (-341)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3275 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3316 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) . T)) -((($) -3275 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-1024)) . T)) ((((-798)) . T)) -((($) -3275 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3316 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((($) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T)) ((($) . T)) -((($) -3275 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3316 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (|has| |#2| (-844)) (|has| |#1| (-844)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-160))) ((((-641)) . T)) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#1|) |has| |#1| (-160))) (((|#1|) |has| |#1| (-160))) ((((-385 (-525))) . T) (($) . T)) (((|#1| (-525)) . T)) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-341)) (|has| |#1| (-341)) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-327))) -(-3275 (|has| |#1| (-160)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3316 (|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)) -(-3275 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) -(-3275 (-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)))) +(-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)))) ((((-525)) . T)) ((((-525)) . T)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-3275 (|has| |#2| (-160)) (|has| |#2| (-669)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-3316 (|has| |#2| (-160)) (|has| |#2| (-669)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((((-1091)) -12 (|has| |#2| (-835 (-1091))) (|has| |#2| (-977)))) -(-3275 (-12 (|has| |#1| (-450)) (|has| |#2| (-450))) (-12 (|has| |#1| (-669)) (|has| |#2| (-669)))) +(-3316 (-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)) -(-3275 (|has| |#1| (-327)) (|has| |#1| (-346))) +(-3316 (|has| |#1| (-327)) (|has| |#1| (-346))) (((|#1| |#2|) . T)) ((($) . T) ((|#1|) . T)) ((((-798)) . T)) @@ -3069,7 +3069,7 @@ ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2|) |has| |#2| (-1020)) (((-525)) -12 (|has| |#2| (-968 (-525))) (|has| |#2| (-1020))) (((-385 (-525))) -12 (|has| |#2| (-968 (-385 (-525)))) (|has| |#2| (-1020)))) ((((-501)) |has| |#1| (-567 (-501)))) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) ((($) . T) (((-385 (-525))) . T)) (|has| |#1| (-844)) (|has| |#1| (-844)) @@ -3078,14 +3078,14 @@ ((((-798)) . T)) (((|#2| |#2|) . T)) (((|#1| |#1|) |has| |#1| (-160))) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3275 (|has| |#1| (-21)) (|has| |#1| (-787))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3316 (|has| |#1| (-21)) (|has| |#1| (-787))) (((|#2|) . T)) -(-3275 (|has| |#1| (-21)) (|has| |#1| (-787))) +(-3316 (|has| |#1| (-21)) (|has| |#1| (-787))) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) (((|#1|) . T)) -((((-798)) -3275 (-12 (|has| |#1| (-566 (-798))) (|has| |#2| (-566 (-798)))) (-12 (|has| |#1| (-1020)) (|has| |#2| (-1020))))) +((((-798)) -3316 (-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)) ((($) . T) (((-385 (-525))) . T)) -(-3275 (|has| |#4| (-160)) (|has| |#4| (-669)) (|has| |#4| (-787)) (|has| |#4| (-977))) -(-3275 (|has| |#3| (-160)) (|has| |#3| (-669)) (|has| |#3| (-787)) (|has| |#3| (-977))) +(-3316 (|has| |#4| (-160)) (|has| |#4| (-669)) (|has| |#4| (-787)) (|has| |#4| (-977))) +(-3316 (|has| |#3| (-160)) (|has| |#3| (-669)) (|has| |#3| (-787)) (|has| |#3| (-977))) (|has| |#4| (-735)) -(-3275 (|has| |#4| (-735)) (|has| |#4| (-787))) +(-3316 (|has| |#4| (-735)) (|has| |#4| (-787))) (|has| |#4| (-787)) (|has| |#3| (-735)) -(-3275 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-3316 (|has| |#3| (-735)) (|has| |#3| (-787))) (|has| |#3| (-787)) ((((-525)) . T)) (((|#2|) . T)) -((((-1091)) -3275 (-12 (|has| (-1089 |#1| |#2| |#3|) (-835 (-1091))) (|has| |#1| (-341))) (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-835 (-1091)))))) +((((-1091)) -3316 (-12 (|has| (-1089 |#1| |#2| |#3|) (-835 (-1091))) (|has| |#1| (-341))) (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-835 (-1091)))))) ((((-1091)) -12 (|has| |#1| (-15 * (|#1| (-385 (-525)) |#1|))) (|has| |#1| (-835 (-1091))))) ((((-1091)) -12 (|has| |#1| (-15 * (|#1| (-713) |#1|))) (|has| |#1| (-835 (-1091))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3122,11 +3122,11 @@ ((((-1089 |#1| |#2| |#3|)) |has| |#1| (-341))) ((((-1089 |#1| |#2| |#3|)) |has| |#1| (-341))) ((((-1056 |#1| |#2|)) . T)) -(((|#2|) . T) (((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) -((((-2 (|:| -3420 (-1091)) (|:| -2542 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) +((((-2 (|:| -3511 (-1091)) (|:| -3631 (-51)))) . T)) ((($) . T)) (|has| |#1| (-953)) -(((|#2|) . T) (((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3511 |#1|) (|:| -3631 |#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)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3316 (|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) (($) -3275 (|has| |#4| (-160)) (|has| |#4| (-787)) (|has| |#4| (-977))) ((|#4|) -3275 (|has| |#4| (-160)) (|has| |#4| (-341)) (|has| |#4| (-977)))) -(((|#2|) . T) (($) -3275 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-977))) ((|#3|) -3275 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-977)))) +(((|#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)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-341)) @@ -3158,7 +3158,7 @@ ((((-798)) . T)) ((((-798)) . T)) (((|#1|) . T)) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) ((((-125)) . T) (((-798)) . T)) ((((-525) |#1|) . T)) (((|#1|) . T)) @@ -3166,30 +3166,30 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-341)) (|has| |#2| (-265 |#2| |#2|))) (($ $) . T)) ((($ $) . 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T)) -((((-798)) -3275 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -3316 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#1|) . T)) (((|#1| |#2|) . T)) ((((-1074) |#1|) . T)) ((((-385 |#2|)) . T)) -((((-2 (|:| -3420 |#1|) (|:| -2542 |#2|))) . T)) +((((-2 (|:| -3511 |#1|) (|:| -3631 |#2|))) . T)) (|has| |#1| (-517)) (|has| |#1| (-517)) ((($) . T) ((|#2|) . T)) @@ -3197,12 +3197,12 @@ (((|#1| |#2|) . T)) (((|#2| $) |has| |#2| (-265 |#2| |#2|))) (((|#1| (-592 |#1|)) |has| |#1| (-787))) -(-3275 (|has| |#1| (-213)) (|has| |#1| (-327))) -(-3275 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3316 (|has| |#1| (-213)) (|has| |#1| (-327))) +(-3316 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-1020)) (((|#1|) . T)) ((((-385 (-525))) . T) (($) . T)) -((((-931 |#1|)) . T) ((|#1|) . T) (((-525)) -3275 (|has| (-931 |#1|) (-968 (-525))) (|has| |#1| (-968 (-525)))) (((-385 (-525))) -3275 (|has| (-931 |#1|) (-968 (-385 (-525)))) (|has| |#1| (-968 (-385 (-525)))))) +((((-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)))))) (((|#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)))) @@ -3213,9 +3213,9 @@ (((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1056 |#1| |#2|) #0#) |has| (-1056 |#1| |#2|) (-288 (-1056 |#1| |#2|)))) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) #0#) |has| (-2 (|:| -3420 |#1|) (|:| -2542 |#2|)) (-288 (-2 (|:| -3420 |#1|) (|:| -2542 |#2|))))) +(((|#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|))))) (((#0=(-112 |#1|)) |has| #0# (-288 #0#))) -(-3275 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-3316 (|has| |#1| (-789)) (|has| |#1| (-1020))) ((($ $) . T)) ((($ $) . T) ((#0=(-800 |#1|) $) . T) ((#0# |#2|) . T)) ((($ $) . T) ((|#2| $) |has| |#1| (-213)) ((|#2| |#1|) |has| |#1| (-213)) ((|#3| |#1|) . T) ((|#3| $) . T)) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 204e5acc..24140b69 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3421035920) +(30 . 3422100674) (4258 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -460,652 +460,649 @@ |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |primintfldpoly| |integerIfCan| |rombergo| |tab1| - |rightFactorIfCan| |cfirst| |any| |superscript| |monomialIntegrate| - |merge!| |graeffe| |integral?| |setFieldInfo| |positiveRemainder| - |df2ef| |internalIntegrate| |raisePolynomial| |cyclotomic| - |eyeDistance| |subst| |removeRedundantFactors| |OMputError| - |univariatePolynomials| |approxNthRoot| |mathieu24| |B1solve| |rk4a| - |bezoutMatrix| |removeSuperfluousCases| |palgextint| |order| - |pushdown| |principalIdeal| |indiceSubResultant| |factorFraction| |op| - |plus| |fortranTypeOf| |leader| |categoryFrame| |resetVariableOrder| - |mirror| |error| |scripted?| |pair?| |printTypes| - |leftMinimalPolynomial| |exp| |sdf2lst| |groebnerFactorize| - |HermiteIntegrate| |zoom| |monomial?| |outputAsTex| |assert| |toScale| - |pushdterm| ~= |poisson| |showFortranOutputStack| |palgLODE0| - |indices| |discriminantEuclidean| |lieAlgebra?| |addPoint| - |deepExpand| |newTypeLists| |coerce| |iisin| |expintegrate| |f01rcf| - |high| |showAll?| |compBound| |consnewpol| |lprop| |construct| - |hasoln| |initiallyReduced?| |iiacosh| |collectQuasiMonic| - |pushuconst| |computeCycleLength| |stoseInvertibleSet| - |linearlyDependentOverZ?| |move| |numeric| |bezoutResultant| - |insertMatch| |var2Steps| |tableau| |e01daf| |useNagFunctions| - |minimumExponent| |intChoose| |optimize| |radical| |invertIfCan| - |leastMonomial| |lhs| |taylorIfCan| |printStatement| |ideal| - |prevPrime| |lazyPseudoQuotient| |powmod| |viewport2D| |univariate?| - |width| |tracePowMod| |euclideanNormalForm| |rhs| |wrregime| - |typeList| |d01asf| |iisqrt3| |e02daf| |check| |d01gaf| |appendPoint| - |expPot| |integralLastSubResultant| |pointSizeDefault| - |internalInfRittWu?| |basisOfCenter| |rangeIsFinite| |OMputEndError| - |stoseInvertible?reg| |rules| |domainOf| |trigs2explogs| |rename| - |nil| |composites| |decrease| |style| |f04atf| |or?| - |changeThreshhold| |paraboloidal| |invmod| |f04arf| - |setLegalFortranSourceExtensions| |upperCase!| |algint| |condition| - |mdeg| |perspective| |safetyMargin| |cosh2sech| |interpretString| - |result| |lowerPolynomial| |cycles| |fullDisplay| |maxrow| - |colorFunction| |zeroSetSplit| |hconcat| |vertConcat| |d01gbf| - |setScreenResolution3D| |optional| |multMonom| F2FG |redpps| |f02awf| - |approximate| |gcdcofactprim| |mpsode| |denomRicDE| |string?| |crest| - |showScalarValues| |complex| |associative?| |fixedPoints| |c06gqf| - |minRowIndex| |rationalIfCan| |OMputAtp| |powerSum| |OMwrite| - |digamma| |iisech| |rightRegularRepresentation| |setStatus!| - |subscript| |viewDefaults| |viewZoomDefault| |head| - |rewriteIdealWithQuasiMonicGenerators| |OMputString| |enterPointData| - |minPoints| |length| |complementaryBasis| |cycleTail| - |clearTheIFTable| |solveLinearPolynomialEquation| |bfKeys| |npcoef| - |clip| |distdfact| |selectNonFiniteRoutines| |cyclicCopy| |scripts| - |radicalOfLeftTraceForm| |padicFraction| |leadingBasisTerm| - |radicalSimplify| |hermiteH| |subResultantGcdEuclidean| |e01bff| |log| - |exponentialOrder| |s13acf| RF2UTS |fortranLogical| - |algebraicDecompose| |meshPar2Var| |subresultantSequence| |ran| - |complexEigenvectors| |showAllElements| |s17dlf| |cyclicEntries| - |setright!| |setelt| |outerProduct| |integerBound| |s13adf| - |setImagSteps| |getProperties| |cSec| |OMgetEndBind| |pack!| - |OMlistSymbols| |orbit| |selectFiniteRoutines| |rightZero| - |LazardQuotient| |OMopenString| |sequences| |bit?| |pushucoef| - |c02agf| |generalizedContinuumHypothesisAssumed| |thetaCoord| |aCubic| - |copy| |nthCoef| |nthRootIfCan| |randnum| |ode2| |lexTriangular| - |returnType!| |removeZeroes| |stopTableGcd!| |printHeader| - |commonDenominator| |backOldPos| |supRittWu?| |infieldIntegrate| - |Frobenius| |coerceP| |unit| |normalizedAssociate| |usingTable?| - |getCurve| |lighting| |autoCoerce| |getMultiplicationMatrix| - |trueEqual| |quoted?| |acosIfCan| |direction| |exptMod| |constant| - |makeFR| |reduceBasisAtInfinity| |bivariate?| - |indiceSubResultantEuclidean| |eulerE| |cosSinInfo| |antiAssociative?| - |wholePart| |integralAtInfinity?| |adjoint| |insertBottom!| - |OMputSymbol| |transcendentalDecompose| |getMultiplicationTable| - |quadraticNorm| |rspace| |pole?| |baseRDE| |numer| - |extendedSubResultantGcd| |cLog| |internal?| |printStats!| - |normalElement| |interpret| |zeroVector| |every?| |signAround| |erf| - |denom| |deepestInitial| |square?| |hostPlatform| |iiabs| |substring?| - |numberOfIrreduciblePoly| |heapSort| |setleft!| |infinityNorm| - |prolateSpheroidal| |s01eaf| |pushNewContour| |stopTable!| |iiasec| - |twoFactor| |linearMatrix| |linearPart| |prinpolINFO| - |sumOfKthPowerDivisors| |fortran| |complexForm| |generateIrredPoly| - |aspFilename| |sec2cos| |stosePrepareSubResAlgo| |defineProperty| |pi| - |numericalOptimization| |cSin| |suffix?| |f07fef| |firstNumer| - |primlimitedint| |sinIfCan| |ignore?| |generic| |chineseRemainder| - |reduceLODE| |infinity| |composite| |queue| |OMgetAttr| - |trivialIdeal?| |countRealRoots| |pdf2df| |rightMinimalPolynomial| - |rowEch| |algebraicCoefficients?| |cAcoth| |content| |fortranInteger| - |dilog| |prefix?| |nonLinearPart| |makeSeries| |setRow!| - |problemPoints| |fortranLiteral| |minColIndex| |expandLog| - |chainSubResultants| |sin| |permutations| |coerceImages| |doubleRank| - |iiasech| |roughBasicSet| |jacobi| ^ |checkRur| |kernel| |e04ucf| - |csch2sinh| |uniform| |status| |cos| |Beta| |changeName| - |useSingleFactorBound?| |pmComplexintegrate| |iCompose| |d03eef| - |trapezoidalo| |characteristicSerie| |draw| |numericIfCan| |box| - |symmetricTensors| |mainMonomial| |infix| |principal?| |rowEchLocal| - |d02ejf| |hitherPlane| |semiResultantEuclidean1| |tan| |localUnquote| - |generalizedInverse| |stoseLastSubResultant| |iiatanh| |leftDivide| - |coordinates| |viewport3D| |mr| |removeRoughlyRedundantFactorsInPols| - |sn| |remove| |bezoutDiscriminant| |duplicates| - |conditionsForIdempotents| |s19adf| |lexico| |shiftRoots| - |factorGroebnerBasis| |figureUnits| |infix?| |overlap| |atrapezoidal| - |purelyAlgebraic?| |polygon?| |selectPolynomials| |pop!| |df2fi| - |exprToXXP| |makeObject| |invmultisect| |mask| |buildSyntax| |last| - |shrinkable| |OMconnectTCP| |expenseOfEvaluationIF| |vark| |fill!| - |choosemon| |e02bdf| |remove!| |nthFlag| |assoc| |atanIfCan| - |compound?| |purelyAlgebraicLeadingMonomial?| |prod| |region| - |pointLists| |monicDecomposeIfCan| |mulmod| |coef| |front| - |convergents| |expandTrigProducts| |write!| |matrix| - |clipPointsDefault| |graphStates| |c06ebf| |lazyPquo| |digit| - |exprHasAlgebraicWeight| |variable?| |rootPoly| |cAcsc| |complement| - |is?| |asinIfCan| |noncommutativeJordanAlgebra?| |infiniteProduct| - |leftLcm| |range| |rangePascalTriangle| |cSinh| |matrixGcd| |measure| - |hdmpToDmp| |exquo| |getProperty| |getZechTable| |acschIfCan| GF2FG - |mapExpon| |solveLinear| |bivariateSLPEBR| |processTemplate| - |lowerCase| |div| |low| |lintgcd| |OMunhandledSymbol| - |changeWeightLevel| |blue| |stoseInvertible?sqfreg| |isQuotient| - |taylorQuoByVar| |dmp2rfi| |index?| |duplicates?| |quo| |insert!| - |ramifiedAtInfinity?| |makeResult| |remainder| |alternating| - |wordInGenerators| |lazy?| |retractable?| |goto| |quatern| - |symmetric?| |ipow| |cond| |f02abf| |subResultantChain| |charClass| - |list?| |push| |karatsubaOnce| |getStream| |monomRDEsys| |rem| - |powerAssociative?| |cCos| |uniform01| |hdmpToP| |algebraicSort| - |modularGcdPrimitive| |e01bhf| |ef2edf| |compose| |firstSubsetGray| - |sncndn| |outputGeneral| |screenResolution| - |stoseInternalLastSubResultant| |trim| |regime| |showClipRegion| - |midpoints| |stFunc1| |integralMatrixAtInfinity| |numberOfChildren| - |zCoord| |singleFactorBound| |symmetricDifference| |height| - |lfextlimint| |cAsech| |diff| |tan2cot| |presub| |binding| |qfactor| - |setPredicates| |linear?| |stoseSquareFreePart| |laplacian| - |addPoint2| |scaleRoots| |numFunEvals| |setPosition| |sortConstraints| - |genericLeftDiscriminant| |schema| |finiteBound| |scale| |e02baf| - |restorePrecision| |d02bhf| |moebiusMu| |ratpart| |unexpand| - |selectPDERoutines| |showRegion| |dimensions| |normalDenom| - |factorset| |s17aff| |ravel| |iicot| |patternVariable| |setMinPoints| - |bombieriNorm| |subResultantGcd| |supersub| |skewSFunction| UTS2UP - |resultantEuclidean| |tubeRadius| |pade| |listRepresentation| |empty?| - |reshape| |parametersOf| |distFact| |equation| |decreasePrecision| - |setMaxPoints3D| |divide| |outputList| |putColorInfo| |ReduceOrder| - |getCode| |shallowCopy| |associatedSystem| |tanh2trigh| |formula| - |create| |laplace| |nlde| |maxPoints| |neglist| |e04ycf| |overbar| - |cyclotomicDecomposition| |iiasinh| |certainlySubVariety?| - |makeViewport2D| |mantissa| |not| |integralBasisAtInfinity| - |sizePascalTriangle| |sts2stst| |reciprocalPolynomial| - |OMconnInDevice| |jacobiIdentity?| |stoseInvertibleSetreg| - |pleskenSplit| |setOfMinN| |f02fjf| |updatF| |complexLimit| - |clearCache| |genus| |iicoth| |back| |reduceByQuasiMonic| - |startPolynomial| |finite?| |s17def| |fortranCompilerName| - |curryRight| |recip| |removeZero| |update| |irreducible?| - |createIrreduciblePoly| |rightTrace| |FormatArabic| |coshIfCan| - |showTypeInOutput| |nrows| |zeroOf| |empty| |reopen!| |cAsec| - |tanh2coth| |zeroDim?| |totalGroebner| |binomial| |KrullNumber| - |pureLex| |s17ahf| |ncols| |unary?| |inverseIntegralMatrix| |weight| - |unitsColorDefault| |exteriorDifferential| |increment| |hessian| - |OMputEndApp| |legendreP| |rotate!| |btwFact| |extend| |character?| - |cyclotomicFactorization| |iiGamma| |alternatingGroup| |medialSet| - |cot2tan| |infieldint| |fprindINFO| |elem?| |d01amf| |generalSqFr| - |label| |tower| |s19acf| |normalized?| |numerator| |integralBasis| - |setVariableOrder| |allRootsOf| |linearlyDependent?| |powers| - |sqfrFactor| |redmat| |splitLinear| |quadratic?| |pointColorDefault| - |createNormalElement| |rightGcd| |beauzamyBound| |subtractIfCan| - |argumentListOf| |coerceS| |evenlambert| |position| |morphism| - |createMultiplicationMatrix| |fortranReal| |antisymmetric?| - |transpose| |f02wef| |forLoop| |cAcsch| |c06fuf| |imagI| - |polarCoordinates| |select!| |mat| |fortranCharacter| - |monicRightFactorIfCan| |iFTable| |hue| |monic?| |setProperties| - |secIfCan| |singular?| |genericLeftTrace| |OMclose| |normalForm| - |cCoth| |belong?| |getBadValues| |isList| |relativeApprox| - |patternMatch| |point?| |prefix| |orbits| |sign| |mathieu23| |powern| - |listYoungTableaus| |partialDenominators| |showSummary| |option| - |plot| |iisinh| |rightRankPolynomial| |reduction| |palgRDE| |badNum| - |characteristicSet| |chiSquare| |setAdaptive| |contractSolve| - |elliptic?| |headRemainder| |pow| |scalarMatrix| - |tryFunctionalDecomposition?| |fracPart| |toseSquareFreePart| - |halfExtendedSubResultantGcd1| |karatsubaDivide| |bernoulli| - |stirling1| |rotatex| |branchPoint?| |f02adf| |showAttributes| - |pseudoRemainder| |useSingleFactorBound| |level| |relationsIdeal| - |f04qaf| |s19abf| |lambert| |color| |drawComplexVectorField| - |createNormalPrimitivePoly| |semiDiscriminantEuclidean| |groebgen| - |c06ekf| |moduloP| |inf| |s17dgf| |cycle| |upDateBranches| - |conjugates| |dark| |critMTonD1| |normal| |subset?| |tablePow| - |prefixRagits| |setRealSteps| |plenaryPower| |antiCommutator| - |Lazard2| |hash| |rquo| |concat| |completeHensel| |second| |nullSpace| - |normalise| |universe| |lazyEvaluate| |ODESolve| |merge| - |alternative?| |copies| |e02dcf| |nsqfree| LODO2FUN |meshPar1Var| - |third| |squareFree| |more?| |chvar| |findCycle| |shellSort| |rur| - |hex| |normDeriv2| |count| |irreducibleRepresentation| - |compiledFunction| |writeLine!| |magnitude| |commaSeparate| - |rightQuotient| |movedPoints| |OMputInteger| |leastAffineMultiple| - |minus!| |nullary?| |asechIfCan| |screenResolution3D| |shallowExpand| - |lfinfieldint| |polyRicDE| |exponent| |countRealRootsMultiple| - |diagonals| |makeViewport3D| |leftExactQuotient| |mainValue| - |repeating?| |s20adf| |round| |multiEuclidean| |basisOfLeftNucleus| - |matrixDimensions| |OMReadError?| |d01bbf| |simplifyLog| |setProperty| - |isobaric?| |s14abf| |crushedSet| |coth2tanh| |perfectSquare?| - |definingPolynomial| |multiple?| |solid| |overlabel| |rubiksGroup| - |lagrange| |companionBlocks| |quartic| |leadingIdeal| |horizConcat| - |removeRoughlyRedundantFactorsInContents| |digit?| |cup| |OMputBind| - |univcase| |OMputEndAtp| |exp1| D |f02ajf| |s18aff| |checkPrecision| - |invertibleSet| |int| |untab| |complexNumeric| |node?| - |SturmHabichtCoefficients| |addBadValue| |sturmVariationsOf| - |removeCosSq| |one?| |notOperand| |reify| |currentEnv| - |jordanAlgebra?| |listConjugateBases| |d01anf| |resultantnaif| - |getGraph| |mindeg| |OMputBVar| |palgextint0| |mapExponents| - |unaryFunction| |kroneckerDelta| |d01akf| |leadingSupport| |cSech| - |OMgetEndBVar| |delay| |acothIfCan| |ode| |Nul| |kernels| |multiset| - |solveLinearPolynomialEquationByRecursion| |exponential| - |permutationGroup| |oddInfiniteProduct| |commutativeEquality| - |currentCategoryFrame| |brillhartTrials| |semicolonSeparate| |sincos| - |factors| |monicCompleteDecompose| |generalTwoFactor| |discriminant| - |dfRange| |maximumExponent| |univariate| |stronglyReduced?| - |leftFactorIfCan| |f02bbf| |fintegrate| |zeroMatrix| |roughBase?| - |linearAssociatedOrder| |expextendedint| |setelt!| |mainContent| - |contours| |squareMatrix| |prime?| |inspect| |wordInStrongGenerators| - |ratDsolve| |sort!| |s21bbf| |realSolve| |aQuartic| |lazyGintegrate| - |relerror| |commutator| |expIfCan| |besselI| - |semiResultantEuclideannaif| |power| |argumentList!| |cot| |cschIfCan| - |simplify| |genericLeftNorm| |factorOfDegree| |OMUnknownCD?| - |expandPower| |coefficients| |constantOperator| |ord| - |representationType| |rightAlternative?| |branchIfCan| |externalList| - |rightNorm| |simpsono| |probablyZeroDim?| |sec| |row| |factor| - |d02gbf| |e02gaf| |numFunEvals3D| |halfExtendedResultant1| - |maxPoints3D| |has?| |arity| |wholeRadix| |autoReduced?| |divergence| - |c06ecf| |lfextendedint| |csc| |sqrt| |getOperands| |alphanumeric| - |cExp| |OMlistCDs| |dmpToP| |showTheRoutinesTable| |edf2fi| - |explogs2trigs| |unitCanonical| |intcompBasis| |f02aef| - |viewThetaDefault| |OMgetObject| |OMserve| |iflist2Result| |asin| - |solveRetract| |real| |size?| |char| |scanOneDimSubspaces| - |viewSizeDefault| |reducedContinuedFraction| |measure2Result| - |numberOfMonomials| |weights| |integralMatrix| |sinhIfCan| |quote| - |selectOptimizationRoutines| |oddlambert| |outputMeasure| |acos| - |imag| |removeSuperfluousQuasiComponents| |resize| |cyclePartition| - |createThreeSpace| |elliptic| |localAbs| |saturate| |pile| |SFunction| - |drawToScale| |e01sbf| |bumprow| |directProduct| |atan| |closed?| - |ricDsolve| |sylvesterSequence| |point| |subscriptedVariables| - |setClosed| |unitNormal| |explicitlyFinite?| |resetNew| - |rischNormalize| |lfintegrate| |bitCoef| |mathieu11| |idealiser| - |totalLex| |acot| |associatorDependence| |pushup| |firstDenom| - |createRandomElement| |rootSimp| |c06fqf| |s18adf| - |exprHasLogarithmicWeights| |f01qef| |linearAssociatedLog| |concat!| - |explimitedint| |OMgetEndAttr| |asec| |symbolTable| |destruct| |solve| - |setColumn!| |att2Result| |bipolarCylindrical| |float| |initTable!| - |extensionDegree| |cTan| |rewriteIdealWithRemainder| - |branchPointAtInfinity?| |tubeRadiusDefault| |limitedIntegrate| - |ddFact| |acsc| |s15aef| |updatD| |series| |d03edf| |subHeight| - |gradient| |bernoulliB| |diagonalProduct| |drawComplex| |findBinding| - |groebner| |tanSum| |elRow2!| |split| |pushFortranOutputStack| |sinh| - |getVariableOrder| |PollardSmallFactor| |listLoops| |evaluate| |lllp| - |rootSplit| |f04faf| |iiasin| |genericRightMinimalPolynomial| - |multisect| |lazyPseudoRemainder| |aQuadratic| |extractProperty| - |readIfCan!| |popFortranOutputStack| |cosh| |quasiAlgebraicSet| - |rroot| |pointData| |euler| |complexNormalize| |equiv| - |iteratedInitials| |cTanh| |knownInfBasis| |perfectSqrt| - |newSubProgram| |viewPhiDefault| |outputAsFortran| |tanh| |monomial| - |cycleRagits| |stirling2| |associator| |setFormula!| |fractRagits| - |idealiserMatrix| |reduced?| |roman| |basisOfLeftAnnihilator| - |vedf2vef| |binarySearchTree| |getConstant| |OMgetApp| - |reducedDiscriminant| |iiacot| |coth| |primlimintfrac| |multivariate| - |heap| |min| |singularitiesOf| |e02bef| |any?| |hasHi| |fractRadix| - |sin?| |setScreenResolution| |hasPredicate?| - |stoseInvertibleSetsqfreg| |sech| |variables| |hexDigit| - |dihedralGroup| |getlo| |subQuasiComponent?| |createZechTable| - |symbolIfCan| |f01rdf| |rootKerSimp| |numberOfComponents| - |nextPrimitivePoly| |match?| |varselect| |bat| |csch| - |stopMusserTrials| |GospersMethod| |pmintegrate| |complexNumericIfCan| - |LiePolyIfCan| |mesh?| |clipBoolean| |irreducibleFactors| |cCot| - |ceiling| |OMread| |torsion?| |open| |asinh| |lowerCase?| |localReal?| - |imagJ| GE |push!| |mapUnivariate| |maxRowIndex| |createNormalPoly| - |internalLastSubResultant| |noLinearFactor?| |nand| |mergeFactors| - |minGbasis| |acosh| |dioSolve| |genericPosition| GT |cyclicSubmodule| - 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|rationalPoints| |printInfo| |d01fcf| |OMencodingXML| |tValues| - |OMgetError| |mainKernel| |exprToGenUPS| |transform| |copy!| - |fortranLiteralLine| |viewWriteAvailable| |leftRankPolynomial| - |numberOfImproperPartitions| |extractSplittingLeaf| |intensity| - |interpolate| |extendedEuclidean| |bitLength| |e01bef| - |OMsupportsSymbol?| |nextLatticePermutation| |message| |PDESolve| - |generate| |numberOfFactors| |f01ref| |selectAndPolynomials| |reseed| - |dn| |safeFloor| |expint| |viewWriteDefault| - |zeroSetSplitIntoTriangularSystems| |multiplyExponents| - |realEigenvectors| |gcdPrimitive| |prepareDecompose| |getMeasure| - |sizeLess?| |primextendedint| |loadNativeModule| BY |splitNodeOf!| - |sinhcosh| |nextsubResultant2| |partitions| |incrementBy| - |resetAttributeButtons| |e04gcf| |showTheIFTable| |tanIfCan| - |shanksDiscLogAlgorithm| |members| |pr2dmp| |print| |coefficient| - |totalDegree| |startTableGcd!| |expand| |tanintegrate| |sup| |maxdeg| - |binary| |complexRoots| |moduleSum| |curry| |insertionSort!| |leftGcd| - 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|scopes| |innerSolve1| |OMencodingUnknown| |minimize| |kovacic| - |collectUnder| |createPrimitiveElement| |component| - |fractionFreeGauss!| |rationalFunction| |iiacoth| |binomThmExpt| - |ffactor| |derivationCoordinates| |critpOrder| |OMputFloat| |dec| - |besselY| |outputSpacing| |squareFreePrim| |extractClosed| - |transcendenceDegree| |leftNorm| |FormatRoman| |polynomialZeros| - |geometric| |iiperm| |makeRecord| |c06gbf| |vspace| |monomRDE| - |retract| |interval| |edf2df| |leftRegularRepresentation| |unparse| - |areEquivalent?| |normalizedDivide| |interReduce| |specialTrigs| - |f02aaf| |indicialEquationAtInfinity| |linearDependence| |dequeue| - |e04mbf| |halfExtendedResultant2| |f2st| |f01mcf| |splitConstant| - |d02kef| |ListOfTerms| |airyBi| |padicallyExpand| - |expenseOfEvaluation| |s14baf| |errorKind| |e01sff| |compactFraction| - |cycleEntry| |rational?| |mapdiv| |bumptab| |resultantEuclideannaif| - |topFortranOutputStack| |eisensteinIrreducible?| |vectorise| - |minimumDegree| |shuffle| |iomode| |makeFloatFunction| |changeBase| - |outputForm| |complexEigenvalues| |testModulus| |init| |fglmIfCan| - |idealSimplify| |mapSolve| |closedCurve| |OMgetBVar| |anticoord| - |octon| |expressIdealMember| |changeVar| |gbasis| |diagonal| |credPol| - |nonQsign| |byte| |pointColor| |leftRemainder| |subCase?| |f01brf| - |makeMulti| |over| |makeSketch| |setEpilogue!| |quadraticForm| - |functionIsFracPolynomial?| |eigenvalues| |realRoots| |logIfCan| - |hyperelliptic| |charpol| |sumOfSquares| |OMputVariable| |zero?| - |OMgetEndApp| |nonSingularModel| |modularGcd| |child| - |definingEquations| |property| |halfExtendedSubResultantGcd2| - |rootDirectory| |argument| |lazyResidueClass| |fillPascalTriangle| - |setref| |setTex!| |solveLinearlyOverQ| |algintegrate| - |extendedIntegrate| |perfectNthRoot| |asecIfCan| |llprop| - |symmetricPower| |plus!| |hcrf| = |cAsin| |semiResultantEuclidean2| - |mapmult| |createPrimitivePoly| |cyclicGroup| |characteristic| - |nthRoot| |doublyTransitive?| |iipow| |diagonalMatrix| |degree| - |setTopPredicate| |element?| |separate| |units| |failed?| - |lazyVariations| |iicosh| |factorSFBRlcUnit| |algSplitSimple| - |userOrdered?| |getGoodPrime| < |getOrder| |extract!| |LyndonBasis| - |insertRoot!| |curve| |leaf?| |basisOfMiddleNucleus| |complexZeros| - |unit?| > |makeYoungTableau| |exprHasWeightCosWXorSinWX| - |setAdaptive3D| |iicsc| |leadingCoefficientRicDE| |dictionary| - |lieAdmissible?| |copyInto!| <= |trigs| |henselFact| - |explicitEntries?| |pdct| |genericRightNorm| - |unrankImproperPartitions1| |aLinear| |unitNormalize| >= |htrigs| - |viewDeltaXDefault| |clearTable!| |separant| - |semiSubResultantGcdEuclidean2| |whileLoop| |pastel| |setClipValue| - |innerSolve| |expintfldpoly| |OMbindTCP| |transcendent?| |inc| - |curryLeft| |outputAsScript| |zerosOf| |less?| |top!| |depth| |e04dgf| - |listexp| |laurentRep| |wordsForStrongGenerators| |setnext!| |code| - |acotIfCan| |bumptab1| |stFunc2| |var1StepsDefault| |inverseLaplace| - |keys| |primitiveElement| |paren| |acoshIfCan| + |monomialIntPoly| - |basisOfRightAnnihilator| |reverseLex| |setButtonValue| |f04mbf| - |cCsc| |realZeros| |psolve| |rectangularMatrix| - - |inverseIntegralMatrixAtInfinity| |realEigenvalues| |extendIfCan| - |polar| |rightCharacteristicPolynomial| |imaginary| - |addMatchRestricted| |conjug| |factorSquareFreeByRecursion| / - |squareTop| |rotatez| |bottom!| |list| |OMgetBind| - |primPartElseUnitCanonical!| |iilog| |ocf2ocdf| |precision| - |definingInequation| |rightRank| |operation| |optAttributes| - |cscIfCan| |car| |isPlus| |algebraicVariables| |computePowers| - |refine| |infinite?| |pointPlot| |quasiMonicPolynomials| |cosIfCan| - |cdr| |viewPosDefault| |computeInt| |setProperty!| - |parabolicCylindrical| |numberOfComposites| |triangularSystems| - |equivOperands| |implies| |callForm?| |df2mf| |setDifference| - |setStatus| |module| |script| |nary?| |oblateSpheroidal| |linear| - |loopPoints| |LowTriBddDenomInv| |varList| |xor| - |rootOfIrreduciblePoly| |palgintegrate| |setIntersection| |positive?| - |failed| |inverseColeman| |bringDown| |contains?| - |solveLinearPolynomialEquationByFractions| |graphImage| |setUnion| - |satisfy?| |components| |LyndonWordsList| |split!| |datalist| - |normal?| |e01bgf| |polynomial| |completeHermite| |properties| - |nextsousResultant2| |setErrorBound| |fortranCarriageReturn| |apply| - |numberOfCycles| |tex| |cothIfCan| |padecf| |generic?| |debug3D| - |arrayStack| |limit| |shift| |janko2| |finiteBasis| |iprint| |entries| - |e02bbf| |overset?| |selectsecond| |stiffnessAndStabilityFactor| - |translate| |rule| |elementary| |size| |resultant| |iibinom| - |external?| |leftScalarTimes!| |s13aaf| |sturmSequence| |rischDEsys| - |getButtonValue| |socf2socdf| |f02aff| |flexibleArray| - |minimalPolynomial| |OMreadFile| |leftZero| |normalizeAtInfinity| - |cRationalPower| |e02ddf| |iiexp| |graphState| |numberOfHues| - |lazyIntegrate| |validExponential| |Is| |leftFactor| |recolor| - |eulerPhi| |eq| |chebyshevT| |integer| |degreePartition| |ref| |rk4| - |OMgetVariable| |calcRanges| |removeRedundantFactorsInPols| |tree| - |d02bbf| |iter| |cap| |d01aqf| |trailingCoefficient| |ParCond| - |exactQuotient| |basisOfRightNucloid| |gcdPolynomial| |pseudoDivide| - |nil| |infinite| |arbitraryExponent| |approximate| |complex| - |shallowMutable| |canonical| |noetherian| |central| - |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| - |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| - |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| - |finiteAggregate| |shallowlyMutable| |commutative|)
\ No newline at end of file + |Record| |Union| |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| |removeZero| |hasoln| |leastAffineMultiple| + |e01baf| |row| |makeFloatFunction| |stFuncN| |irreducible?| + |mapMatrixIfCan| |rightFactorCandidate| |initiallyReduced?| + |commutative?| |optional| |minus!| |d02gbf| |getSyntaxFormsFromFile| + |approximate| |genericRightTraceForm| |changeBase| + |createIrreduciblePoly| |column| |Hausdorff| + |semiResultantReduitEuclidean| |nullary?| |complex| |e02gaf| |smith| + |outputForm| |cyclicEqual?| |iiacosh| |rightTrace| |karatsubaOnce| + |toseInvertibleSet| |create3Space| |outerProduct| |weierstrass| + |asechIfCan| |dihedral| |numFunEvals3D| |complexEigenvalues| + |rightDivide| |internalIntegrate0| |getStream| |FormatArabic| + |numberOfVariables| |s21baf| |screenResolution3D| |critM| + |halfExtendedResultant1| |brillhartIrreducible?| |testModulus| + |monomRDEsys| |doubleComplex?| |LyndonWordsList1| |qroot| + |shallowExpand| |OMgetSymbol| |maxPoints3D| |entry?| |fglmIfCan| + |makeRecord| |log| |jordanAdmissible?| |powerAssociative?| |coshIfCan| + |startTableInvSet!| |zeroDimPrimary?| |lfinfieldint| |has?| + |integralDerivationMatrix| |rk4f| |idealSimplify| |showTypeInOutput| + |cCos| |simpson| |continuedFraction| |setelt| |infLex?| |polyRicDE| + |arity| |sumSquares| |selectMultiDimensionalRoutines| |mapSolve| + |zeroOf| |uniform01| |surface| |SturmHabichtSequence| |block| + |hypergeometric0F1| |wholeRadix| |cyclicParents| |closedCurve| + |constant| |makeCrit| |hdmpToP| |algebraicOf| |empty| |copy| + |nextSublist| |exponent| |coHeight| |autoReduced?| |OMgetBVar| + |symbol?| |reopen!| |algebraicSort| |exQuo| |putGraph| |f02akf| + |anticoord| |countRealRootsMultiple| |divergence| |makeSUP| |numer| + |truncate| |substring?| |double?| |interpret| |coerceL| |autoCoerce| + |makeprod| |length| |mkPrim| |diagonals| |c06ecf| |lexGroebner| + |octon| |denom| |divisor| |leadingExponent| |cAsec| |iiacos| |scripts| + |lfextendedint| |makeViewport3D| |erf| |weighted| |expressIdealMember| + |fmecg| |suffix?| |lfunc| |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| |leftScalarTimes!| + |internalDecompose| |brillhartTrials| |modTree| |tubeRadius| + |derivationCoordinates| |subNode?| |deriv| |eq?| |s13aaf| |setRow!| + |critpOrder| |hash| |semicolonSeparate| |concat| |e04jaf| |pade| + |twist| |constant?| |sturmSequence| |tubePointsDefault| + |problemPoints| |s17dcf| |sincos| |OMputFloat| |listRepresentation| + |imagk| |possiblyNewVariety?| |reindex| |rischDEsys| |count| + |fortranLiteral| |factors| |stoseInvertible?| |besselY| + |resetBadValues| |augment| |getButtonValue| |antiCommutative?| + |outputSpacing| |monicCompleteDecompose| |atanhIfCan| |minColIndex| + |empty?| |complexNumeric| |currentEnv| |Ei| |and?| |socf2socdf| + |s17agf| |squareFreePrim| |generalTwoFactor| |floor| |expandLog| + |isMult| |f04maf| |f02aff| |coleman| |discriminant| + |chainSubResultants| |ridHack1| |extractClosed| |kernels| |rootRadius| + |cycleElt| |previous| |mathieu22| |flexibleArray| D |alphabetic?| + |dfRange| |permutations| |transcendenceDegree| |univariate| + |constantKernel| |e02ajf| |polyPart| |minimalPolynomial| |leftNorm| + |numericIfCan| |maximumExponent| |coerceImages| |inverse| |tan| + |iidsum| |OMgetInteger| |tanh2coth| |makeUnit| |OMreadFile| + |doubleRank| |symmetricTensors| |stronglyReduced?| |FormatRoman| |cot| + |setfirst!| |simpleBounds?| |zeroDim?| |internalSubQuasiComponent?| + |status| |leftZero| |s19aaf| |iiasech| |polynomialZeros| + |mainMonomial| |normalizeIfCan| |leftFactorIfCan| |symbolTable| |sec| + |factor| |central?| |directSum| |totalGroebner| |normalizeAtInfinity| + |removeSinSq| |f02bbf| |infix| |rank| |roughBasicSet| |setchildren!| + |geometric| |csc| |sqrt| |elColumn2!| |binomial| |internalSubPolSet?| + |cRationalPower| |singRicDE| |iiperm| |principal?| + |pushFortranOutputStack| |jacobi| |fintegrate| |radicalSolve| + |replace| |asin| |real| |rootNormalize| |KrullNumber| |cyclic?| + |sylvesterMatrix| |e02ddf| |popFortranOutputStack| |checkRur| + |rowEchLocal| |zeroMatrix| |c06gbf| |parametric?| |acos| |imag| + |pureLex| |subresultantVector| |unitVector| |iiexp| + |firstUncouplingMatrix| |d02ejf| |roughBase?| |vspace| |fixedDivisor| + |outputAsFortran| |atan| |directProduct| |getIdentifier| + |factorsOfDegree| |s17ahf| |triangular?| |graphState| + |linearAssociatedOrder| |hitherPlane| |e04ucf| |monomRDE| + |antisymmetricTensors| |acot| |unary?| |char| |virtualDegree| + |laurentIfCan| |numberOfHues| |gcdprim| |partialNumerators| + |semiResultantEuclidean1| |interval| |expextendedint| |asec| + |csch2sinh| |destruct| |inverseIntegralMatrix| |normFactors| + |maxColIndex| |rdHack1| |lazyIntegrate| |localUnquote| |conical| + |lists| |edf2df| |setelt!| |uniform| |acsc| |mapUp!| |cyclic| |weight| + |validExponential| |flexible?| |leftRegularRepresentation| + |generalizedInverse| |mainContent| |Beta| |sinh| |slex| |derivative| + |leftTrace| |unitsColorDefault| |Is| |getPickedPoints| |changeName| + |stoseLastSubResultant| |unparse| |contours| |exponential1| |cosh| + |exteriorDifferential| |float| |extractBottom!| |euclideanGroebner| + |f07adf| |leftFactor| |iiatanh| |returns| |lift| |squareMatrix| + |areEquivalent?| |tanh| |monomial| |overlap| |critBonD| |increment| + |complete| |recolor| |startTable!| |useSingleFactorBound?| |critB| + |reduce| |prime?| |normalizedDivide| |coth| |multivariate| + |atrapezoidal| FG2F |hessian| |OMputAttr| |eulerPhi| |setCondition!| + |leftDivide| |inspect| |groebner?| |interReduce| |sech| |variables| + |purelyAlgebraic?| |const| |OMputEndApp| |coerceListOfPairs| |s15adf| + |chebyshevT| |arguments| |coordinates| |specialTrigs| + |wordInStrongGenerators| |c06frf| |csch| |polygon?| |OMencodingSGML| + |legendreP| |baseRDEsys| |degreePartition| |removeSinhSq| |viewport3D| + |f02aaf| |ratDsolve| |asinh| |integrate| |selectPolynomials| + |primeFrobenius| |rotate!| |closeComponent| |ref| |normal01| |next| + |removeRoughlyRedundantFactorsInPols| |sort!| + |indicialEquationAtInfinity| |acosh| |generalLambert| |pop!| |sn| + |btwFact| |sechIfCan| |LazardQuotient2| |leftDiscriminant| |rk4| + |nthExponent| |clipPointsDefault| |linearDependence| |match?| |s21bbf| + |atanh| |parametersOf| |vector| |df2fi| |objectOf| |adaptive?| + |extend| |OMgetVariable| |patternMatchTimes| |dequeue| |distFact| + |rk4qc| |acoth| |realSolve| |differentiate| |graphStates| |taylor| + |exprToXXP| |character?| |OMputEndError| GE |basis| |repeating| + |df2st| |calcRanges| |bezoutDiscriminant| + |stiffnessAndStabilityOfODEIF| |getMultiplicationTable| + |decreasePrecision| |c06ebf| |aQuartic| |e04mbf| |asech| |mapDown!| + |laurent| |call| |invmultisect| |stoseInvertible?reg| GT |permutation| + |cyclotomicFactorization| |physicalLength| + |removeRedundantFactorsInPols| |domainOf| |quadraticNorm| + |halfExtendedResultant2| |setMaxPoints3D| |lazyGintegrate| + |showTheSymbolTable| |lazyPquo| |iiGamma| |puiseux| |palglimint0| + |buildSyntax| LE |max| |d02bbf| |f02xef| |collectQuasiMonic| + |drawStyle| |digit| |f2st| |rspace| |relerror| |monicRightDivide| + |multiple| |divide| |cap| |makeGraphImage| |shrinkable| + |trigs2explogs| LT |OMgetEndError| |alternatingGroup| |dAndcExp| + |pushuconst| |applyQuote| |pole?| |redPo| |commutator| |putColorInfo| + |f01mcf| |inv| |computeCycleLength| |OMconnectTCP| |e02adf| |rename| + |partialFraction| |medialSet| |d01aqf| |f01qdf| |outputList| + |exprHasAlgebraicWeight| |baseRDE| |splitConstant| |expIfCan| + |ReduceOrder| |extractIfCan| |ground?| |pol| |lflimitedint| + |trailingCoefficient| |composites| |completeSmith| |cot2tan| |expr| + |stoseInvertibleSet| |getCode| |extendedSubResultantGcd| |d02kef| + |besselI| |OMmakeConn| |variable?| |ground| |decrease| + |balancedFactorisation| |infieldint| |limitedint| |leftQuotient| + |linearlyDependentOverZ?| |ParCond| |rootPoly| |cLog| |OMgetAtp| + |ListOfTerms| |semiResultantEuclideannaif| |lp| |ruleset| + |shallowCopy| |leadingMonomial| |style| |fprindINFO| + |semiLastSubResultantEuclidean| |polygon| |move| |digits| + |exactQuotient| |associatedSystem| |internal?| |cAcsc| |power| + |normInvertible?| |airyBi| |leadingCoefficient| |basisOfRightNucloid| + |logical?| |f04atf| |elem?| |roughSubIdeal?| |bezoutResultant| + |cylindrical| |complement| |printStats!| |padicallyExpand| + |argumentList!| |tanh2trigh| |shiftRight| |primitiveMonomials| |log2| + |jacobian| |d01amf| |or?| |OMParseError?| |insertMatch| |variable| + |gcdPolynomial| |expenseOfEvaluation| |normalElement| |fi2df| + |cschIfCan| |suchThat| |create| |reductum| |sparsityIF| |var2Steps| + |changeThreshhold| |lllip| |generalSqFr| |getDatabase| |pseudoDivide| + |zeroVector| |laplace| |s14baf| |simplify| |largest| |is?| + |paraboloidal| |s19acf| |subResultantsChain| |adaptive3D?| + |hasTopPredicate?| |retractIfCan| |every?| |genericLeftNorm| + |errorKind| |subTriSet?| |invmod| |seed| |radicalEigenvalues| + |normalized?| |s17aef| |tableau| |comp| |regularRepresentation| + |signAround| |factorOfDegree| |plusInfinity| |e01sff| |nlde| |f04arf| + |rightExactQuotient| |numerator| |mainVariable| |e01daf| |modifyPoint| + |s17ajf| |deepestInitial| |minusInfinity| |OMUnknownCD?| + |compactFraction| |maxPoints| |ldf2vmf| + |setLegalFortranSourceExtensions| |monicDivide| |integralBasis| + |useNagFunctions| |recur| |square?| |neglist| |expandPower| + |possiblyInfinite?| |cycleEntry| |isobaric?| |c02aff| |upperCase!| + |mainVariables| |setVariableOrder| |minimumExponent| |nil?| + |hostPlatform| |e04ycf| |eval| |isExpt| |rational?| |s14abf| |algint| + |equiv?| |allRootsOf| |addiag| |intChoose| |atoms| |iiabs| |overbar| + |mapdiv| |lex| |crushedSet| |leftAlternative?| |linearlyDependent?| + |mdeg| |printInfo| |rotate| |invertIfCan| |primPartElseUnitCanonical| + |numberOfIrreduciblePoly| |iFTable| |pmComplexintegrate| |bumptab| + |divideIfCan| |coth2tanh| |function| |powers| |perspective| + |nextColeman| |sinh2csch| |deleteProperty!| |leastMonomial| |heapSort| + |hue| |cyclotomicDecomposition| |iCompose| |f04mcf| + |resultantEuclideannaif| |perfectSquare?| |safetyMargin| |flatten| + |taylorIfCan| |evenInfiniteProduct| |setleft!| |type| |monic?| + |topFortranOutputStack| |compile| |d03eef| |multiplyCoefficients| + |definingPolynomial| |hexDigit| |f01bsf| |cosh2sech| |printStatement| + |absolutelyIrreducible?| |setProperties| |infinityNorm| + |eisensteinIrreducible?| |s20acf| |trapezoidalo| |multiple?| + |directory| |indicialEquation| |dihedralGroup| |interpretString| |/\\| + |true| |badValues| |prolateSpheroidal| |map| |adaptive| |secIfCan| + |parts| |vectorise| |characteristicSerie| |zero| |solid| |getlo| + |seriesToOutputForm| |\\/| |e02akf| |singular?| |overlabel| + |lowerPolynomial| |subQuasiComponent?| |bat1| |e02def| + |genericLeftTrace| |insert| |s01eaf| |symmetricGroup| + |removeRedundantFactorsInContents| |And| |rubiksGroup| ** + |createZechTable| |term| |cycles| |gramschmidt| |nilFactor| |OMclose| + |pushNewContour| |limitPlus| SEGMENT |Or| |lagrange| |fullDisplay| + |symbolIfCan| |typeLists| |revert| |symmetricRemainder| |stopTable!| + |normalForm| |ptree| |quasiMonic?| |Not| |companionBlocks| + |divisorCascade| |f01rdf| |maxrow| EQ |convert| |iiasec| |cCoth| + |constantLeft| |whatInfinity| |quartic| |rootKerSimp| |chvar| + |colorFunction| |child?| |computePowers| |quasiRegular| |belong?| + |twoFactor| |phiCoord| |besselJ| |leadingIdeal| |rootProduct| + |approxSqrt| |numberOfComponents| |refine| |findCycle| |getBadValues| + |unravel| |lazyPseudoDivide| |horizConcat| |nextPrimitivePoly| + |append| |zeroSetSplit| |nextPrime| |infinite?| |setvalue!| + |linearMatrix| |isList| |ratPoly| |quasiComponent| + |removeRoughlyRedundantFactorsInContents| |shellSort| |lcm| + |varselect| |cAcos| |constantIfCan| |pointPlot| |relativeApprox| + |basisOfRightNucleus| |option?| |cup| |discreteLog| |chebyshevU| |bat| + |search| |quasiMonicPolynomials| |patternMatch| |yCoordinates| + |deepCopy| |OMputBind| |stopMusserTrials| |OMputObject| |cosIfCan| + |selectSumOfSquaresRoutines| |dom| |point?| |fibonacci| + |stronglyReduce| |univcase| |GospersMethod| |gcd| |mainMonomials| + |createLowComplexityNormalBasis| |viewPosDefault| |orbits| |f02bjf| + |showIntensityFunctions| |OMputEndAtp| |pmintegrate| |logpart| |union| + |computeInt| |enterInCache| |rationalIfCan| |sign| |f07aef| |subSet| + |exp1| |false| |complexNumericIfCan| |clipSurface| |setProperty!| + |bandedHessian| |modularGcdPrimitive| |OMputAtp| + |setAttributeButtonStep| |mathieu23| |sort| |rational| |f02ajf| + |mainForm| |LiePolyIfCan| |parabolicCylindrical| |rationalPower| + |powerSum| |e01bhf| |powern| |dimensionsOf| |tube| |s18aff| |frst| + |mesh?| |mergeDifference| |numberOfComposites| |ef2edf| + |OMputEndObject| |listYoungTableaus| |denominator| |title| + |invertibleSet| |clipBoolean| |close| |deepestTail| + |initializeGroupForWordProblem| |triangularSystems| |merge| |OMwrite| + |compose| |stop| |partialDenominators| |extendedint| |member?| |int| + |alternative?| |matrixConcat3D| |irreducibleFactors| |e01sef| + |equivOperands| |firstSubsetGray| |digamma| |genericLeftTraceForm| + |endSubProgram| |untab| |callForm?| |display| |cCot| |OMreceive| + |abelianGroup| |rightTrim| |iisech| |sncndn| |e| |contract| |plot| + |random| |exactQuotient!| |node?| |copies| |df2mf| |moebius| |ceiling| + |squareFreeLexTriangular| |leftTrim| |outputGeneral| + |rightRegularRepresentation| |iisinh| |polCase| |aromberg| + |SturmHabichtCoefficients| |OMread| |andOperands| |setStatus| + |listOfLists| |screenResolution| |setStatus!| |rightRankPolynomial| + |ScanFloatIgnoreSpaces| |algebraic?| |addBadValue| + |integralCoordinates| |cAtanh| |torsion?| |module| |leaves| + |stoseInternalLastSubResultant| |reduction| |solid?| + |recoverAfterFail| |sturmVariationsOf| |lowerCase?| |OMgetEndAtp| + |nary?| |e02bcf| |trim| |subscript| |palgRDE| |zeroSquareMatrix| + |diophantineSystem| |input| |oblateSpheroidal| |removeCosSq| + |localReal?| |top| |e02dcf| |term?| |output| |inGroundField?| |regime| + |tail| |createPrimitiveNormalPoly| |scan| |continue| |library| |one?| + |nsqfree| |keys| |imagJ| |SturmHabichtMultiple| |superHeight| + |loopPoints| |depth| |showClipRegion| |badNum| |applyRules| + |leadingTerm| |notOperand| |comment| |identityMatrix| |besselK| + |push!| |LowTriBddDenomInv| LODO2FUN |midpoints| + |combineFeatureCompatibility| |topPredicate| |reify| |distribute| + |mapUnivariate| |f04asf| |rootOfIrreduciblePoly| |meshPar1Var| |lazy?| + |minPol| |wronskianMatrix| |jordanAlgebra?| |palgintegrate| + |maxRowIndex| |factorSquareFree| |replaceKthElement| |squareFree| + |stFunc1| |retractable?| |tanQ| |tensorProduct| |listConjugateBases| + |rotatey| |set| |createNormalPoly| |xCoord| |positive?| |more?| + |integralMatrixAtInfinity| |goto| |trace2PowMod| |csc2sin| |d01anf| + |internalLastSubResultant| |terms| |ranges| |inverseColeman| + |numberOfChildren| |viewDefaults| |quatern| |factorial| + |nextPrimitiveNormalPoly| |resultantnaif| |noLinearFactor?| + |genericRightTrace| |bringDown| |generators| |zCoord| + |viewZoomDefault| |symmetric?| |denomLODE| |rightLcm| |getGraph| + |nand| |conjugate| |contains?| |bandedJacobian| |singleFactorBound| + |head| |characteristicSet| |ParCondList| |positiveSolve| |mindeg| + |mergeFactors| |reverse!| |generalizedEigenvectors| + |solveLinearPolynomialEquationByFractions| + |rewriteIdealWithQuasiMonicGenerators| |ipow| |chiSquare| |pquo| + |invertible?| |OMputBVar| |minGbasis| |norm| |graphImage| |divisors| + |OMputString| |symmetricDifference| |getMultiplicationMatrix| |f02abf| + |setAdaptive| |fixPredicate| |minordet| |palgextint0| + |associatedEquations| |dioSolve| |stack| |nor| |satisfy?| + |enterPointData| |simplifyPower| |contractSolve| |subResultantChain| + |trueEqual| |maxrank| |mapExponents| |genericPosition| |minIndex| + |linkToFortran| |components| |minPoints| |charClass| |elliptic?| + |primextintfrac| |quoted?| |rootOf| |unaryFunction| |solveInField| + |cyclicSubmodule| |checkForZero| |LyndonWordsList| + |complementaryBasis| |headRemainder| |acosIfCan| |list?| |nthExpon| + |quasiRegular?| |kroneckerDelta| |mkcomm| |show| |rationalPoint?| + |bitTruth| |rur| |split!| |cycleTail| |mkAnswer| |pow| |direction| + |readLineIfCan!| |d01akf| |hex| |factor1| |normalize| |pattern| + |normal?| |open?| |clearTheIFTable| |push| |extractTop!| + |scalarMatrix| |close!| |exptMod| |leadingSupport| |trace| + |highCommonTerms| |linears| |nextNormalPoly| |e01bgf| + |solveLinearPolynomialEquation| |makeFR| |tryFunctionalDecomposition?| + |palgRDE0| |swapColumns!| |normDeriv2| |d01ajf| |nthFractionalTerm| + |completeHermite| |colorDef| |bfKeys| |reduceBasisAtInfinity| + |fracPart| |li| |linear| |OMsetEncoding| |squareFreeFactors| + |setImagSteps| |LyndonCoordinates| |endOfFile?| |d03faf| + |nextsousResultant2| |npcoef| |symbol| |mapCoef| |toseSquareFreePart| + |bivariate?| |quoByVar| |getProperties| |setErrorBound| |f02axf| + |OMencodingBinary| |bit?| |csubst| |clip| |bindings| + |halfExtendedSubResultantGcd1| |polynomial| + |indiceSubResultantEuclidean| |particularSolution| |cSec| + |fortranCarriageReturn| |scalarTypeOf| |permanent| |pushucoef| + |returnTypeOf| |distdfact| |constantToUnaryFunction| |karatsubaDivide| + |eulerE| |simplifyExp| |OMgetEndBind| |freeOf?| |newReduc| |s21bcf| + |c02agf| |numberOfCycles| |selectNonFiniteRoutines| |bernoulli| + |repeatUntilLoop| |sPol| |pack!| + |generalizedContinuumHypothesisAssumed| |explicitlyEmpty?| + |triangSolve| |denominators| |cothIfCan| |constructorName| + |cyclicCopy| |hexDigit?| |stirling1| |flagFactor| |cosSinInfo| + |OMlistSymbols| |elRow1!| |clearCache| |thetaCoord| |resultantReduit| + |padecf| |imagK| |radicalOfLeftTraceForm| |multiEuclideanTree| + |rotatex| |antiAssociative?| |collectUpper| |say| |innerEigenvectors| + |aCubic| |clikeUniv| |generic?| |mvar| |padicFraction| |branchPoint?| + |reducedQPowers| |wholePart| |selectIntegrationRoutines| |orbit| + |substitute| |body| |tubePlot| |nthCoef| |mathieu12| + |LagrangeInterpolation| |debug3D| |leadingBasisTerm| + |integralAtInfinity?| |f02adf| |meshFun2Var| |toseInvertible?| + |selectFiniteRoutines| |removeDuplicates| |arrayStack| |string| + |clearFortranOutputStack| |f04jgf| |nthRootIfCan| + |radicalEigenvectors| |radicalSimplify| |countable?| |pseudoRemainder| + |primeFactor| |adjoint| |rightZero| |basisOfCommutingElements| + |oneDimensionalArray| |iExquo| |limit| |randnum| |hermiteH| |bright| + |scopes| |difference| |LazardQuotient| |rationalApproximation| |ode2| + |asinIfCan| |curve?| |janko2| |divideExponents| |insertBottom!| + |innerSolve1| |getOperator| |OMopenString| |reflect| |subst| + |sizeMultiplication| |noncommutativeJordanAlgebra?| |moreAlgebraic?| + |finiteBasis| |lexTriangular| |subResultantGcdEuclidean| |Aleph| + |OMencodingUnknown| |writable?| |solve1| |infiniteProduct| |postfix| + |iprint| |returnType!| |e01bff| |operators| |minimize| |sequences| + |radPoly| |leftLcm| |entries| |removeZeroes| |exponentialOrder| + |delete| |read!| |kovacic| |groebner| |sin2csc| |range| |e02bbf| + |asinhIfCan| |s13acf| |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| + |approximate| |complex| |shallowMutable| |canonical| |noetherian| + |central| |partiallyOrderedSet| |arbitraryPrecision| + |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| + |additiveValuation| |unitsKnown| |canonicalUnitNormal| + |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| + |commutative|)
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T) ((-23) . T) ((-25) . T) ((-37 #0=(-385 (-525))) -3316 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-37 |#1|) . T) ((-37 $) -3316 (|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#) -3316 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-107 |#1| |#1|) . T) ((-107 $ $) . T) ((-126) . T) ((-136) -3316 (|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) ((-486 |#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((-594 |#2|) -3275 (|has| |#2| (-977)) (|has| |#2| (-341)) (|has| |#2| (-160))) ((-594 $) -3275 (|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|) -3275 (|has| |#2| (-341)) (|has| |#2| (-160))) ((-669) -3275 (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-669)) (|has| |#2| (-160))) ((-733) |has| |#2| (-787)) ((-734) -3275 (|has| |#2| (-787)) (|has| |#2| (-735))) ((-735) |has| |#2| (-735)) ((-736) -3275 (|has| |#2| (-787)) (|has| |#2| (-735))) ((-737) -3275 (|has| |#2| (-787)) (|has| |#2| (-735))) ((-787) |has| |#2| (-787)) ((-789) -3275 (|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|) -3275 (|has| |#2| (-977)) (|has| |#2| (-341)) (|has| |#2| (-160))) ((-983 $) |has| |#2| (-160)) ((-977) -3275 (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-160))) ((-984) -3275 (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-160))) ((-1032) -3275 (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-669)) (|has| |#2| (-160))) ((-1020) -3275 (|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) . T) ((-1180 |#2|) |has| |#2| (-341))) -((-3836 (((-220 |#1| |#3|) (-1 |#3| |#2| |#3|) (-220 |#1| |#2|) |#3|) 21)) (-3497 ((|#3| (-1 |#3| |#2| |#3|) (-220 |#1| |#2|) |#3|) 23)) (-2688 (((-220 |#1| |#3|) (-1 |#3| |#2|) (-220 |#1| |#2|)) 18))) -(((-219 |#1| |#2| |#3|) (-10 -7 (-15 -3836 ((-220 |#1| |#3|) (-1 |#3| |#2| |#3|) (-220 |#1| |#2|) |#3|)) (-15 -3497 (|#3| (-1 |#3| |#2| |#3|) (-220 |#1| |#2|) |#3|)) (-15 -2688 ((-220 |#1| |#3|) (-1 |#3| |#2|) (-220 |#1| |#2|)))) (-713) (-1127) (-1127)) (T -219)) -((-2688 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-220 *5 *6)) (-14 *5 (-713)) (-4 *6 (-1127)) (-4 *7 (-1127)) (-5 *2 (-220 *5 *7)) (-5 *1 (-219 *5 *6 *7)))) (-3497 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-220 *5 *6)) (-14 *5 (-713)) (-4 *6 (-1127)) (-4 *2 (-1127)) (-5 *1 (-219 *5 *6 *2)))) (-3836 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-220 *6 *7)) (-14 *6 (-713)) (-4 *7 (-1127)) (-4 *5 (-1127)) (-5 *2 (-220 *6 *5)) (-5 *1 (-219 *6 *7 *5))))) -(-10 -7 (-15 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|#2|)) NIL (|has| |#2| (-977)))) (-2041 (((-713) (-1 (-108) |#2|) $) NIL (|has| $ (-6 -4255))) (((-713) |#2| $) NIL (-12 (|has| $ (-6 -4255)) (|has| |#2| (-1020))))) (-1454 (($ $) NIL)) (-1271 (((-1173 |#2|) $) 10) (($ (-525)) NIL (-3275 (-12 (|has| |#2| (-968 (-525))) (|has| |#2| (-1020))) (|has| |#2| (-977)))) (($ (-385 (-525))) NIL (-12 (|has| |#2| (-968 (-385 (-525)))) (|has| |#2| (-1020)))) (($ |#2|) 13 (|has| |#2| (-1020))) (((-798) $) NIL (|has| |#2| (-566 (-798))))) (-3998 (((-713)) NIL (|has| |#2| (-977)))) (-2375 (((-108) (-1 (-108) |#2|) $) NIL (|has| $ (-6 -4255)))) (-3297 (($ $) NIL (|has| |#2| (-787)))) (-1581 (($ $ (-713)) NIL (|has| |#2| (-669))) (($ $ (-856)) NIL (|has| |#2| (-669)))) (-3351 (($) 35 (|has| |#2| (-126)) CONST)) (-3362 (($) 38 (|has| |#2| (-669)) CONST)) (-2096 (($ $) NIL (-12 (|has| |#2| (-213)) (|has| |#2| (-977)))) (($ $ (-713)) NIL (-12 (|has| |#2| (-213)) (|has| |#2| (-977)))) (($ $ (-1091)) NIL (-12 (|has| |#2| (-835 (-1091))) (|has| |#2| (-977)))) 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T) ((-37 |#2|) |has| |#2| (-160)) ((-97) -3316 (|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))) ((-107 |#2| |#2|) -3316 (|has| |#2| (-977)) (|has| |#2| (-341)) (|has| |#2| (-160))) ((-107 $ $) |has| |#2| (-160)) ((-126) -3316 (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-735)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-126))) ((-566 (-798)) -3316 (|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| (-566 (-798))) (|has| |#2| (-126)) (|has| |#2| (-25))) ((-566 (-1173 |#2|)) . T) ((-160) |has| |#2| (-160)) ((-211 |#2|) |has| |#2| (-977)) ((-213) -12 (|has| |#2| (-213)) (|has| |#2| (-977))) ((-265 #0=(-525) |#2|) . T) ((-267 #0# |#2|) . 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|) . 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T) ((-355 |#1|) . T) ((-389 |#1|) . T) ((-429) -3275 (|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) -3275 (|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 $) -3275 (|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))) -((-1261 (((-108) $ $) 19 (|has| |#1| (-1020)))) (-4061 ((|#1| $) 54)) (-2933 ((|#1| $) 44)) (-2230 (((-108) $ (-713)) 8)) (-3347 (($) 7 T CONST)) (-1884 (($ $) 60)) (-3533 (($ $) 48)) (-2416 ((|#1| |#1| $) 46)) (-1634 ((|#1| $) 45)) (-3700 (((-592 |#1|) $) 30 (|has| $ (-6 -4255)))) (-2034 (((-108) $ (-713)) 9)) (-3780 (((-592 |#1|) $) 29 (|has| $ (-6 -4255)))) (-2741 (((-108) |#1| $) 27 (-12 (|has| |#1| (-1020)) (|has| $ (-6 -4255))))) (-2608 (($ (-1 |#1| |#1|) $) 34 (|has| $ (-6 -4256)))) (-2688 (($ (-1 |#1| |#1|) $) 35)) (-4060 (((-108) $ (-713)) 10)) (-1399 (((-713) $) 61)) (-3803 (((-1074) $) 22 (|has| |#1| (-1020)))) (-2163 ((|#1| $) 39)) (-2957 ((|#1| |#1| $) 52)) (-1493 ((|#1| |#1| $) 51)) (-1710 (($ |#1| $) 40)) (-1756 (((-713) $) 55)) (-2015 (((-1038) $) 21 (|has| |#1| (-1020)))) (-1661 ((|#1| $) 62)) (-3851 ((|#1| $) 50)) (-2485 ((|#1| $) 49)) (-4017 ((|#1| $) 41)) (-1509 (((-108) (-1 (-108) |#1|) $) 32 (|has| $ (-6 -4255)))) (-2597 (($ $ (-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))))) (-3107 (((-108) $ $) 14)) (-2937 ((|#1| |#1| $) 58)) (-1802 (((-108) $) 11)) (-1864 (($) 12)) (-3211 ((|#1| $) 59)) (-3906 (($) 57) (($ (-592 |#1|)) 56)) (-4062 (((-713) $) 43)) (-2041 (((-713) (-1 (-108) |#1|) $) 31 (|has| $ (-6 -4255))) (((-713) |#1| $) 28 (-12 (|has| |#1| (-1020)) (|has| $ (-6 -4255))))) (-1454 (($ $) 13)) (-1271 (((-798) $) 18 (|has| |#1| (-566 (-798))))) (-4101 ((|#1| $) 53)) (-3353 (($ (-592 |#1|)) 42)) (-1846 ((|#1| $) 63)) (-2375 (((-108) (-1 (-108) |#1|) $) 33 (|has| $ (-6 -4255)))) (-3992 (((-108) $ $) 20 (|has| |#1| (-1020)))) (-3594 (((-713) $) 6 (|has| $ (-6 -4255))))) +((-1777 (*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)))) (-4167 (*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)))) (-3517 (*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)))) (-3517 (*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)))) (-3958 (*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)))) (-1725 (*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))))) (-2135 (*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)))) (-1725 (*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))))) (-2135 (*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)))) (-2472 (*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)))) (-3675 (*1 *2 *1) (-12 (-4 *1 (-232 *3 *4 *2 *5)) (-4 *3 (-977)) (-4 *4 (-789)) (-4 *5 (-735)) (-4 *2 (-245 *4)))) (-3655 (*1 *1 *1) (-12 (-4 *1 (-232 *2 *3 *4 *5)) (-4 *2 (-977)) (-4 *3 (-789)) (-4 *4 (-245 *3)) (-4 *5 (-735)))) (-1308 (*1 *1 *1) (-12 (-4 *1 (-232 *2 *3 *4 *5)) (-4 *2 (-977)) (-4 *3 (-789)) (-4 *4 (-245 *3)) (-4 *5 (-735)))) (-1777 (*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 -1777 ((-1 $ (-713)) |t#2|)) (-15 -4167 ((-592 |t#2|) $)) (-15 -3517 ((-713) $ |t#2|)) (-15 -3517 ((-713) $)) (-15 -3958 ((-713) $ |t#2|)) (-15 -1725 ((-592 (-713)) $)) (-15 -2135 ((-713) $)) (-15 -1725 ((-592 (-713)) $ |t#2|)) (-15 -2135 ((-713) $ |t#2|)) (-15 -2472 ((-108) $)) (-15 -3675 (|t#3| $)) (-15 -3655 ($ $)) (-15 -1308 ($ $)) (IF (|has| |t#1| (-213)) (PROGN (-6 (-486 |t#2| |t#1|)) (-6 (-486 |t#2| $)) (-6 (-288 $)) (-15 -1777 ((-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 $) -3316 (|has| |#1| (-844)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-97) . T) ((-107 #0# #0#) |has| |#1| (-37 (-385 (-525)))) ((-107 |#1| |#1|) . T) ((-107 $ $) -3316 (|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) -3316 (|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) -3316 (|has| |#1| (-844)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-288 $) . T) ((-304 |#1| |#4|) . 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|) . 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 $) -3316 (|has| |#1| (-844)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-160))) ((-977) . T) ((-984) . T) ((-1032) . T) ((-1020) . 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))))) (((-233 |#1|) (-131) (-1127)) (T -233)) -((-3906 (*1 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1127)))) (-3906 (*1 *1 *2) (-12 (-5 *2 (-592 *3)) (-4 *3 (-1127)) (-4 *1 (-233 *3)))) (-1756 (*1 *2 *1) (-12 (-4 *1 (-233 *3)) (-4 *3 (-1127)) (-5 *2 (-713)))) (-4061 (*1 *2 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1127)))) (-4101 (*1 *2 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1127)))) (-2957 (*1 *2 *2 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1127)))) (-1493 (*1 *2 *2 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1127)))) (-3851 (*1 *2 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1127)))) (-2485 (*1 *2 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1127)))) (-3533 (*1 *1 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1127))))) -(-13 (-1039 |t#1|) (-927 |t#1|) (-10 -8 (-15 -3906 ($)) (-15 -3906 ($ (-592 |t#1|))) (-15 -1756 ((-713) $)) (-15 -4061 (|t#1| $)) (-15 -4101 (|t#1| $)) (-15 -2957 (|t#1| |t#1| $)) (-15 -1493 (|t#1| |t#1| $)) (-15 -3851 (|t#1| $)) (-15 -2485 (|t#1| $)) (-15 -3533 ($ $)))) -(((-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 $) -3316 (|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 $ $) -3316 (|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) -3316 (|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 -2711 (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 3149551 3149556 3149561 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-2 3149536 3149541 3149546 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1 3149521 3149526 3149531 NIL NIL NIL NIL (NIL) -8 NIL NIL) (0 3149506 3149511 3149516 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1199 3148636 3149381 3149458 "ZMOD" 3149463 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1198 3147746 3147910 3148119 "ZLINDEP" 3148468 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1197 3137150 3138895 3140847 "ZDSOLVE" 3145895 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1196 3136396 3136537 3136726 "YSTREAM" 3136996 NIL YSTREAM (NIL T) -7 NIL NIL) (-1195 3134165 3135701 3135904 "XRPOLY" 3136239 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1194 3130627 3131956 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) 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(|:| |Return| "return") - (|:| |Block| "block") (|:| |Comment| "comment") - (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") - (|:| |Repeat| "repeat") (|:| |Goto| "goto") - (|:| |Continue| "continue") - (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") - (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print"))) - (-5 *1 (-308))))) -(((*1 *2 *3) - (-12 (-4 *4 (-517)) (-5 *2 (-713)) (-5 *1 (-42 *4 *3)) - (-4 *3 (-395 *4))))) -(((*1 *2 *1) - (-12 (-4 *2 (-884 *3 *5 *4)) (-5 *1 (-920 *3 *4 *5 *2)) - (-4 *3 (-429)) (-4 *4 (-789)) (-4 *5 (-735))))) -(((*1 *2 *2) (-12 (-5 *2 (-856)) (|has| *1 (-6 -4246)) (-4 *1 (-382)))) - ((*1 *2) (-12 (-4 *1 (-382)) (-5 *2 (-856)))) - ((*1 *2 *2) (-12 (-5 *2 (-856)) (-5 *1 (-641)))) - ((*1 *2) (-12 (-5 *2 (-856)) (-5 *1 (-641))))) + (-12 (-4 *3 (-517)) (-5 *2 (-592 *4)) (-5 *1 (-42 *3 *4)) + (-4 *4 (-395 *3))))) +(((*1 *2) + (-12 (-5 *2 (-1178)) (-5 *1 (-1105 *3 *4)) (-4 *3 (-1020)) + (-4 *4 (-1020))))) +(((*1 *2 *1) (-12 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|c| (-1193 *3))))) + (-5 *1 (-1193 *3)) (-4 *3 (-977)))) + ((*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))))) (((*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 -3405 ((-1074) $ (-1091))) (-15 -2863 ((-1178) $)) - (-15 -1358 ((-1178) $))))))) + (-10 -8 (-15 -3494 ((-1074) $ (-1091))) (-15 -2746 ((-1178) $)) + (-15 -2591 ((-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) @@ -764,178 +632,84 @@ ((*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 *2) 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(-525)))))) - (-5 *1 (-951 *3)) (-4 *3 (-1149 (-525))))) - ((*1 *2 *3 *4) - (-12 - (-5 *2 - (-592 (-2 (|:| -3592 (-385 (-525))) (|:| -3601 (-385 (-525)))))) - (-5 *1 (-951 *3)) (-4 *3 (-1149 (-525))) - (-5 *4 (-2 (|:| -3592 (-385 (-525))) (|:| -3601 (-385 (-525))))))) - ((*1 *2 *3 *4) - (-12 - (-5 *2 - (-592 (-2 (|:| -3592 (-385 (-525))) (|:| -3601 (-385 (-525)))))) - (-5 *1 (-951 *3)) (-4 *3 (-1149 (-525))) (-5 *4 (-385 (-525))))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-385 (-525))) - (-5 *2 (-592 (-2 (|:| -3592 *5) (|:| -3601 *5)))) (-5 *1 (-951 *3)) - (-4 *3 (-1149 (-525))) (-5 *4 (-2 (|:| -3592 *5) (|:| -3601 *5))))) - ((*1 *2 *3) - (-12 - (-5 *2 - (-592 (-2 (|:| -3592 (-385 (-525))) (|:| -3601 (-385 (-525)))))) - (-5 *1 (-952 *3)) (-4 *3 (-1149 (-385 (-525)))))) - ((*1 *2 *3 *4) - (-12 - (-5 *2 - (-592 (-2 (|:| -3592 (-385 (-525))) (|:| -3601 (-385 (-525)))))) - (-5 *1 (-952 *3)) (-4 *3 (-1149 (-385 (-525)))) - (-5 *4 (-2 (|:| -3592 (-385 (-525))) (|:| -3601 (-385 (-525))))))) - ((*1 *2 *3 *4) + (-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 *2 - (-592 (-2 (|:| -3592 (-385 (-525))) (|:| -3601 (-385 (-525)))))) - (-5 *1 (-952 *3)) (-4 *3 (-1149 (-385 (-525)))) - (-5 *4 (-385 (-525))))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-385 (-525))) - (-5 *2 (-592 (-2 (|:| -3592 *5) (|:| -3601 *5)))) (-5 *1 (-952 *3)) - (-4 *3 (-1149 (-385 (-525)))) - (-5 *4 (-2 (|:| -3592 *5) (|:| -3601 *5)))))) + (-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") + (|:| |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 *2 (-966)) (-5 *1 (-284))))) (((*1 *1 *1) - (-12 (-5 *1 (-550 *2)) (-4 *2 (-37 (-385 (-525)))) (-4 *2 (-977))))) -(((*1 *2 *3 *4 *5 *6 *3 *3 *3 *3 *6 *3 *7 *8) - (-12 (-5 *3 (-525)) (-5 *4 (-632 (-205))) (-5 *5 (-108)) - (-5 *6 (-205)) (-5 *7 (-3 (|:| |fn| (-366)) (|:| |fp| (-66 APROD)))) - 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(-1023 *3 *4 *5 *6 *7)) (-4 *3 (-1020)) (-4 *4 (-1020)) + (-4 *5 (-1020)) (-4 *6 (-1020)) (-4 *7 (-1020)) (-5 *2 (-108))))) (((*1 *1 *1 *1) (-4 *1 (-25))) ((*1 *1 *1 *1) (-5 *1 (-146))) ((*1 *1 *1 *1) (-12 (-5 *1 (-195 *2)) (-4 *2 (-13 (-789) - (-10 -8 (-15 -3405 ((-1074) $ (-1091))) (-15 -2863 ((-1178) $)) - (-15 -1358 ((-1178) $))))))) + (-10 -8 (-15 -3494 ((-1074) $ (-1091))) (-15 -2746 ((-1178) $)) + (-15 -2591 ((-1178) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-273 *2)) (-4 *2 (-25)) (-4 *2 (-1127)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-273 *2)) (-4 *2 (-25)) (-4 *2 (-1127)))) ((*1 *1 *2 *1) @@ -958,80 +732,34 @@ (-12 (-5 *2 (-1072 *3)) (-4 *3 (-977)) (-5 *1 (-1076 *3)))) ((*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 (-25))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-916 *2)) (-4 *2 (-1113))))) -(((*1 *1 *2) (-12 (-5 *2 (-592 *1)) (-4 *1 (-281)))) - ((*1 *1 *1) (-4 *1 (-281))) - ((*1 *1 *2) (-12 (-5 *2 (-592 (-798))) (-5 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*4 (-13 (-517) (-789) (-968 (-525)))) (-5 *2 (-108)) + (-5 *1 (-170 *4 *3)) (-4 *3 (-13 (-27) (-1113) (-408 (-157 *4)))))) + ((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-412)))) + ((*1 *2 *3) + (-12 (-4 *4 (-13 (-429) (-789) (-968 (-525)) (-588 (-525)))) + (-5 *2 (-108)) (-5 *1 (-1117 *4 *3)) + (-4 *3 (-13 (-27) (-1113) (-408 *4)))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-525)) (-4 *1 (-55 *4 *5 *3)) (-4 *4 (-1127)) + (-4 *5 (-351 *4)) (-4 *3 (-351 *4))))) +(((*1 *1 *2) (-12 (-4 *1 (-612 *2)) (-4 *2 (-1127)))) + ((*1 *2 *1) (-12 (-5 *2 (-592 (-1091))) (-5 *1 (-1091))))) (((*1 *2 *1) (-12 (-5 *2 @@ -1040,7 +768,7 @@ (-2 (|:| |var| (-1091)) (|:| |arrayIndex| (-592 (-887 (-525)))) (|:| |rand| - (-2 (|:| |ints2Floats?| (-108)) (|:| -2529 (-798)))))) + (-2 (|:| |ints2Floats?| (-108)) (|:| -2345 (-798)))))) (|:| |arrayAssignmentBranch| (-2 (|:| |var| (-1091)) (|:| |rand| (-798)) (|:| |ints2Floats?| (-108)))) @@ -1048,204 +776,514 @@ (-2 (|:| |switch| (-1090)) (|:| |thenClause| (-308)) (|:| 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((*1 *1 *2 *1) (-12 (-14 *3 (-592 (-1091))) (-4 *4 (-160)) - (-4 *6 (-218 (-3594 *3) (-713))) + (-4 *6 (-218 (-3674 *3) (-713))) (-14 *7 - (-1 (-108) (-2 (|:| -3636 *5) (|:| -2058 *6)) - (-2 (|:| -3636 *5) (|:| -2058 *6)))) + (-1 (-108) (-2 (|:| -3703 *5) (|:| -1474 *6)) + (-2 (|:| -3703 *5) (|:| -1474 *6)))) (-5 *1 (-438 *3 *4 *5 *6 *7 *2)) (-4 *5 (-789)) (-4 *2 (-884 *4 *6 (-800 *3))))) ((*1 *1 *1 *2) @@ -4679,50 +4400,116 @@ (-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 (-5 *2 (-592 (-273 *3))) (-5 *1 (-273 *3)) (-4 *3 (-517)) - (-4 *3 (-1127))))) -(((*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)))) - ((*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)))) - ((*1 *1 *2 *3) (-12 (-5 *3 (-713)) (-4 *1 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(-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 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(-789) (-517))) (-5 *1 (-255 *3 *2)) @@ -10825,316 +12084,55 @@ ((*1 *2 *2) (-12 (-5 *2 (-1072 *3)) (-4 *3 (-37 (-385 (-525)))) (-5 *1 (-1078 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *2 (-592 (-2 (|:| -2197 *3) (|:| -4003 (-525))))) - (-5 *1 (-638 *3)) (-4 *3 (-1149 (-525))) (-5 *4 (-525))))) -(((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *4 (-1091)) (-5 *5 (-592 (-385 (-887 *6)))) - (-4 *6 (-13 (-517) (-968 (-525)) (-138))) - (-5 *2 - (-2 (|:| |mainpart| (-385 (-887 *6))) - (|:| |limitedlogs| - (-592 - (-2 (|:| |coeff| (-385 (-887 *6))) - (|:| |logand| (-385 (-887 *6)))))))) - (-5 *1 (-531 *6)) (-5 *3 (-385 (-887 *6)))))) -(((*1 *2 *3) (-12 (-5 *3 (-357)) (-5 *2 (-205)) (-5 *1 (-1176)))) - ((*1 *2) (-12 (-5 *2 (-205)) (-5 *1 (-1176))))) -(((*1 *2) - (-12 (-4 *1 (-320 *3 *4 *5)) (-4 *3 (-1131)) (-4 *4 (-1149 *3)) - (-4 *5 (-1149 (-385 *4))) (-5 *2 (-108))))) -(((*1 *2 *2 *1) - (-12 (-5 *2 (-592 *6)) (-4 *1 (-909 *3 *4 *5 *6)) (-4 *3 (-977)) - (-4 *4 (-735)) (-4 *5 (-789)) (-4 *6 (-991 *3 *4 *5)) 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(-735)) + (-4 *7 (-789)) (-5 *2 (-713)) (-5 *1 (-994 *5 *6 *7 *8 *9)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-592 *8)) (-5 *4 (-592 *9)) (-4 *8 (-991 *5 *6 *7)) + (-4 *9 (-1029 *5 *6 *7 *8)) (-4 *5 (-429)) (-4 *6 (-735)) + (-4 *7 (-789)) (-5 *2 (-713)) (-5 *1 (-1061 *5 *6 *7 *8 *9))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-565 *2)) (-4 *2 (-13 (-27) (-1113) (-408 *4))) + (-4 *4 (-13 (-517) (-789) (-968 (-525)) (-588 (-525)))) + (-5 *1 (-256 *4 *2))))) (((*1 *2 *1) (-12 (-4 *1 (-154 *2)) (-4 *2 (-160)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-517) (-789) (-968 (-525)))) (-5 *2 (-294 *4)) @@ -11501,10 +12381,6 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-429) (-789) (-968 (-525)) (-588 (-525)))) (-5 *1 (-1117 *3 *2)) (-4 *2 (-13 (-27) (-1113) (-408 *3)))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-592 (-887 *6))) (-5 *4 (-592 (-1091))) - (-4 *6 (-13 (-517) (-968 *5))) (-4 *5 (-517)) - (-5 *2 (-592 (-592 (-273 (-385 (-887 *6)))))) (-5 *1 (-969 *5 *6))))) (((*1 *1 *1) (-4 *1 (-91))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-789) (-517))) (-5 *1 (-255 *3 *2)) @@ -11524,40 +12400,90 @@ ((*1 *2 *2) (-12 (-5 *2 (-1072 *3)) (-4 *3 (-37 (-385 (-525)))) (-5 *1 (-1078 *3))))) +(((*1 *1 *1 *2 *1) (-12 (-4 *1 (-1060)) (-5 *2 (-1140 (-525)))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-385 (-887 *5))) (-5 *4 (-1091)) + (-4 *5 (-13 (-286) (-789) (-138))) (-5 *2 (-592 (-273 (-294 *5)))) + (-5 *1 (-1047 *5)))) + ((*1 *2 *3) + (-12 (-5 *3 (-385 (-887 *4))) (-4 *4 (-13 (-286) (-789) (-138))) + (-5 *2 (-592 (-273 (-294 *4)))) (-5 *1 (-1047 *4)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-273 (-385 (-887 *5)))) (-5 *4 (-1091)) + (-4 *5 (-13 (-286) (-789) (-138))) (-5 *2 (-592 (-273 (-294 *5)))) + (-5 *1 (-1047 *5)))) + ((*1 *2 *3) + (-12 (-5 *3 (-273 (-385 (-887 *4)))) + (-4 *4 (-13 (-286) (-789) (-138))) (-5 *2 (-592 (-273 (-294 *4)))) + (-5 *1 (-1047 *4)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-592 (-385 (-887 *5)))) (-5 *4 (-592 (-1091))) + (-4 *5 (-13 (-286) (-789) (-138))) + (-5 *2 (-592 (-592 (-273 (-294 *5))))) (-5 *1 (-1047 *5)))) + ((*1 *2 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*2 (-1 (-525))) (-5 *1 (-975)) + (-5 *3 (-525))))) +(((*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 *1 *1) (-12 (-5 *1 (-317 *2 *3 *4)) (-14 *2 (-592 (-1091))) (-14 *3 (-592 (-1091))) (-4 *4 (-365)))) @@ -11583,38 +12509,68 @@ (-12 (-5 *2 (-1072 *3)) (-4 *3 (-37 (-385 (-525)))) (-5 *1 (-1078 *3)))) ((*1 *1 *1) (-4 *1 (-1116)))) -(((*1 *2 *3 *4 *3) - (|partial| -12 (-5 *4 (-1091)) - (-4 *5 (-13 (-429) (-789) (-138) (-968 (-525)) (-588 (-525)))) - (-5 *2 (-2 (|:| -1781 *3) (|:| |coeff| *3))) (-5 *1 (-518 *5 *3)) - (-4 *3 (-13 (-27) (-1113) (-408 *5)))))) -(((*1 *2 *3 *4 *4 *3) - (-12 (-5 *3 (-525)) (-5 *4 (-632 (-205))) (-5 *2 (-966)) - (-5 *1 (-690))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-1020)) (-4 *2 (-835 *5)) (-5 *1 (-634 *5 *2 *3 *4)) - (-4 *3 (-351 *2)) (-4 *4 (-13 (-351 *5) (-10 -7 (-6 -4255))))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-1 (-108) *7 (-592 *7))) (-4 *1 (-1121 *4 *5 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+ (-12 (-5 *2 (-592 (-887 *4))) (-5 *3 (-592 (-1091))) (-4 *4 (-429)) + (-5 *1 (-853 *4))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-602 *2)) (-4 *2 (-977)) (-4 *2 (-341)))) + ((*1 *2 *2 *2 *3) + (-12 (-5 *3 (-1 *4 *4)) (-4 *4 (-341)) (-5 *1 (-605 *4 *2)) + (-4 *2 (-602 *4))))) +(((*1 *2 *3 *3 *4) + (-12 (-5 *3 (-205)) (-5 *4 (-592 (-294 (-205)))) (-5 *2 (-108)) + (-5 *1 (-192))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-592 (-47))) (-5 *2 (-396 *3)) (-5 *1 (-38 *3)) (-4 *3 (-1149 (-47))))) @@ -11663,8 +12619,8 @@ (-12 (-4 *4 (-13 (-789) - (-10 -8 (-15 -2745 ((-1091) $)) - (-15 -2575 ((-3 $ "failed") (-1091)))))) + (-10 -8 (-15 -2606 ((-1091) $)) + (-15 -2404 ((-3 $ "failed") (-1091)))))) (-4 *5 (-735)) (-4 *7 (-517)) (-5 *2 (-396 *3)) (-5 *1 (-433 *4 *5 *6 *7 *3)) (-4 *6 (-517)) (-4 *3 (-884 *7 *5 *4)))) @@ -11713,13 +12669,13 @@ (-12 (-4 *4 (-735)) (-4 *5 (-13 (-789) - (-10 -8 (-15 -2745 ((-1091) $)) - (-15 -2575 ((-3 $ "failed") (-1091)))))) + (-10 -8 (-15 -2606 ((-1091) $)) + (-15 -2404 ((-3 $ "failed") (-1091)))))) (-4 *6 (-286)) (-5 *2 (-396 *3)) (-5 *1 (-673 *4 *5 *6 *3)) (-4 *3 (-884 (-887 *6) *4 *5)))) ((*1 *2 *3) (-12 (-4 *4 (-735)) - (-4 *5 (-13 (-789) (-10 -8 (-15 -2745 ((-1091) $))))) (-4 *6 (-517)) + (-4 *5 (-13 (-789) (-10 -8 (-15 -2606 ((-1091) $))))) (-4 *6 (-517)) (-5 *2 (-396 *3)) (-5 *1 (-675 *4 *5 *6 *3)) (-4 *3 (-884 (-385 (-887 *6)) *4 *5)))) ((*1 *2 *3) @@ -11755,12 +12711,6 @@ ((*1 *2 *1) (-12 (-5 *2 (-396 *1)) (-4 *1 (-1131)))) ((*1 *2 *3) (-12 (-5 *2 (-396 *3)) (-5 *1 (-1138 *3)) (-4 *3 (-1149 (-525)))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-525)) (-4 *1 (-55 *4 *2 *5)) (-4 *4 (-1127)) - (-4 *5 (-351 *4)) (-4 *2 (-351 *4)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-525)) (-4 *1 (-980 *4 *5 *6 *2 *7)) (-4 *6 (-977)) - (-4 *7 (-218 *4 *6)) (-4 *2 (-218 *5 *6))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-789) (-517))) (-5 *1 (-255 *3 *2)) (-4 *2 (-13 (-408 *3) (-934))))) @@ -11777,89 +12727,96 @@ (-12 (-5 *2 (-1072 *3)) (-4 *3 (-37 (-385 (-525)))) (-5 *1 (-1078 *3)))) ((*1 *1 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|localSymbols| (-1095)) (|:| -4090 (-592 (-308))))) (-5 *1 (-376 *3 *4 *5 *6)) (-14 *3 (-1091)) - (-14 *4 (-3 (|:| |fst| (-412)) (|:| -3322 "void"))) + (-14 *4 (-3 (|:| |fst| (-412)) (|:| -3348 "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)) (|:| -3322 "void"))) + (-14 *3 (-1091)) (-14 *4 (-3 (|:| |fst| (-412)) (|:| -3348 "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)) (|:| -3322 "void"))) + (-14 *4 (-3 (|:| |fst| (-412)) (|:| -3348 "void"))) (-14 *5 (-592 (-1091))) (-14 *6 (-1095)))) ((*1 *1 *2) (-12 (-5 *2 (-309 *4)) (-4 *4 (-13 (-789) (-21))) @@ -16726,14 +16839,14 @@ ((*1 *2 *1) (-12 (-5 *2 (-798)) (-5 *1 (-415)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1095)) (|:| -4068 (-592 (-308))))) + (-5 *2 (-2 (|:| |localSymbols| (-1095)) (|:| -4090 (-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)) (|:| -4068 (-592 (-308))))) + (-5 *2 (-2 (|:| |localSymbols| (-1095)) (|:| -4090 (-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)))) @@ -16800,24 +16913,24 @@ ((*1 *1 *2) (-12 (-4 *3 (-977)) (-5 *1 (-655 *3 *2)) (-4 *2 (-1149 *3)))) ((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| -3636 *3) (|:| -2058 *4))) + (-12 (-5 *2 (-2 (|:| -3703 *3) (|:| -1474 *4))) (-5 *1 (-656 *3 *4 *5)) (-4 *3 (-789)) (-4 *4 (-1020)) (-14 *5 - (-1 (-108) (-2 (|:| -3636 *3) (|:| -2058 *4)) - (-2 (|:| -3636 *3) (|:| -2058 *4)))))) + (-1 (-108) (-2 (|:| -3703 *3) (|:| -1474 *4)) + (-2 (|:| -3703 *3) (|:| -1474 *4)))))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| -3636 *3) (|:| -2058 *4))) (-4 *3 (-789)) + (-12 (-5 *2 (-2 (|:| -3703 *3) (|:| -1474 *4))) (-4 *3 (-789)) (-4 *4 (-1020)) (-14 *5 - (-1 (-108) (-2 (|:| -3636 *3) (|:| -2058 *4)) - (-2 (|:| -3636 *3) (|:| -2058 *4)))) + (-1 (-108) (-2 (|:| -3703 *3) (|:| -1474 *4)) + (-2 (|:| -3703 *3) (|:| -1474 *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 (|:| -1660 *3) (|:| -3215 *4)))) (-4 *3 (-977)) + (-12 (-5 *2 (-592 (-2 (|:| -1631 *3) (|:| -3205 *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) @@ -16826,25 +16939,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1091)) (|:| |fn| (-294 (-205))) - (|:| -1681 (-1015 (-782 (-205)))) (|:| |abserr| (-205)) + (|:| -3157 (-1015 (-782 (-205)))) (|:| |abserr| (-205)) (|:| |relerr| (-205)))) (|:| |mdnia| (-2 (|:| |fn| (-294 (-205))) - (|:| -1681 (-592 (-1015 (-782 (-205))))) + (|:| -3157 (-592 (-1015 (-782 (-205))))) (|:| |abserr| (-205)) (|:| |relerr| (-205)))))) (-5 *1 (-711)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-294 (-205))) - (|:| -1681 (-592 (-1015 (-782 (-205))))) (|:| |abserr| (-205)) + (|:| -3157 (-592 (-1015 (-782 (-205))))) (|:| |abserr| (-205)) (|:| |relerr| (-205)))) (-5 *1 (-711)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1091)) (|:| |fn| (-294 (-205))) - (|:| -1681 (-1015 (-782 (-205)))) (|:| |abserr| (-205)) + (|:| -3157 (-1015 (-782 (-205)))) (|:| |abserr| (-205)) (|:| |relerr| (-205)))) (-5 *1 (-711)))) ((*1 *2 *1) (-12 (-5 *2 (-798)) (-5 *1 (-711)))) @@ -16870,23 +16983,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-294 (-205))) (|:| -3937 (-592 (-205))) + (-2 (|:| |fn| (-294 (-205))) (|:| -3347 (-592 (-205))) (|:| |lb| (-592 (-782 (-205)))) (|:| |cf| (-592 (-294 (-205)))) (|:| |ub| (-592 (-782 (-205)))))) (|:| |lsa| (-2 (|:| |lfn| (-592 (-294 (-205)))) - (|:| -3937 (-592 (-205))))))) + (|:| -3347 (-592 (-205))))))) (-5 *1 (-780)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-592 (-294 (-205)))) (|:| -3937 (-592 (-205))))) + (-2 (|:| |lfn| (-592 (-294 (-205)))) (|:| -3347 (-592 (-205))))) (-5 *1 (-780)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-294 (-205))) (|:| -3937 (-592 (-205))) + (-2 (|:| |fn| (-294 (-205))) (|:| -3347 (-592 (-205))) (|:| |lb| (-592 (-782 (-205)))) (|:| |cf| (-592 (-294 (-205)))) (|:| |ub| (-592 (-782 (-205)))))) (-5 *1 (-780)))) @@ -17045,57 +17158,76 @@ (-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 *1) (-12 (-5 *2 (-1024)) (-5 *1 (-1095))))) -(((*1 *2 *1) - (-12 (-5 *2 (-798)) (-5 *1 (-368 *3 *4 *5)) (-14 *3 (-713)) - (-14 *4 (-713)) (-4 *5 (-160))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-878 *5)) (-4 *5 (-977)) (-5 *2 (-713)) - (-5 *1 (-1080 *4 *5)) (-14 *4 (-856)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-592 (-713))) (-5 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