diff options
| -rw-r--r-- | src/share/algebra/browse.daase | 756 | ||||
| -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 | 8288 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 31441 |
5 files changed, 21455 insertions, 21453 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 967cece3..a4b02073 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2236562 . 3416411997) +(2236562 . 3417125209) (-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."))) -((-4249 . T) (-4248 . T) (-4069 . T)) +((-4249 . T) (-4248 . T) (-2500 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4245 . T) (-4243 . T) (-4242 . T) ((-4250 "*") . T) (-4241 . T) (-4246 . T) (-4240 . T) (-4069 . T)) +((-4245 . T) (-4243 . T) (-4242 . T) ((-4250 "*") . T) (-4241 . T) (-4246 . T) (-4240 . T) (-2500 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -3539) +(-31 R -3894) ((|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 -964) (QUOTE (-523))))) @@ -62,7 +62,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4248))) (-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|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-4069 . T)) +((-2500 . T)) NIL (-34) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\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| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4248 . T) (-4249 . T) (-4069 . T)) +((-4248 . T) (-4249 . T) (-2500 . T)) NIL (-36 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#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 -3539 UP UPUP -2547) +(-39 -3894 UP UPUP -3014) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4241 |has| (-383 |#2|) (-339)) (-4246 |has| (-383 |#2|) (-339)) (-4240 |has| (-383 |#2|) (-339)) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| (-383 |#2|) (QUOTE (-134))) (|HasCategory| (-383 |#2|) (QUOTE (-136))) (|HasCategory| (-383 |#2|) (QUOTE (-325))) (-3172 (|HasCategory| (-383 |#2|) (QUOTE (-339))) (|HasCategory| (-383 |#2|) (QUOTE (-325)))) (|HasCategory| (-383 |#2|) (QUOTE (-339))) (|HasCategory| (-383 |#2|) (QUOTE (-344))) (-3172 (-12 (|HasCategory| (-383 |#2|) (QUOTE (-211))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (|HasCategory| (-383 |#2|) (QUOTE (-325)))) (-3172 (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-325))))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-344))) (-3172 (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (QUOTE (-211))) (|HasCategory| (-383 |#2|) (QUOTE (-339))))) -(-40 R -3539) +((|HasCategory| (-383 |#2|) (QUOTE (-134))) (|HasCategory| (-383 |#2|) (QUOTE (-136))) (|HasCategory| (-383 |#2|) (QUOTE (-325))) (-3255 (|HasCategory| (-383 |#2|) (QUOTE (-339))) (|HasCategory| (-383 |#2|) (QUOTE (-325)))) (|HasCategory| (-383 |#2|) (QUOTE (-339))) (|HasCategory| (-383 |#2|) (QUOTE (-344))) (-3255 (-12 (|HasCategory| (-383 |#2|) (QUOTE (-211))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (|HasCategory| (-383 |#2|) (QUOTE (-325)))) (-3255 (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-325))))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-344))) (-3255 (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (QUOTE (-211))) (|HasCategory| (-383 |#2|) (QUOTE (-339))))) +(-40 R -3894) ((|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 (-427))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -406) (|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."))) ((-4248 . T) (-4249 . T)) -((-3172 (-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-786))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|))))))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-786))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-786))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-786))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2402) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2746) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2402) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2746) (|devaluate| |#2|))))))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-786))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-786))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (-12 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2402) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2746) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -140,7 +140,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-53 |Base| R -3539) +(-53 |Base| R -3894) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -150,7 +150,7 @@ NIL NIL (-55 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|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"))) -((-4248 . T) (-4249 . T) (-4069 . T)) +((-4248 . T) (-4249 . T) (-2500 . 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}"))) ((-4249 . T) (-4248 . T)) -((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3255 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-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}."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) -(-59 -4198) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +(-59 -1522) ((|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 -4198) +(-60 -1522) ((|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 -4198) +(-61 -1522) ((|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 -4198) +(-62 -1522) ((|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 -4198) +(-63 -1522) ((|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 -4198) +(-64 -1522) ((|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 -4198) +(-65 -1522) ((|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 -4198) +(-66 -1522) ((|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 -4198) +(-67 -1522) ((|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 -4198) +(-68 -1522) ((|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 -4198) +(-69 -1522) ((|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 -4198) +(-70 -1522) ((|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 -4198) +(-71 -1522) ((|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 -4198) +(-72 -1522) ((|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 -4198) +(-75 -1522) ((|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 -4198) +(-76 -1522) ((|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 -4198) +(-77 -1522) ((|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 -4198) +(-78 -1522) ((|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 -4198) +(-79 -1522) ((|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 -4198) +(-80 -1522) ((|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 -4198) +(-81 -1522) ((|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 -4198) +(-82 -1522) ((|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 -4198) +(-83 -1522) ((|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 -4198) +(-84 -1522) ((|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 -4198) +(-85 -1522) ((|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 -4198) +(-86 -1522) ((|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 -4198) +(-87 -1522) ((|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}."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-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}."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-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."))) -((-4249 . T) (-4069 . T)) +((-4249 . T) (-2500 . 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."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| (-523) (QUOTE (-840))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-523) (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-136))) (|HasCategory| (-523) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-949))) (|HasCategory| (-523) (QUOTE (-759))) (-3172 (|HasCategory| (-523) (QUOTE (-759))) (|HasCategory| (-523) (QUOTE (-786)))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-1063))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-523) (QUOTE (-211))) (|HasCategory| (-523) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-523) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -286) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -263) (QUOTE (-523)) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-284))) (|HasCategory| (-523) (QUOTE (-508))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-523) (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (|HasCategory| (-523) (QUOTE (-134))))) +((|HasCategory| (-523) (QUOTE (-840))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-523) (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-136))) (|HasCategory| (-523) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-949))) (|HasCategory| (-523) (QUOTE (-759))) (-3255 (|HasCategory| (-523) (QUOTE (-759))) (|HasCategory| (-523) (QUOTE (-786)))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-1063))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-523) (QUOTE (-211))) (|HasCategory| (-523) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-523) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -286) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -263) (QUOTE (-523)) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-284))) (|HasCategory| (-523) (QUOTE (-508))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-523) (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (|HasCategory| (-523) (QUOTE (-134))))) (-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 -3539 UP) +(-111 -3894 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}."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| (-112 |#1|) (QUOTE (-840))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-112 |#1|) (QUOTE (-134))) (|HasCategory| (-112 |#1|) (QUOTE (-136))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-112 |#1|) (QUOTE (-949))) (|HasCategory| (-112 |#1|) (QUOTE (-759))) (-3172 (|HasCategory| (-112 |#1|) (QUOTE (-759))) (|HasCategory| (-112 |#1|) (QUOTE (-786)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-112 |#1|) (QUOTE (-1063))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-112 |#1|) (QUOTE (-211))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -484) (QUOTE (-1087)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -263) (LIST (QUOTE -112) (|devaluate| |#1|)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (QUOTE (-284))) (|HasCategory| (-112 |#1|) (QUOTE (-508))) (|HasCategory| (-112 |#1|) (QUOTE (-786))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-112 |#1|) (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-112 |#1|) (QUOTE (-840)))) (|HasCategory| (-112 |#1|) (QUOTE (-134))))) +((|HasCategory| (-112 |#1|) (QUOTE (-840))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-112 |#1|) (QUOTE (-134))) (|HasCategory| (-112 |#1|) (QUOTE (-136))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-112 |#1|) (QUOTE (-949))) (|HasCategory| (-112 |#1|) (QUOTE (-759))) (-3255 (|HasCategory| (-112 |#1|) (QUOTE (-759))) (|HasCategory| (-112 |#1|) (QUOTE (-786)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-112 |#1|) (QUOTE (-1063))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-112 |#1|) (QUOTE (-211))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -484) (QUOTE (-1087)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -263) (LIST (QUOTE -112) (|devaluate| |#1|)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (QUOTE (-284))) (|HasCategory| (-112 |#1|) (QUOTE (-508))) (|HasCategory| (-112 |#1|) (QUOTE (-786))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-112 |#1|) (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-112 |#1|) (QUOTE (-840)))) (|HasCategory| (-112 |#1|) (QUOTE (-134))))) (-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| (($ $) "\\spad{left(u)} returns the left child."))) NIL ((|HasAttribute| |#1| (QUOTE -4249))) (-115 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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."))) -((-4069 . T)) +((-2500 . 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"))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-118 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-119) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4249 . T) (-4248 . T) (-4069 . T)) +((-4249 . T) (-4248 . T) (-2500 . T)) NIL (-120 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -414,16 +414,16 @@ NIL NIL (-121 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4248 . T) (-4249 . T) (-4069 . T)) +((-4248 . T) (-4249 . T) (-2500 . T)) NIL (-122 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-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."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-124) ((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\spad{ a+b = a+c => b=c }. This is formalised by the partial subtraction operator,{} which satisfies the axioms listed below: \\blankline")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x,{} y)} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists."))) NIL @@ -436,11 +436,11 @@ 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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4250 "*") . T)) NIL -(-127 |minix| -1996 S T$) +(-127 |minix| -3765 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-128 |minix| -1996 R) +(-128 |minix| -3765 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -451,7 +451,7 @@ NIL (-130) ((|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}."))) ((-4248 . T) (-4238 . T) (-4249 . T)) -((-3172 (-12 (|HasCategory| (-133) (QUOTE (-344))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133)))))) (|HasCategory| (-133) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-133) (QUOTE (-344))) (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-133) (QUOTE (-1016))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (|HasCategory| (-133) (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| (-133) (QUOTE (-344))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133)))))) (|HasCategory| (-133) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-133) (QUOTE (-344))) (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-133) (QUOTE (-1016))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (|HasCategory| (-133) (LIST (QUOTE -563) (QUOTE (-794))))) (-131 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 @@ -476,7 +476,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4245 . T)) NIL -(-137 -3539 UP UPUP) +(-137 -3894 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 @@ -490,7 +490,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasAttribute| |#1| (QUOTE -4248))) (-140 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."))) -((-4069 . T)) +((-2500 . T)) NIL (-141 |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."))) @@ -508,7 +508,7 @@ 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 -(-145 R -3539) +(-145 R -3894) ((|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 @@ -538,7 +538,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-840))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-930))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-982))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-339))) (|HasAttribute| |#2| (QUOTE -4244)) (|HasAttribute| |#2| (QUOTE -4247)) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-786)))) (-152 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})"))) -((-4241 -3172 (|has| |#1| (-515)) (-12 (|has| |#1| (-284)) (|has| |#1| (-840)))) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4244 |has| |#1| (-6 -4244)) (-4247 |has| |#1| (-6 -4247)) (-4115 . T) (-4069 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-4241 -3255 (|has| |#1| (-515)) (-12 (|has| |#1| (-284)) (|has| |#1| (-840)))) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4244 |has| |#1| (-6 -4244)) (-4247 |has| |#1| (-6 -4247)) (-2531 . T) (-2500 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-153 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."))) @@ -550,8 +550,8 @@ NIL NIL (-155 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}."))) -((-4241 -3172 (|has| |#1| (-515)) (-12 (|has| |#1| (-284)) (|has| |#1| (-840)))) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4244 |has| |#1| (-6 -4244)) (-4247 |has| |#1| (-6 -4247)) (-4115 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . 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T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . 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(QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#1| (QUOTE (-982))) (-12 (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-508))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339)))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-840))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-339)))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-211))) (-12 (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasAttribute| |#1| (QUOTE -4244)) (|HasAttribute| |#1| (QUOTE -4247)) (-12 (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (QUOTE (-339)))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087))))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-325))))) (-156 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 @@ -600,7 +600,7 @@ 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|) $) "\\spad{constructorName c} returns the name of the constructor"))) NIL NIL -(-168 R -3539) +(-168 R -3894) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -704,19 +704,19 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|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 -(-194 -3539 UP UPUP R) +(-194 -3894 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 -(-195 -3539 FP) +(-195 -3894 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 (-196) ((|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."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| (-523) (QUOTE (-840))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-523) (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-136))) (|HasCategory| (-523) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-949))) (|HasCategory| (-523) (QUOTE (-759))) (-3172 (|HasCategory| (-523) (QUOTE (-759))) (|HasCategory| (-523) (QUOTE (-786)))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-1063))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-523) (QUOTE (-211))) (|HasCategory| (-523) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-523) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -286) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -263) (QUOTE (-523)) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-284))) (|HasCategory| (-523) (QUOTE (-508))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-523) (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (|HasCategory| (-523) (QUOTE (-134))))) -(-197 R -3539) +((|HasCategory| (-523) (QUOTE (-840))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-523) (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-136))) (|HasCategory| (-523) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-949))) (|HasCategory| (-523) (QUOTE (-759))) (-3255 (|HasCategory| (-523) (QUOTE (-759))) (|HasCategory| (-523) (QUOTE (-786)))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-1063))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-523) (QUOTE (-211))) (|HasCategory| (-523) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-523) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -286) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -263) (QUOTE (-523)) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-284))) (|HasCategory| (-523) (QUOTE (-508))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-523) (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (|HasCategory| (-523) (QUOTE (-134))))) +(-197 R -3894) ((|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 @@ -731,18 +731,18 @@ NIL (-200 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}."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-201 |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}."))) ((-4245 . T)) NIL -(-202 R -3539) +(-202 R -3894) ((|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 (-203) ((|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}."))) -((-4108 . T) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-2523 . T) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-204) ((|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)}.}"))) @@ -751,14 +751,14 @@ NIL (-205 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}"))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-515))) (|HasAttribute| |#1| (QUOTE (-4250 "*"))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-515))) (|HasAttribute| |#1| (QUOTE (-4250 "*"))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-206 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 (-207 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."))) -((-4249 . T) (-4069 . T)) +((-4249 . T) (-2500 . T)) NIL (-208 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}."))) @@ -782,28 +782,28 @@ NIL ((|HasAttribute| |#1| (QUOTE -4248))) (-213 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}."))) -((-4249 . T) (-4069 . T)) +((-4249 . T) (-2500 . T)) NIL (-214) ((|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 -(-215 S -1996 R) +(-215 S -3765 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 (-339))) (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (QUOTE (-784))) (|HasAttribute| |#3| (QUOTE -4245)) (|HasCategory| |#3| (QUOTE (-158))) (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (QUOTE (-666))) (|HasCategory| |#3| (QUOTE (-124))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-973))) (|HasCategory| |#3| (QUOTE (-1016)))) -(-216 -1996 R) +(-216 -3765 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"))) -((-4242 |has| |#2| (-973)) (-4243 |has| |#2| (-973)) (-4245 |has| |#2| (-6 -4245)) ((-4250 "*") |has| |#2| (-158)) (-4248 . T) (-4069 . T)) +((-4242 |has| |#2| (-973)) (-4243 |has| |#2| (-973)) (-4245 |has| |#2| (-6 -4245)) ((-4250 "*") |has| |#2| (-158)) (-4248 . T) (-2500 . T)) NIL -(-217 -1996 A B) +(-217 -3765 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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(NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -818,12 +818,12 @@ NIL NIL (-222 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."))) -((-4069 . T)) +((-2500 . T)) NIL (-223 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}"))) ((-4249 . T) (-4248 . T)) -((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3255 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-224 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 @@ -831,19 +831,19 @@ NIL (-225 |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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Date Last Updated: January 19,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall")) (|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}."))) 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In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\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 @@ -854,7 +854,7 @@ NIL NIL (-231 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}."))) -((-4248 . T) (-4249 . T) (-4069 . T)) +((-4248 . T) (-4249 . T) (-2500 . T)) NIL (-232) ((|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."))) @@ -895,7 +895,7 @@ NIL (-241 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"))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) -((|HasCategory| |#1| (QUOTE (-840))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#3| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#3| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#3| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#3| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#3| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) +((|HasCategory| |#1| (QUOTE (-840))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#3| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#3| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#3| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#3| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#3| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-339))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) (-242 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 @@ -940,11 +940,11 @@ 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 -(-253 R -3539) +(-253 R -3894) ((|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 -(-254 R -3539) +(-254 R -3894) ((|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 @@ -966,7 +966,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016)))) (-259 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}."))) -((-4249 . T) (-4069 . T)) +((-4249 . T) (-2500 . T)) NIL (-260 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}."))) @@ -992,7 +992,7 @@ 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 -(-266 S R |Mod| -1327 -3780 |exactQuo|) +(-266 S R |Mod| -1345 -3123 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL @@ -1014,21 +1014,21 @@ NIL NIL (-271 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4245 -3172 (|has| |#1| (-973)) (|has| |#1| (-448))) (-4242 |has| |#1| (-973)) (-4243 |has| |#1| (-973))) -((|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-973)))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339)))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-973)))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-973)))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-973)))) (-3172 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#1| (QUOTE (-666)))) (|HasCategory| |#1| (QUOTE (-448))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-1016)))) (-3172 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-1028)))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-279))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-448)))) (-3172 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-666)))) (-3172 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#1| (QUOTE (-973)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25)))) +((-4245 -3255 (|has| |#1| (-973)) (|has| |#1| (-448))) (-4242 |has| |#1| (-973)) (-4243 |has| |#1| (-973))) +((|HasCategory| |#1| (QUOTE (-339))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-973)))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339)))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-973)))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-973)))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-973)))) (-3255 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#1| (QUOTE (-666)))) (|HasCategory| |#1| (QUOTE (-448))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-1016)))) (-3255 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-1028)))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-279))) (-3255 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-448)))) (-3255 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-666)))) (-3255 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#1| (QUOTE (-973)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25)))) (-272 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|)))))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2402) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2746) (|devaluate| |#2|)))))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) (-273) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",{}\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-274 -3539 S) +(-274 -3894 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 -(-275 E -3539) +(-275 E -3894) ((|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 @@ -1076,7 +1076,7 @@ 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 -(-287 -3539) +(-287 -3894) ((|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 @@ -1087,7 +1087,7 @@ NIL (-289 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))}."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-840))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-949))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-759))) (-3172 (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-759))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-786)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-1063))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-211))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -484) (QUOTE (-1087)) (LIST (QUOTE -1155) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1155) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -263) (LIST (QUOTE -1155) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1155) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-284))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-508))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-786))) (-12 (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-840))) (|HasCategory| $ (QUOTE (-134)))) (-3172 (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-134))) (-12 (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-840))) (|HasCategory| $ (QUOTE (-134)))))) +((|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-840))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-949))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-759))) (-3255 (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-759))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-786)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-1063))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-211))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -484) (QUOTE (-1087)) (LIST (QUOTE -1155) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1155) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (LIST (QUOTE -263) (LIST (QUOTE -1155) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1155) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-284))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-508))) (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-786))) (-12 (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-840))) (|HasCategory| $ (QUOTE (-134)))) (-3255 (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-134))) (-12 (|HasCategory| (-1155 |#1| |#2| |#3| |#4|) (QUOTE (-840))) (|HasCategory| $ (QUOTE (-134)))))) (-290 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 @@ -1098,9 +1098,9 @@ NIL NIL (-292 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."))) -((-4245 -3172 (-3147 (|has| |#1| (-973)) (|has| |#1| (-585 (-523)))) (-12 (|has| |#1| (-515)) (-3172 (-3147 (|has| |#1| (-973)) (|has| |#1| (-585 (-523)))) (|has| |#1| (-973)) (|has| |#1| (-448)))) (|has| |#1| (-973)) (|has| |#1| (-448))) (-4243 |has| |#1| (-158)) (-4242 |has| |#1| (-158)) ((-4250 "*") |has| |#1| (-515)) (-4241 |has| |#1| (-515)) (-4246 |has| 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(QUOTE (-973))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))))) (-3255 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#1| (QUOTE (-973)))) (-3255 (-12 (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| $ (QUOTE (-973))) (|HasCategory| $ (LIST (QUOTE -964) (QUOTE (-523))))) +(-293 R -3894) ((|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 @@ -1111,7 +1111,7 @@ NIL (-295 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."))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|)))) (|HasCategory| (-383 (-523)) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasSignature| |#1| (LIST (QUOTE -1691) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3172 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2814) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1292) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|)))) (|HasCategory| (-383 (-523)) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-3255 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasSignature| |#1| (LIST (QUOTE -3976) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3255 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2669) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -3716) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) (-296 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 @@ -1143,12 +1143,12 @@ NIL (-303 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."))) ((-4249 . T) (-4248 . T)) -((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) -(-304 S -3539) +((-3255 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3255 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +(-304 S -3894) ((|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 (-344)))) -(-305 -3539) +(-305 -3894) ((|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."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL @@ -1168,15 +1168,15 @@ 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 -(-310 S -3539 UP UPUP R) +(-310 S -3894 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 -(-311 -3539 UP UPUP R) +(-311 -3894 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 -(-312 -3539 UP UPUP R) +(-312 -3894 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 @@ -1196,26 +1196,26 @@ 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 -(-317 S -3539 UP UPUP) +(-317 S -3894 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 (-344))) (|HasCategory| |#2| (QUOTE (-339)))) -(-318 -3539 UP UPUP) +(-318 -3894 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."))) ((-4241 |has| (-383 |#2|) (-339)) (-4246 |has| (-383 |#2|) (-339)) (-4240 |has| (-383 |#2|) (-339)) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-319 |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."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((-3172 (|HasCategory| (-841 |#1|) (QUOTE (-134))) (|HasCategory| (-841 |#1|) (QUOTE (-344)))) (|HasCategory| (-841 |#1|) (QUOTE (-136))) (|HasCategory| (-841 |#1|) (QUOTE (-344))) (|HasCategory| (-841 |#1|) (QUOTE (-134)))) +((-3255 (|HasCategory| (-841 |#1|) (QUOTE (-134))) (|HasCategory| (-841 |#1|) (QUOTE (-344)))) (|HasCategory| (-841 |#1|) (QUOTE (-136))) (|HasCategory| (-841 |#1|) (QUOTE (-344))) (|HasCategory| (-841 |#1|) (QUOTE (-134)))) (-320 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."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((-3172 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) +((-3255 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) (-321 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."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((-3172 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) +((-3255 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) (-322 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 @@ -1232,31 +1232,31 @@ 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."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-326 R UP -3539) +(-326 R UP -3894) ((|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 (-327 |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."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((-3172 (|HasCategory| (-841 |#1|) (QUOTE (-134))) (|HasCategory| (-841 |#1|) (QUOTE (-344)))) (|HasCategory| (-841 |#1|) (QUOTE (-136))) (|HasCategory| (-841 |#1|) (QUOTE (-344))) (|HasCategory| (-841 |#1|) (QUOTE (-134)))) +((-3255 (|HasCategory| (-841 |#1|) (QUOTE (-134))) (|HasCategory| (-841 |#1|) (QUOTE (-344)))) (|HasCategory| (-841 |#1|) (QUOTE (-136))) (|HasCategory| (-841 |#1|) (QUOTE (-344))) (|HasCategory| (-841 |#1|) (QUOTE (-134)))) (-328 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."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((-3172 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) +((-3255 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) (-329 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."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((-3172 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) +((-3255 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) (-330 |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}."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((-3172 (|HasCategory| (-841 |#1|) (QUOTE (-134))) (|HasCategory| (-841 |#1|) (QUOTE (-344)))) (|HasCategory| (-841 |#1|) (QUOTE (-136))) (|HasCategory| (-841 |#1|) (QUOTE (-344))) (|HasCategory| (-841 |#1|) (QUOTE (-134)))) +((-3255 (|HasCategory| (-841 |#1|) (QUOTE (-134))) (|HasCategory| (-841 |#1|) (QUOTE (-344)))) (|HasCategory| (-841 |#1|) (QUOTE (-136))) (|HasCategory| (-841 |#1|) (QUOTE (-344))) (|HasCategory| (-841 |#1|) (QUOTE (-134)))) (-331 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."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((-3172 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) -(-332 -3539 GF) +((-3255 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) +(-332 -3894 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 @@ -1264,14 +1264,14 @@ 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 -(-334 -3539 FP FPP) +(-334 -3894 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 (-335 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}."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((-3172 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) +((-3255 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) (-336 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 @@ -1326,7 +1326,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4249)) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016)))) (-349 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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4248 . T) (-4069 . T)) +((-4248 . T) (-2500 . T)) NIL (-350 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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."))) @@ -1350,7 +1350,7 @@ NIL NIL (-355) ((|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}."))) -((-4231 . T) (-4239 . T) (-4108 . T) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-4231 . T) (-4239 . T) (-2523 . T) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-356 |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}."))) @@ -1366,11 +1366,11 @@ NIL NIL (-359) ((|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}."))) -((-4069 . T)) +((-2500 . T)) NIL (-360) ((|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.}"))) -((-4069 . T)) +((-2500 . T)) NIL (-361 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."))) @@ -1400,7 +1400,7 @@ 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 -(-368 -3539 UP UPUP R) +(-368 -3894 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 @@ -1414,27 +1414,27 @@ NIL NIL (-371) ((|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."))) -((-4069 . T)) +((-2500 . T)) NIL (-372) ((|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.}"))) -((-4069 . T)) +((-2500 . T)) NIL (-373) ((|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 -(-374 -4198 |returnType| -2134 |symbols|) +(-374 -1522 |returnType| -1858 |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 -(-375 -3539 UP) +(-375 -3894 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-376 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-4069 . T)) +((-2500 . T)) NIL (-377 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1450,7 +1450,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4231)) (|HasAttribute| |#1| (QUOTE -4239))) (-380) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-4108 . T) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-2523 . T) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-381 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."))) @@ -1463,7 +1463,7 @@ NIL (-383 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."))) ((-4235 -12 (|has| |#1| (-6 -4246)) (|has| |#1| (-427)) (|has| |#1| (-6 -4235))) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-759))) (-3172 (|HasCategory| |#1| (QUOTE (-759))) (|HasCategory| |#1| (QUOTE (-786)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767)))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-1063))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767))))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767)))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-508))) (-12 (|HasAttribute| |#1| (QUOTE -4246)) (|HasAttribute| |#1| (QUOTE -4235)) (|HasCategory| |#1| (QUOTE (-427)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) +((|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-759))) (-3255 (|HasCategory| |#1| (QUOTE (-759))) (|HasCategory| |#1| (QUOTE (-786)))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767)))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-1063))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767))))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767)))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-508))) (-12 (|HasAttribute| |#1| (QUOTE -4246)) (|HasAttribute| |#1| (QUOTE -4235)) (|HasCategory| |#1| (QUOTE (-427)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) (-384 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1484,11 +1484,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-389 R -3539 UP A) +(-389 R -3894 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4245 . T)) NIL -(-390 R -3539 UP A |ibasis|) +(-390 R -3894 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 -964) (|devaluate| |#2|)))) @@ -1507,7 +1507,7 @@ NIL (-394 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."))) ((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -263) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-1127))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-1127)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-427)))) +((|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -263) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-1127))) (-3255 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-1127)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-427)))) (-395 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 @@ -1534,9 +1534,9 @@ NIL ((|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-344)))) (-401 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4248 . T) (-4238 . T) (-4249 . T) (-4069 . T)) +((-4248 . T) (-4238 . T) (-4249 . T) (-2500 . T)) NIL -(-402 R -3539) +(-402 R -3894) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1544,7 +1544,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4235 -12 (|has| |#1| (-6 -4235)) (|has| |#2| (-6 -4235))) (-4242 . T) (-4243 . T) (-4245 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4235)) (|HasAttribute| |#2| (QUOTE -4235)))) -(-404 R -3539) +(-404 R -3894) ((|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 @@ -1554,17 +1554,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-448))) (|HasCategory| |#2| (QUOTE (-1028))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (-406 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}."))) -((-4245 -3172 (|has| |#1| (-973)) (|has| |#1| (-448))) (-4243 |has| |#1| (-158)) (-4242 |has| |#1| (-158)) ((-4250 "*") |has| |#1| (-515)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-515)) (-4240 |has| |#1| (-515)) (-4069 . T)) +((-4245 -3255 (|has| |#1| (-973)) (|has| |#1| (-448))) (-4243 |has| |#1| (-158)) (-4242 |has| |#1| (-158)) ((-4250 "*") |has| |#1| (-515)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-515)) (-4240 |has| |#1| (-515)) (-2500 . T)) NIL -(-407 R -3539) +(-407 R -3894) ((|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 -(-408 R -3539) +(-408 R -3894) ((|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)))) -(-409 R -3539) +(-409 R -3894) ((|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 @@ -1572,7 +1572,7 @@ 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 -(-411 R -3539 UP) +(-411 R -3894 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 -964) (QUOTE (-47))))) @@ -1590,17 +1590,17 @@ NIL NIL (-415) ((|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}."))) -((-4069 . T)) +((-2500 . T)) NIL (-416) ((|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.}"))) -((-4069 . T)) +((-2500 . T)) NIL (-417 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 -(-418 R UP -3539) +(-418 R UP -3894) ((|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 @@ -1647,7 +1647,7 @@ NIL (-429 |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"))) (((-4250 "*") |has| |#2| (-158)) (-4241 |has| |#2| (-515)) (-4246 |has| |#2| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) -((|HasCategory| |#2| (QUOTE (-840))) (-3172 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-158))) (-3172 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-515)))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-339))) (-3172 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#2| (QUOTE -4246)) (|HasCategory| |#2| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-134))))) +((|HasCategory| |#2| (QUOTE (-840))) (-3255 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3255 (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3255 (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-158))) (-3255 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-515)))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-339))) (-3255 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#2| (QUOTE -4246)) (|HasCategory| |#2| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-134))))) (-430 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 @@ -1712,7 +1712,7 @@ 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 -(-446 |lv| -3539 R) +(-446 |lv| -3894 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 @@ -1727,11 +1727,11 @@ NIL (-449 |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."))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|)))) (|HasCategory| (-383 (-523)) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasSignature| |#1| (LIST (QUOTE -1691) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3172 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2814) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1292) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|)))) (|HasCategory| (-383 (-523)) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-3255 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasSignature| |#1| (LIST (QUOTE -3976) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3255 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2669) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -3716) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) (-450 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4249 . T)) -((-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|)))))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-786))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2402) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2746) (|devaluate| |#2|)))))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-786))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) (-451 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)}"))) ((-4249 . T) (-4248 . T)) @@ -1743,7 +1743,7 @@ NIL (-453 |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."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|)))))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2402) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2746) (|devaluate| |#2|)))))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) (-454) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1751,16 +1751,16 @@ NIL (-455 |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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((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) 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T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) -(-458 -3539 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +(-458 -3894 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1771,14 +1771,14 @@ NIL (-460) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion.")) (|coerce| (((|RadixExpansion| 16) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a radix expansion with base 16.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| (-523) (QUOTE (-840))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-523) (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-136))) (|HasCategory| (-523) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-949))) (|HasCategory| (-523) (QUOTE (-759))) (-3172 (|HasCategory| (-523) (QUOTE (-759))) (|HasCategory| (-523) (QUOTE (-786)))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-1063))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-523) (QUOTE (-211))) (|HasCategory| (-523) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-523) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -286) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -263) (QUOTE (-523)) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-284))) (|HasCategory| (-523) (QUOTE (-508))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-523) (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (|HasCategory| (-523) (QUOTE (-134))))) +((|HasCategory| (-523) (QUOTE (-840))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-523) (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-136))) (|HasCategory| (-523) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-949))) (|HasCategory| (-523) (QUOTE (-759))) (-3255 (|HasCategory| (-523) (QUOTE (-759))) (|HasCategory| (-523) (QUOTE (-786)))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-1063))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-523) (QUOTE (-211))) (|HasCategory| (-523) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-523) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -286) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -263) (QUOTE (-523)) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-284))) (|HasCategory| (-523) (QUOTE (-508))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-523) (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (|HasCategory| (-523) (QUOTE (-134))))) (-461 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL ((|HasAttribute| |#1| (QUOTE -4248)) (|HasAttribute| |#1| (QUOTE -4249)) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (-462 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-4069 . T)) +((-2500 . T)) NIL (-463 S) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) @@ -1788,7 +1788,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-465 -3539 UP |AlExt| |AlPol|) +(-465 -3894 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 @@ -1799,16 +1799,16 @@ NIL (-467 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4249 . T) (-4248 . T)) -((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3255 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-468 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."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-469 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 -(-470 R UP -3539) +(-470 R UP -3894) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1828,7 +1828,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-475 -3539 |Expon| |VarSet| |DPoly|) +(-475 -3894 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -564) (QUOTE (-1087))))) @@ -1875,19 +1875,19 @@ NIL (-486 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4249 . T) (-4248 . T)) -((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3255 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-487 |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}."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((-3172 (|HasCategory| (-536 |#1|) (QUOTE (-134))) (|HasCategory| (-536 |#1|) (QUOTE (-344)))) (|HasCategory| (-536 |#1|) (QUOTE (-136))) (|HasCategory| (-536 |#1|) (QUOTE (-344))) (|HasCategory| (-536 |#1|) (QUOTE (-134)))) +((-3255 (|HasCategory| (-536 |#1|) (QUOTE (-134))) (|HasCategory| (-536 |#1|) (QUOTE (-344)))) (|HasCategory| (-536 |#1|) (QUOTE (-136))) (|HasCategory| (-536 |#1|) (QUOTE (-344))) (|HasCategory| (-536 |#1|) (QUOTE (-134)))) (-488 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}."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-489 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."))) ((-4249 . T) (-4248 . T)) -((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3255 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-490 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 @@ -1899,7 +1899,7 @@ NIL (-492 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."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-515))) (|HasAttribute| |#1| (QUOTE (-4250 "*"))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-515))) (|HasAttribute| |#1| (QUOTE (-4250 "*"))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-493 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 @@ -1912,7 +1912,7 @@ NIL ((|constructor| (NIL "converts entire exponents to OutputForm"))) NIL NIL -(-496 K -3539 |Par|) +(-496 K -3894 |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 @@ -1932,7 +1932,7 @@ 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 -(-501 K -3539 |Par|) +(-501 K -3894 |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 @@ -1967,12 +1967,12 @@ NIL (-509 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|)))))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) -(-510 R -3539) +((-12 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2402) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2746) (|devaluate| |#2|)))))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) +(-510 R -3894) ((|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 -(-511 R0 -3539 UP UPUP R) +(-511 R0 -3894 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 @@ -1982,7 +1982,7 @@ NIL NIL (-513 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."))) -((-4108 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-2523 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-514 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."))) @@ -1992,7 +1992,7 @@ 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."))) ((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-516 R -3539) +(-516 R -3894) ((|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 @@ -2004,7 +2004,7 @@ 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 -(-519 R -3539 L) +(-519 R -3894 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 -599) (|devaluate| |#2|)))) @@ -2012,11 +2012,11 @@ 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 -(-521 -3539 UP UPUP R) +(-521 -3894 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 -(-522 -3539 UP) +(-522 -3894 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 @@ -2028,15 +2028,15 @@ 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 -(-525 R -3539 L) +(-525 R -3894 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 -599) (|devaluate| |#2|)))) -(-526 R -3539) +(-526 R -3894) ((|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 -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-1051)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-575))))) -(-527 -3539 UP) +(-527 -3894 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 @@ -2044,27 +2044,27 @@ 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 -(-529 -3539) +(-529 -3894) ((|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 (-530 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."))) -((-4108 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-2523 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-531) ((|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 -(-532 R -3539) +(-532 R -3894) ((|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 -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-261))) (|HasCategory| |#2| (QUOTE (-575))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087))))) (-12 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-261)))) (|HasCategory| |#1| (QUOTE (-515)))) -(-533 -3539 UP) +(-533 -3894 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 -(-534 R -3539) +(-534 R -3894) ((|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 @@ -2080,15 +2080,15 @@ 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 -(-538 R -3539) +(-538 R -3894) ((|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 -(-539 E -3539) +(-539 E -3894) ((|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 -(-540 -3539) +(-540 -3894) ((|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}."))) ((-4243 . T) (-4242 . T)) ((|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-1087))))) @@ -2115,7 +2115,7 @@ NIL (-546 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4249 . T) (-4248 . T)) -((-3172 (-12 (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133)))))) (-3172 (|HasCategory| (-133) (LIST (QUOTE -563) (QUOTE (-794)))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133)))))) (|HasCategory| (-133) (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-133) (QUOTE (-1016)))) (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-133) (QUOTE (-1016))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (|HasCategory| (-133) (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133)))))) (-3255 (|HasCategory| (-133) (LIST (QUOTE -563) (QUOTE (-794)))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133)))))) (|HasCategory| (-133) (LIST (QUOTE -564) (QUOTE (-499)))) (-3255 (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-133) (QUOTE (-1016)))) (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-133) (QUOTE (-1016))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (|HasCategory| (-133) (LIST (QUOTE -563) (QUOTE (-794))))) (-547 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 @@ -2123,7 +2123,7 @@ NIL (-548 |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}."))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-523)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-523)) (|devaluate| |#1|)))) (|HasCategory| (-523) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -1691) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-523)))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-523)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-523)) (|devaluate| |#1|)))) (|HasCategory| (-523) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -3976) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-523)))))) (-549 |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.}"))) ((-4243 |has| |#1| (-515)) (-4242 |has| |#1| (-515)) ((-4250 "*") |has| |#1| (-515)) (-4241 |has| |#1| (-515)) (-4245 . T)) @@ -2136,7 +2136,7 @@ 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 -(-552 R -3539 FG) +(-552 R -3894 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 @@ -2147,30 +2147,30 @@ NIL (-554 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4249 . T) (-4248 . T)) -((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-973)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3255 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-973)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-555 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 -4249)) (|HasCategory| |#2| (QUOTE (-786))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#3| (QUOTE (-1016)))) (-556 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-4069 . T)) +((-2500 . T)) NIL (-557 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4245 -3172 (-3147 (|has| |#2| (-343 |#1|)) (|has| |#1| (-515))) (-12 (|has| |#2| (-393 |#1|)) (|has| |#1| (-515)))) (-4243 . T) (-4242 . T)) -((-3172 (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|)))) +((-4245 -3255 (-2819 (|has| |#2| (-343 |#1|)) (|has| |#1| (-515))) (-12 (|has| |#2| (-393 |#1|)) (|has| |#1| (-515)))) (-4243 . T) (-4242 . T)) +((-3255 (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|)))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|)))) (-558 |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."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (QUOTE (-1070))) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| (-1070) (QUOTE (-786))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2402) (QUOTE (-1070))) (LIST (QUOTE |:|) (QUOTE -2746) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| (-1070) (QUOTE (-786))) (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (LIST (QUOTE -563) (QUOTE (-794))))) (-559 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 (-560 |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}."))) -((-4249 . T) (-4069 . T)) +((-4249 . T) (-2500 . T)) NIL (-561 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"))) @@ -2188,7 +2188,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-565 -3539 UP) +(-565 -3894 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2204,7 +2204,7 @@ 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}."))) ((-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| |#1| (QUOTE (-784)))) -(-569 R -3539) +(-569 R -3894) ((|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 @@ -2232,18 +2232,18 @@ 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 -(-576 R -3539) +(-576 R -3894) ((|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 -(-577 |lv| -3539) +(-577 |lv| -3894) ((|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 (-578) ((|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."))) ((-4249 . T)) -((-12 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (QUOTE (-1070))) (LIST (QUOTE |:|) (QUOTE -2482) (QUOTE (-51))))))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-51) (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -286) (QUOTE (-51))))) (|HasCategory| (-1070) (QUOTE (-786))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 (-51))) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2402) (QUOTE (-1070))) (LIST (QUOTE |:|) (QUOTE -2746) (QUOTE (-51))))))) (-3255 (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 (-51))) (QUOTE (-1016))) (|HasCategory| (-51) (QUOTE (-1016)))) (-3255 (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 (-51))) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -286) (QUOTE (-51))))) (|HasCategory| (-1070) (QUOTE (-786))) (-3255 (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 (-51))) (LIST (QUOTE -563) (QUOTE (-794))))) (-579 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2254,8 +2254,8 @@ NIL NIL (-581 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4245 -3172 (-3147 (|has| |#2| (-343 |#1|)) (|has| |#1| (-515))) (-12 (|has| |#2| (-393 |#1|)) (|has| |#1| (-515)))) (-4243 . T) (-4242 . T)) -((-3172 (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|)))) +((-4245 -3255 (-2819 (|has| |#2| (-343 |#1|)) (|has| |#1| (-515))) (-12 (|has| |#2| (-393 |#1|)) (|has| |#1| (-515)))) (-4243 . T) (-4242 . T)) +((-3255 (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|)))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|)))) (-582 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 @@ -2267,7 +2267,7 @@ NIL (-584 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 -((-4179 (|HasCategory| |#1| (QUOTE (-339)))) (|HasCategory| |#1| (QUOTE (-339)))) +((-2575 (|HasCategory| |#1| (QUOTE (-339)))) (|HasCategory| |#1| (QUOTE (-339)))) (-585 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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4245 . T)) @@ -2287,11 +2287,11 @@ NIL (-589 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4249 . T) (-4248 . T)) -((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3255 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-590 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|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-591 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2306,9 +2306,9 @@ NIL ((|HasAttribute| |#1| (QUOTE -4249))) (-594 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})}."))) -((-4069 . T)) +((-2500 . T)) NIL -(-595 R -3539 L) +(-595 R -3894 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 @@ -2328,11 +2328,11 @@ 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}."))) ((-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-600 -3539 UP) +(-600 -3894 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)))) -(-601 A -2576) +(-601 A -2208) ((|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}}"))) ((-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-339)))) @@ -2366,13 +2366,13 @@ NIL NIL (-609 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}."))) -((-4249 . T) (-4248 . T) (-4069 . T)) +((-4249 . T) (-4248 . T) (-2500 . T)) NIL -(-610 -3539) +(-610 -3894) ((|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 -(-611 -3539 |Row| |Col| M) +(-611 -3894 |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 @@ -2383,7 +2383,7 @@ NIL (-613 |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."))) ((-4245 . T) (-4248 . T) (-4242 . T) (-4243 . T)) -((|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211))) (|HasAttribute| |#2| (QUOTE (-4250 "*"))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (-3172 (-12 (|HasCategory| |#2| (QUOTE (-211))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-515))) (-3172 (|HasAttribute| |#2| (QUOTE (-4250 "*"))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-158)))) +((|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211))) (|HasAttribute| |#2| (QUOTE (-4250 "*"))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (-3255 (-12 (|HasCategory| |#2| (QUOTE (-211))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-515))) (-3255 (|HasAttribute| |#2| (QUOTE (-4250 "*"))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-158)))) (-614 |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|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL @@ -2394,12 +2394,12 @@ NIL NIL (-616 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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)]}."))) -((-4069 . T)) +((-2500 . T)) NIL (-617 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 -((-3172 (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-618 |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 @@ -2438,7 +2438,7 @@ NIL ((|HasAttribute| |#2| (QUOTE (-4250 "*"))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-515)))) (-627 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"))) -((-4248 . T) (-4249 . T) (-4069 . T)) +((-4248 . T) (-4249 . T) (-2500 . T)) NIL (-628 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."))) @@ -2447,12 +2447,12 @@ NIL (-629 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."))) ((-4248 . T) (-4249 . T)) -((-3172 (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-515))) (|HasAttribute| |#1| (QUOTE (-4250 "*"))) (|HasCategory| |#1| (QUOTE (-339))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-515))) (|HasAttribute| |#1| (QUOTE (-4250 "*"))) (|HasCategory| |#1| (QUOTE (-339))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-630 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 -(-631 S -3539 FLAF FLAS) +(-631 S -3894 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 @@ -2462,11 +2462,11 @@ NIL NIL (-633) ((|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"))) -((-4241 . T) (-4246 |has| (-638) (-339)) (-4240 |has| (-638) (-339)) (-4115 . T) (-4247 |has| (-638) (-6 -4247)) (-4244 |has| (-638) (-6 -4244)) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| (-638) (QUOTE (-136))) (|HasCategory| (-638) (QUOTE (-134))) (|HasCategory| (-638) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-638) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-638) (QUOTE (-344))) (|HasCategory| (-638) (QUOTE (-339))) (|HasCategory| (-638) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-638) (QUOTE (-211))) (-3172 (|HasCategory| (-638) (QUOTE (-339))) (|HasCategory| (-638) (QUOTE (-325)))) (|HasCategory| (-638) (QUOTE (-325))) (|HasCategory| (-638) (LIST (QUOTE -263) (QUOTE (-638)) (QUOTE (-638)))) (|HasCategory| (-638) (LIST (QUOTE -286) (QUOTE (-638)))) (|HasCategory| (-638) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-638)))) (|HasCategory| (-638) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-638) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-638) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-638) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (-3172 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-339))) (|HasCategory| (-638) (QUOTE (-325)))) (|HasCategory| (-638) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-638) (QUOTE (-949))) (|HasCategory| (-638) (QUOTE (-1109))) (-12 (|HasCategory| (-638) (QUOTE (-930))) (|HasCategory| (-638) (QUOTE (-1109)))) (-3172 (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-339))) (-12 (|HasCategory| (-638) (QUOTE (-325))) (|HasCategory| (-638) (QUOTE (-840))))) (-3172 (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (-12 (|HasCategory| (-638) (QUOTE (-339))) (|HasCategory| (-638) (QUOTE (-840)))) (-12 (|HasCategory| (-638) (QUOTE (-325))) (|HasCategory| (-638) (QUOTE (-840))))) (|HasCategory| (-638) (QUOTE (-508))) (-12 (|HasCategory| (-638) (QUOTE (-982))) (|HasCategory| (-638) (QUOTE (-1109)))) (|HasCategory| (-638) (QUOTE (-982))) (-3172 (|HasCategory| (-638) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-638) (QUOTE (-339)))) (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840))) (-3172 (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-339)))) (-3172 (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-515)))) (-12 (|HasCategory| (-638) (QUOTE (-211))) (|HasCategory| (-638) (QUOTE (-339)))) (-12 (|HasCategory| (-638) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-638) (QUOTE (-339)))) (|HasCategory| (-638) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-638) (QUOTE (-786))) (|HasCategory| (-638) (QUOTE (-515))) (|HasAttribute| (-638) (QUOTE -4247)) (|HasAttribute| (-638) (QUOTE -4244)) (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-134)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-325))))) +((-4241 . T) (-4246 |has| (-638) (-339)) (-4240 |has| (-638) (-339)) (-2531 . T) (-4247 |has| (-638) (-6 -4247)) (-4244 |has| (-638) (-6 -4244)) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| (-638) (QUOTE (-136))) (|HasCategory| (-638) (QUOTE (-134))) (|HasCategory| (-638) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-638) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-638) (QUOTE (-344))) (|HasCategory| (-638) (QUOTE (-339))) (|HasCategory| (-638) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-638) (QUOTE (-211))) (-3255 (|HasCategory| (-638) (QUOTE (-339))) (|HasCategory| (-638) (QUOTE (-325)))) (|HasCategory| (-638) (QUOTE (-325))) (|HasCategory| (-638) (LIST (QUOTE -263) (QUOTE (-638)) (QUOTE (-638)))) (|HasCategory| (-638) (LIST (QUOTE -286) (QUOTE (-638)))) (|HasCategory| (-638) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-638)))) (|HasCategory| (-638) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-638) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-638) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-638) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (-3255 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-339))) (|HasCategory| (-638) (QUOTE (-325)))) (|HasCategory| (-638) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-638) (QUOTE (-949))) (|HasCategory| (-638) (QUOTE (-1109))) (-12 (|HasCategory| (-638) (QUOTE (-930))) (|HasCategory| (-638) (QUOTE (-1109)))) (-3255 (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-339))) (-12 (|HasCategory| (-638) (QUOTE (-325))) (|HasCategory| (-638) (QUOTE (-840))))) (-3255 (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (-12 (|HasCategory| (-638) (QUOTE (-339))) (|HasCategory| (-638) (QUOTE (-840)))) (-12 (|HasCategory| (-638) (QUOTE (-325))) (|HasCategory| (-638) (QUOTE (-840))))) (|HasCategory| (-638) (QUOTE (-508))) (-12 (|HasCategory| (-638) (QUOTE (-982))) (|HasCategory| (-638) (QUOTE (-1109)))) (|HasCategory| (-638) (QUOTE (-982))) (-3255 (|HasCategory| (-638) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-638) (QUOTE (-339)))) (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840))) (-3255 (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-339)))) (-3255 (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-515)))) (-12 (|HasCategory| (-638) (QUOTE (-211))) (|HasCategory| (-638) (QUOTE (-339)))) (-12 (|HasCategory| (-638) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-638) (QUOTE (-339)))) (|HasCategory| (-638) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-638) (QUOTE (-786))) (|HasCategory| (-638) (QUOTE (-515))) (|HasAttribute| (-638) (QUOTE -4247)) (|HasAttribute| (-638) (QUOTE -4244)) (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-134)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-325))))) (-634 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}."))) -((-4249 . T) (-4069 . T)) +((-4249 . T) (-2500 . T)) NIL (-635 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}."))) @@ -2476,13 +2476,13 @@ 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 -(-637 OV E -3539 PG) +(-637 OV E -3894 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 (-638) ((|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}"))) -((-4108 . T) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-2523 . T) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-639 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."))) @@ -2512,7 +2512,7 @@ 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 -(-646 S -2909 I) +(-646 S -1943 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 @@ -2532,14 +2532,14 @@ 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 -(-651 R |Mod| -1327 -3780 |exactQuo|) +(-651 R |Mod| -1345 -3123 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-652 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4244 |has| |#1| (-339)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) -((|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-325))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) +((|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-325))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) (-653 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| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2548,7 +2548,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4243 |has| |#1| (-158)) (-4242 |has| |#1| (-158)) (-4245 . T)) ((|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136)))) -(-655 R |Mod| -1327 -3780 |exactQuo|) +(-655 R |Mod| -1345 -3123 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4245 . T)) NIL @@ -2560,7 +2560,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4243 . T) (-4242 . T)) NIL -(-658 -3539) +(-658 -3894) ((|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]]}."))) ((-4245 . T)) NIL @@ -2596,7 +2596,7 @@ 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 -(-667 -3539 UP) +(-667 -3894 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 @@ -2615,7 +2615,7 @@ NIL (-671 |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."))) (((-4250 "*") |has| |#2| (-158)) (-4241 |has| |#2| (-515)) (-4246 |has| |#2| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) -((|HasCategory| |#2| (QUOTE (-840))) (-3172 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-158))) (-3172 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-515)))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-339))) (-3172 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#2| (QUOTE -4246)) (|HasCategory| |#2| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-134))))) +((|HasCategory| |#2| (QUOTE (-840))) (-3255 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3255 (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3255 (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-158))) (-3255 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-515)))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-339))) (-3255 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#2| (QUOTE -4246)) (|HasCategory| |#2| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-134))))) (-672 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2634,7 +2634,7 @@ NIL ((-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-786)))) (-676 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4238 . T) (-4249 . T) (-4069 . T)) +((-4238 . T) (-4249 . T) (-2500 . T)) NIL (-677 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|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}."))) @@ -2748,15 +2748,15 @@ 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 -(-705 -3539) +(-705 -3894) ((|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 -(-706 P -3539) +(-706 P -3894) ((|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 -(-707 UP -3539) +(-707 UP -3894) ((|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 @@ -2772,7 +2772,7 @@ 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."))) (((-4250 "*") . T)) NIL -(-711 R -3539) +(-711 R -3894) ((|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 @@ -2792,7 +2792,7 @@ 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 -(-716 -3539 |ExtF| |SUEx| |ExtP| |n|) +(-716 -3894 |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 @@ -2807,7 +2807,7 @@ NIL (-719 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."))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) -((|HasCategory| |#1| (QUOTE (-840))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) 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(QUOTE -37) (QUOTE (-523))))) (-2575 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-1087)))) (-2575 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-523))))))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) (-720 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 @@ -2815,14 +2815,14 @@ NIL (-721 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)}"))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4244 |has| |#1| (-339)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) -((|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) +((|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) (-722 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 -383) (QUOTE (-523)))))) (-723 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.}"))) -((-4249 . T) (-4248 . T) (-4069 . T)) +((-4249 . T) (-4248 . T) (-2500 . T)) NIL (-724 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}."))) @@ -2876,23 +2876,23 @@ 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-737 -3172 R OS S) +(-737 -3255 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-738 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (-3172 (|HasCategory| (-927 |#1|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3172 (|HasCategory| (-927 |#1|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| (-927 |#1|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-927 |#1|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (-3255 (|HasCategory| (-927 |#1|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3255 (|HasCategory| (-927 |#1|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| (-927 |#1|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-927 |#1|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (-739) ((|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 -(-740 R -3539 L) +(-740 R -3894 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 -(-741 R -3539) +(-741 R -3894) ((|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 @@ -2900,7 +2900,7 @@ 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 -(-743 R -3539) +(-743 R -3894) ((|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 @@ -2908,11 +2908,11 @@ 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 -(-745 -3539 UP UPUP R) +(-745 -3894 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 -(-746 -3539 UP L LQ) +(-746 -3894 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 @@ -2920,38 +2920,38 @@ 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 -(-748 -3539 UP L LQ) +(-748 -3894 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 -(-749 -3539 UP) +(-749 -3894 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 -(-750 -3539 L UP A LO) +(-750 -3894 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 -(-751 -3539 UP) +(-751 -3894 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)))) -(-752 -3539 LO) +(-752 -3894 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 -(-753 -3539 LODO) +(-753 -3894 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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((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. 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T)) -((|HasCategory| |#1| (QUOTE (-840))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) +((|HasCategory| |#1| (QUOTE (-840))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-339))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) (-756 |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."))) (((-4250 "*") |has| |#2| (-339)) (-4241 |has| |#2| (-339)) (-4246 |has| |#2| (-339)) (-4240 |has| |#2| (-339)) (-4245 . T) (-4243 . T) (-4242 . T)) @@ -3006,7 +3006,7 @@ NIL NIL (-769 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4248 . T) (-4238 . T) (-4249 . T) (-4069 . T)) +((-4248 . T) (-4238 . T) (-4249 . T) (-2500 . T)) NIL (-770) ((|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."))) @@ -3019,7 +3019,7 @@ NIL (-772 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."))) ((-4245 |has| |#1| (-784))) -((|HasCategory| |#1| (QUOTE (-784))) (-3172 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-784)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-508))) (-3172 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-784))) (-3255 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-784)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-508))) (-3255 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-21)))) (-773 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) ((-4243 |has| |#1| (-158)) (-4242 |has| |#1| (-158)) (-4245 . T)) @@ -3047,12 +3047,12 @@ NIL (-779 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."))) ((-4245 |has| |#1| (-784))) -((|HasCategory| |#1| (QUOTE (-784))) (-3172 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-784)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-508))) (-3172 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-784))) (-3255 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-784)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-508))) (-3255 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-21)))) (-780) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-781 -1996 S) +(-781 -3765 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 @@ -3088,11 +3088,11 @@ 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 (-339))) (|HasCategory| |#1| (QUOTE (-515)))) -(-790 R |sigma| -1566) +(-790 R |sigma| -3414) ((|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."))) ((-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-339)))) -(-791 |x| R |sigma| -1566) +(-791 |x| R |sigma| -3414) ((|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."))) ((-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-339)))) @@ -3139,15 +3139,15 @@ NIL (-802 |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)."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| (-801 |#1|) (QUOTE (-840))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-801 |#1|) (QUOTE (-134))) (|HasCategory| (-801 |#1|) (QUOTE (-136))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-801 |#1|) (QUOTE (-949))) (|HasCategory| (-801 |#1|) (QUOTE (-759))) (-3172 (|HasCategory| (-801 |#1|) (QUOTE (-759))) (|HasCategory| (-801 |#1|) (QUOTE (-786)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-801 |#1|) (QUOTE (-1063))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-801 |#1|) (QUOTE (-211))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -484) (QUOTE (-1087)) (LIST (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -263) (LIST (QUOTE -801) (|devaluate| |#1|)) (LIST (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| (-801 |#1|) (QUOTE (-284))) (|HasCategory| (-801 |#1|) (QUOTE (-508))) (|HasCategory| (-801 |#1|) (QUOTE (-786))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-801 |#1|) (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-801 |#1|) (QUOTE (-840)))) (|HasCategory| (-801 |#1|) (QUOTE (-134))))) +((|HasCategory| (-801 |#1|) (QUOTE (-840))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-801 |#1|) (QUOTE (-134))) (|HasCategory| (-801 |#1|) (QUOTE (-136))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-801 |#1|) (QUOTE (-949))) (|HasCategory| (-801 |#1|) (QUOTE (-759))) (-3255 (|HasCategory| (-801 |#1|) (QUOTE (-759))) (|HasCategory| (-801 |#1|) (QUOTE (-786)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-801 |#1|) (QUOTE (-1063))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-801 |#1|) (QUOTE (-211))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -484) (QUOTE (-1087)) (LIST (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -263) (LIST (QUOTE -801) (|devaluate| |#1|)) (LIST (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| (-801 |#1|) (QUOTE (-284))) (|HasCategory| (-801 |#1|) (QUOTE (-508))) (|HasCategory| (-801 |#1|) (QUOTE (-786))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-801 |#1|) (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-801 |#1|) (QUOTE (-840)))) (|HasCategory| (-801 |#1|) (QUOTE (-134))))) (-803 |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)}."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| |#2| (QUOTE (-840))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-759))) (-3172 (|HasCategory| |#2| (QUOTE (-759))) (|HasCategory| |#2| (QUOTE (-786)))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-211))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -263) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-786))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-134))))) +((|HasCategory| |#2| (QUOTE (-840))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-759))) (-3255 (|HasCategory| |#2| (QUOTE (-759))) (|HasCategory| |#2| (QUOTE (-786)))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-211))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -263) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-786))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-134))))) (-804 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 (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))))) (-805) ((|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 @@ -3203,7 +3203,7 @@ NIL (-818 |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 (-4179 (|HasCategory| |#2| (QUOTE (-973)))) (-4179 (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087)))))) (-12 (|HasCategory| |#2| (QUOTE (-973))) (-4179 (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087)))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087))))) +((-12 (-2575 (|HasCategory| |#2| (QUOTE (-973)))) (-2575 (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087)))))) (-12 (|HasCategory| |#2| (QUOTE (-973))) (-2575 (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087)))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087))))) (-819 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 @@ -3212,7 +3212,7 @@ 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 -(-821 R -2909) +(-821 R -1943) ((|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 @@ -3236,7 +3236,7 @@ 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 -(-827 UP -3539) +(-827 UP -3894) ((|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 @@ -3259,7 +3259,7 @@ NIL (-832 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 (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-833 |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 @@ -3275,7 +3275,7 @@ NIL (-836 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."))) ((-4245 . T)) -((-3172 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-786)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-786)))) +((-3255 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-786)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-786)))) (-837 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 @@ -3296,7 +3296,7 @@ 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."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| $ (QUOTE (-136))) (|HasCategory| $ (QUOTE (-134))) (|HasCategory| $ (QUOTE (-344)))) -(-842 R0 -3539 UP UPUP R) +(-842 R0 -3894 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 @@ -3324,7 +3324,7 @@ 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 -(-849 -3539) +(-849 -3894) ((|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 @@ -3340,11 +3340,11 @@ 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}."))) (((-4250 "*") . T)) NIL -(-853 -3539 P) +(-853 -3894 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-854 |xx| -3539) +(-854 |xx| -3894) ((|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 @@ -3368,7 +3368,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-860 R -3539) +(-860 R -3894) ((|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 @@ -3380,7 +3380,7 @@ 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 -(-863 S R -3539) +(-863 S R -3894) ((|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 @@ -3400,11 +3400,11 @@ 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 -817) (|devaluate| |#1|)))) -(-868 R -3539 -2909) +(-868 R -3894 -1943) ((|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 -(-869 -2909) +(-869 -1943) ((|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 @@ -3427,7 +3427,7 @@ NIL (-874 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4249 . T) (-4248 . T)) -((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-973)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3255 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-973)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-875 |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 @@ -3452,7 +3452,7 @@ 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}."))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) NIL -(-881 E V R P -3539) +(-881 E V R P -3894) ((|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 @@ -3463,8 +3463,8 @@ NIL (-883 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}."))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) -((|HasCategory| |#1| (QUOTE (-840))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) -(-884 E V R P -3539) +((|HasCategory| |#1| (QUOTE (-840))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) +(-884 E V R P -3894) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-427)))) @@ -3483,12 +3483,12 @@ NIL (-888 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4249 . T) (-4248 . T)) -((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3255 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-889) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-890 -3539) +(-890 -3894) ((|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 @@ -3503,11 +3503,11 @@ NIL (-893 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}"))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-124)))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-124)))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246))) (-894 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"))) ((-4245 -12 (|has| |#2| (-448)) (|has| |#1| (-448)))) -((-3172 (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-786))))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#2| (QUOTE (-448)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#2| (QUOTE (-448)))) (-12 (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#2| (QUOTE (-666))))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-344)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#2| (QUOTE (-448)))) (-12 (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#2| (QUOTE (-666)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#2| (QUOTE (-666)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-786))))) +((-3255 (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-786))))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#2| (QUOTE (-448)))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#2| (QUOTE (-448)))) (-12 (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#2| (QUOTE (-666))))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-344)))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#2| (QUOTE (-448)))) (-12 (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#2| (QUOTE (-666)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#2| (QUOTE (-666)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-786))))) (-895) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3522,7 +3522,7 @@ NIL NIL (-898 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4248 . T) (-4249 . T) (-4069 . T)) +((-4248 . T) (-4249 . T) (-2500 . T)) NIL (-899 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}}"))) @@ -3550,7 +3550,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-515)))) (-905 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."))) -((-4248 . T) (-4069 . T)) +((-4248 . T) (-2500 . T)) NIL (-906 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."))) @@ -3566,7 +3566,7 @@ NIL NIL (-909 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}."))) -((-4249 . T) (-4248 . T) (-4069 . T)) +((-4249 . T) (-4248 . T) (-2500 . T)) NIL (-910 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3584,7 +3584,7 @@ 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 -(-914 K R UP -3539) +(-914 K R UP -3894) ((|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 @@ -3614,7 +3614,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-840))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-759))) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-1063)))) (-921 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}."))) -((-4069 . T) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-2500 . T) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-922 |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}."))) @@ -3622,7 +3622,7 @@ NIL NIL (-923 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."))) -((-4248 . T) (-4249 . T) (-4069 . T)) +((-4248 . T) (-4249 . T) (-2500 . T)) NIL (-924 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}."))) @@ -3639,11 +3639,11 @@ NIL (-927 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.}"))) ((-4241 |has| |#1| (-267)) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (QUOTE (-267))) (|HasCategory| |#1| (QUOTE (-339)))) (|HasCategory| |#1| (QUOTE (-267))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-508))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339))))) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-339))) (-3255 (|HasCategory| |#1| (QUOTE (-267))) (|HasCategory| |#1| (QUOTE (-339)))) (|HasCategory| |#1| (QUOTE (-267))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-508))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339))))) (-928 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}."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-929 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3652,14 +3652,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-931 -3539 UP UPUP |radicnd| |n|) +(-931 -3894 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4241 |has| (-383 |#2|) (-339)) (-4246 |has| (-383 |#2|) (-339)) (-4240 |has| (-383 |#2|) (-339)) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| (-383 |#2|) (QUOTE (-134))) (|HasCategory| (-383 |#2|) (QUOTE (-136))) (|HasCategory| (-383 |#2|) (QUOTE (-325))) (-3172 (|HasCategory| (-383 |#2|) (QUOTE (-339))) (|HasCategory| (-383 |#2|) (QUOTE (-325)))) (|HasCategory| (-383 |#2|) (QUOTE (-339))) (|HasCategory| (-383 |#2|) (QUOTE (-344))) (-3172 (-12 (|HasCategory| (-383 |#2|) (QUOTE (-211))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (|HasCategory| (-383 |#2|) (QUOTE (-325)))) (-3172 (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-325))))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-344))) (-3172 (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (QUOTE (-211))) (|HasCategory| (-383 |#2|) (QUOTE (-339))))) +((|HasCategory| (-383 |#2|) (QUOTE (-134))) (|HasCategory| (-383 |#2|) (QUOTE (-136))) (|HasCategory| (-383 |#2|) (QUOTE (-325))) (-3255 (|HasCategory| (-383 |#2|) (QUOTE (-339))) (|HasCategory| (-383 |#2|) (QUOTE (-325)))) (|HasCategory| (-383 |#2|) (QUOTE (-339))) (|HasCategory| (-383 |#2|) (QUOTE (-344))) (-3255 (-12 (|HasCategory| (-383 |#2|) (QUOTE (-211))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (|HasCategory| (-383 |#2|) (QUOTE (-325)))) (-3255 (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-325))))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-344))) (-3255 (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (QUOTE (-211))) (|HasCategory| (-383 |#2|) (QUOTE (-339))))) (-932 |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."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| (-523) (QUOTE (-840))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-523) (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-136))) (|HasCategory| (-523) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-949))) (|HasCategory| (-523) (QUOTE (-759))) (-3172 (|HasCategory| (-523) (QUOTE (-759))) (|HasCategory| (-523) (QUOTE (-786)))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-1063))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-523) (QUOTE (-211))) (|HasCategory| (-523) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-523) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -286) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -263) (QUOTE (-523)) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-284))) (|HasCategory| (-523) (QUOTE (-508))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-523) (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (|HasCategory| (-523) (QUOTE (-134))))) +((|HasCategory| (-523) (QUOTE (-840))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-523) (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-136))) (|HasCategory| (-523) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-949))) (|HasCategory| (-523) (QUOTE (-759))) (-3255 (|HasCategory| (-523) (QUOTE (-759))) (|HasCategory| (-523) (QUOTE (-786)))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-1063))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-523) (QUOTE (-211))) (|HasCategory| (-523) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-523) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -286) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -263) (QUOTE (-523)) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-284))) (|HasCategory| (-523) (QUOTE (-508))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-523) (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (|HasCategory| (-523) (QUOTE (-134))))) (-933) ((|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 @@ -3682,7 +3682,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4249)) (|HasCategory| |#2| (QUOTE (-1016)))) (-938 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}."))) -((-4069 . T)) +((-2500 . T)) NIL (-939 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) @@ -3692,19 +3692,19 @@ 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)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4241 . T) (-4246 . T) (-4240 . T) (-4243 . T) (-4242 . T) ((-4250 "*") . T) (-4245 . T)) NIL -(-941 R -3539) +(-941 R -3894) ((|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 -(-942 R -3539) +(-942 R -3894) ((|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 -(-943 -3539 UP) +(-943 -3894 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 -(-944 -3539 UP) +(-944 -3894 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 @@ -3735,8 +3735,8 @@ NIL (-951 |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"))) ((-4241 . T) (-4246 . T) (-4240 . T) (-4243 . T) (-4242 . T) ((-4250 "*") . T) (-4245 . T)) -((-3172 (|HasCategory| (-383 (-523)) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-383 (-523)) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 (-523)) (LIST (QUOTE -964) (QUOTE (-523))))) -(-952 -3539 L) +((-3255 (|HasCategory| (-383 (-523)) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-383 (-523)) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 (-523)) (LIST (QUOTE -964) (QUOTE (-523))))) +(-952 -3894 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 @@ -3772,14 +3772,14 @@ 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 -(-961 -3539 |Expon| |VarSet| |FPol| |LFPol|) +(-961 -3894 |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"))) (((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-962) ((|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.}"))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (QUOTE (-1087))) (LIST (QUOTE |:|) (QUOTE -2482) (QUOTE (-51))))))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-51) (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -286) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-1087) (QUOTE (-786))) (|HasCategory| (-51) (QUOTE (-1016))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2402) (QUOTE (-1087))) (LIST (QUOTE |:|) (QUOTE -2746) (QUOTE (-51))))))) (-3255 (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (QUOTE (-1016))) (|HasCategory| (-51) (QUOTE (-1016)))) (-3255 (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -286) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (QUOTE (-1016))) (|HasCategory| (-1087) (QUOTE (-786))) (|HasCategory| (-51) (QUOTE (-1016))) (-3255 (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (LIST (QUOTE -563) (QUOTE (-794))))) (-963 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 @@ -3824,7 +3824,7 @@ 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."))) ((-4245 . T)) NIL -(-974 |xx| -3539) +(-974 |xx| -3894) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -3834,12 +3834,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-284))) (|HasCategory| |#4| (QUOTE (-339))) (|HasCategory| |#4| (QUOTE (-515))) (|HasCategory| |#4| (QUOTE (-158)))) (-976 |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"))) -((-4248 . T) (-4069 . T) (-4243 . T) (-4242 . T)) +((-4248 . T) (-2500 . T) (-4243 . T) (-4242 . T)) NIL (-977 |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}."))) ((-4248 . T) (-4243 . T) (-4242 . T)) -((-3172 (-12 (|HasCategory| |#3| (QUOTE (-158))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-339))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#3| (QUOTE (-158))) (|HasCategory| |#3| (QUOTE (-339)))) (|HasCategory| |#3| (QUOTE (-339))) (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (QUOTE (-284))) (|HasCategory| |#3| (QUOTE (-515))) (|HasCategory| |#3| (QUOTE (-158))) (|HasCategory| |#3| (LIST (QUOTE -563) (QUOTE (-794)))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|))))) +((-3255 (-12 (|HasCategory| |#3| (QUOTE (-158))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-339))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -564) (QUOTE (-499)))) (-3255 (|HasCategory| |#3| (QUOTE (-158))) (|HasCategory| |#3| (QUOTE (-339)))) (|HasCategory| |#3| (QUOTE (-339))) (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (QUOTE (-284))) (|HasCategory| |#3| (QUOTE (-515))) (|HasCategory| |#3| (QUOTE (-158))) (|HasCategory| |#3| (LIST (QUOTE -563) (QUOTE (-794)))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|))))) (-978 |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 @@ -3871,7 +3871,7 @@ NIL (-985) ((|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}"))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (QUOTE (-1087))) (LIST (QUOTE |:|) (QUOTE -2482) (QUOTE (-51))))))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-51) (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -286) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-1087) (QUOTE (-786))) (|HasCategory| (-51) (QUOTE (-1016))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2402) (QUOTE (-1087))) (LIST (QUOTE |:|) (QUOTE -2746) (QUOTE (-51))))))) (-3255 (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (QUOTE (-1016))) (|HasCategory| (-51) (QUOTE (-1016)))) (-3255 (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -286) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (QUOTE (-1016))) (|HasCategory| (-1087) (QUOTE (-786))) (|HasCategory| (-51) (QUOTE (-1016))) (-3255 (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (LIST (QUOTE -563) (QUOTE (-794))))) (-986 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 @@ -3898,7 +3898,7 @@ NIL NIL (-992 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}."))) -((-4249 . T) (-4248 . T) (-4069 . T)) +((-4249 . T) (-4248 . T) (-2500 . T)) NIL (-993 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."))) @@ -3908,11 +3908,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-995 |Base| R -3539) +(-995 |Base| R -3894) ((|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 -(-996 |Base| R -3539) +(-996 |Base| R -3894) ((|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 @@ -3927,7 +3927,7 @@ NIL (-999 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."))) ((-4241 |has| |#1| (-339)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-325))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-325)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-344))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (QUOTE (-339)))) (|HasCategory| |#1| (QUOTE (-325)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087))))) (-12 (|HasCategory| |#1| (QUOTE (-325))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087))))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339)))) (-12 (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (QUOTE (-339))))) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-325))) (-3255 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-325)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-344))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (QUOTE (-339)))) (|HasCategory| |#1| (QUOTE (-325)))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087))))) (-12 (|HasCategory| |#1| (QUOTE (-325))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087))))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339)))) (-12 (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (QUOTE (-339))))) (-1000 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 @@ -3951,7 +3951,7 @@ NIL (-1005 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"))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) -((|HasCategory| |#1| (QUOTE (-840))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) +((|HasCategory| |#1| (QUOTE (-840))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-339))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) (-1006 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -3970,7 +3970,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-1016)))) (-1010 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."))) -((-4069 . T)) +((-2500 . T)) NIL (-1011 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) @@ -3978,7 +3978,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1016)))) (-1012 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| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-4069 . T)) +((-2500 . T)) NIL (-1013 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) @@ -3986,7 +3986,7 @@ NIL NIL (-1014 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) -((-4238 . T) (-4069 . T)) +((-4238 . T) (-2500 . T)) NIL (-1015 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}."))) @@ -4003,7 +4003,7 @@ NIL (-1018 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)}}"))) ((-4248 . T) (-4238 . T) (-4249 . T)) -((-3172 (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-1019 |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 @@ -4030,7 +4030,7 @@ NIL NIL (-1025 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.}"))) -((-4249 . T) (-4248 . T) (-4069 . T)) +((-4249 . T) (-4248 . T) (-2500 . T)) NIL (-1026) ((|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."))) @@ -4047,12 +4047,12 @@ NIL (-1029 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4242 |has| |#3| (-973)) (-4243 |has| |#3| (-973)) (-4245 |has| |#3| (-6 -4245)) ((-4250 "*") |has| |#3| (-158)) (-4248 . 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((|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 (-427)))) -(-1031 R -3539) +(-1031 R -3894) ((|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 @@ -4070,7 +4070,7 @@ NIL NIL (-1035 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4248 . T) (-4249 . T) (-4069 . T)) +((-4248 . T) (-4249 . T) (-2500 . T)) NIL (-1036 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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."))) @@ -4078,7 +4078,7 @@ NIL ((|HasCategory| |#3| (QUOTE (-339))) (|HasAttribute| |#3| (QUOTE (-4250 "*"))) (|HasCategory| |#3| (QUOTE (-158)))) (-1037 |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."))) -((-4069 . T) (-4248 . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-2500 . T) (-4248 . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-1038 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}."))) @@ -4087,16 +4087,16 @@ NIL (-1039 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."))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) -((|HasCategory| |#1| (QUOTE (-840))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) +((|HasCategory| |#1| (QUOTE (-840))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) (-1040 |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}."))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4243 . T) (-4242 . T) (-4245 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-339)))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-339)))) (-1041 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}"))) -((-4249 . T) (-4248 . T) (-4069 . T)) +((-4249 . T) (-4248 . T) (-2500 . T)) NIL -(-1042 UP -3539) +(-1042 UP -3894) ((|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 @@ -4143,18 +4143,18 @@ NIL (-1053 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."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| (-1052 |#1| |#2|) (LIST (QUOTE -286) (LIST (QUOTE -1052) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1016)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1016))) (-3172 (|HasCategory| (-1052 |#1| |#2|) (LIST (QUOTE -563) (QUOTE (-794)))) (-12 (|HasCategory| (-1052 |#1| |#2|) (LIST (QUOTE -286) (LIST (QUOTE -1052) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1016))))) (|HasCategory| (-1052 |#1| |#2|) (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| (-1052 |#1| |#2|) (LIST (QUOTE -286) (LIST (QUOTE -1052) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1016)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1016))) (-3255 (|HasCategory| (-1052 |#1| |#2|) (LIST (QUOTE -563) (QUOTE (-794)))) (-12 (|HasCategory| (-1052 |#1| |#2|) (LIST (QUOTE -286) (LIST (QUOTE -1052) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1016))))) (|HasCategory| (-1052 |#1| |#2|) (LIST (QUOTE -563) (QUOTE (-794))))) (-1054 |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}."))) ((-4245 . T) (-4237 |has| |#2| (-6 (-4250 "*"))) (-4248 . T) (-4242 . T) (-4243 . T)) -((|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211))) (|HasAttribute| |#2| (QUOTE (-4250 "*"))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (-3172 (-12 (|HasCategory| |#2| (QUOTE (-211))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-339))) (-3172 (|HasAttribute| |#2| (QUOTE (-4250 "*"))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-158)))) +((|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211))) (|HasAttribute| |#2| (QUOTE (-4250 "*"))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (-3255 (-12 (|HasCategory| |#2| (QUOTE (-211))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-339))) (-3255 (|HasAttribute| |#2| (QUOTE (-4250 "*"))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-158)))) (-1055 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1056) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4249 . T) (-4248 . T) (-4069 . T)) +((-4249 . T) (-4248 . T) (-2500 . T)) NIL (-1057 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4167,19 +4167,19 @@ NIL (-1059 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-1060 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 (-1061 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})}."))) -((-4069 . T)) +((-2500 . T)) NIL (-1062 |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."))) ((-4249 . T)) -((-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|)))))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-786))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2402) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2746) (|devaluate| |#2|)))))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-786))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) (-1063) ((|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 @@ -4203,19 +4203,19 @@ NIL (-1068 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."))) ((-4249 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-1069) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4249 . T) (-4248 . T) (-4069 . T)) +((-4249 . T) (-4248 . T) (-2500 . T)) NIL (-1070) NIL ((-4249 . T) (-4248 . T)) -((-3172 (-12 (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133)))))) (|HasCategory| (-133) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-133) (QUOTE (-1016))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (|HasCategory| (-133) (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133)))))) (|HasCategory| (-133) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-133) (QUOTE (-1016))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (|HasCategory| (-133) (LIST (QUOTE -563) (QUOTE (-794))))) (-1071 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (QUOTE (-1070))) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#1|)))))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (QUOTE (-1016))) (|HasCategory| (-1070) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2402) (QUOTE (-1070))) (LIST (QUOTE |:|) (QUOTE -2746) (|devaluate| |#1|)))))) (-3255 (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-1016)))) (-3255 (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (QUOTE (-1016))) (|HasCategory| (-1070) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (LIST (QUOTE -563) (QUOTE (-794))))) (-1072 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 @@ -4242,9 +4242,9 @@ NIL NIL (-1078 |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. 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sums of top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n),{} n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL @@ -4263,15 +4263,15 @@ NIL (-1083 R) ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) 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(-840)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3255 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) (-1084 |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."))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|)))) (|HasCategory| (-383 (-523)) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasSignature| |#1| (LIST (QUOTE -1691) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3172 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2814) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1292) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|)))) (|HasCategory| (-383 (-523)) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-3255 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasSignature| |#1| (LIST (QUOTE -3976) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3255 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2669) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -3716) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) (-1085 |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}."))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-710)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-710)) (|devaluate| |#1|)))) (|HasCategory| (-710) (QUOTE (-1028))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-710))))) (|HasSignature| |#1| (LIST (QUOTE -1691) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-710))))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2814) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1292) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-710)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-710)) (|devaluate| |#1|)))) (|HasCategory| (-710) (QUOTE (-1028))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-710))))) (|HasSignature| |#1| (LIST (QUOTE -3976) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-710))))) (|HasCategory| |#1| (QUOTE (-339))) (-3255 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2669) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -3716) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) (-1086) ((|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 @@ -4287,7 +4287,7 @@ NIL (-1089 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| (-900) (QUOTE (-124))) (|HasCategory| |#1| (QUOTE (-515)))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| (-900) (QUOTE (-124))) (|HasCategory| |#1| (QUOTE (-515)))) (-3255 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246))) (-1090) ((|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 @@ -4319,7 +4319,7 @@ NIL (-1097 |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}"))) ((-4248 . T) (-4249 . T)) -((-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|)))))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2402) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2746) (|devaluate| |#2|)))))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (-3255 (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) (-1098 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 @@ -4330,7 +4330,7 @@ NIL NIL (-1100 |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})}."))) -((-4249 . T) (-4069 . T)) +((-4249 . T) (-2500 . T)) NIL (-1101 |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."))) @@ -4371,7 +4371,7 @@ NIL (-1110 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4249 . T) (-4248 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-1111 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4380,7 +4380,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1113 R -3539) +(-1113 R -3894) ((|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 @@ -4388,7 +4388,7 @@ 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 -(-1115 R -3539) +(-1115 R -3894) ((|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 -564) (LIST (QUOTE -823) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -817) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -817) (|devaluate| |#1|))))) @@ -4398,12 +4398,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-344)))) (-1117 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4249 . T) (-4248 . T) (-4069 . T)) +((-4249 . T) (-4248 . T) (-2500 . T)) NIL (-1118 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4243 . T) (-4242 . T) (-4245 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-339)))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-339)))) (-1119 |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 @@ -4416,13 +4416,13 @@ 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 (-1016))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) -(-1122 -3539) +(-1122 -3894) ((|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 (-1123) ((|constructor| (NIL "The fundamental Type."))) -((-4069 . T)) +((-2500 . T)) NIL (-1124 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}.}"))) @@ -4454,16 +4454,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-339)))) (-1131 |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)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) -(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4069 |has| |#1| (-339)) (-4242 . T) (-4243 . T) (-4245 . T)) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-2500 |has| |#1| (-339)) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-1132 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) 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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 @@ -4499,7 +4499,7 @@ NIL (-1142 |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."))) (((-4250 "*") |has| |#2| (-158)) (-4241 |has| |#2| (-515)) (-4244 |has| |#2| (-339)) (-4246 |has| |#2| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . 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(|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4515,7 +4515,7 @@ NIL (-1146 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 -831) (QUOTE (-1087)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1028))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -1691) (LIST (|devaluate| |#2|) (QUOTE (-1087)))))) +((|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1028))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3976) (LIST (|devaluate| |#2|) (QUOTE (-1087)))))) (-1147 |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."))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4242 . T) (-4243 . T) (-4245 . T)) @@ -4543,22 +4543,22 @@ NIL (-1153 |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)}."))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|)))) (|HasCategory| (-383 (-523)) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasSignature| |#1| (LIST (QUOTE -1691) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3172 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2814) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1292) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) +((|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|)))) (|HasCategory| (-383 (-523)) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-3255 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasSignature| |#1| (LIST (QUOTE -3976) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3255 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2669) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -3716) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-1154 |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."))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|)))) (|HasCategory| (-383 (-523)) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasSignature| |#1| (LIST (QUOTE -1691) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3172 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2814) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1292) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|)))) (|HasCategory| (-383 (-523)) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-3255 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasSignature| |#1| (LIST (QUOTE -3976) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3255 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2669) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -3716) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) (-1155 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))}."))) (((-4250 "*") |has| (-1154 |#2| |#3| |#4|) (-158)) (-4241 |has| (-1154 |#2| |#3| |#4|) (-515)) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| (-1154 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-158))) (|HasCategory| (-1154 |#2| |#3| |#4|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-1154 |#2| |#3| |#4|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-339))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-427))) (-3172 (|HasCategory| (-1154 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-1154 |#2| |#3| |#4|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-515)))) +((|HasCategory| (-1154 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-158))) (|HasCategory| (-1154 |#2| |#3| |#4|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-1154 |#2| |#3| |#4|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-339))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-427))) (-3255 (|HasCategory| (-1154 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-1154 |#2| |#3| |#4|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-515)))) (-1156 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL ((|HasAttribute| |#1| (QUOTE -4249))) (-1157 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-4069 . T)) +((-2500 . T)) NIL (-1158 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) @@ -4567,7 +4567,7 @@ NIL (-1159 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-523)))) (|HasCategory| |#2| (QUOTE (-889))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasSignature| |#2| (LIST (QUOTE -1292) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2814) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1087))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-339)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-889))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasSignature| |#2| (LIST (QUOTE -3716) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2669) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1087))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-339)))) (-1160 |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."))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4242 . T) (-4243 . T) (-4245 . T)) @@ -4575,18 +4575,18 @@ NIL (-1161 |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}."))) (((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4242 . T) (-4243 . T) (-4245 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-710)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-710)) (|devaluate| |#1|)))) (|HasCategory| (-710) (QUOTE (-1028))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-710))))) (|HasSignature| |#1| (LIST (QUOTE -1691) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-710))))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2814) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1292) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3255 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-710)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-710)) (|devaluate| |#1|)))) (|HasCategory| (-710) (QUOTE (-1028))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-710))))) (|HasSignature| |#1| (LIST (QUOTE -3976) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-710))))) (|HasCategory| |#1| (QUOTE (-339))) (-3255 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2669) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -3716) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) (-1162 |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 -(-1163 -3539 UP L UTS) +(-1163 -3894 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 (-515)))) (-1164) ((|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."))) -((-4069 . T)) +((-2500 . T)) NIL (-1165 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) @@ -4598,7 +4598,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-930))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-666))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1167 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4249 . T) (-4248 . T) (-4069 . T)) +((-4249 . T) (-4248 . T) (-2500 . T)) NIL (-1168 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4607,7 +4607,7 @@ NIL (-1169 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4249 . T) (-4248 . T)) -((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-973)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-3255 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3255 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3255 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-973)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-1170) ((|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 @@ -4640,7 +4640,7 @@ 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 -(-1178 K R UP -3539) +(-1178 K R UP -3894) ((|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 @@ -4668,11 +4668,11 @@ 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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4241 |has| |#2| (-6 -4241)) (-4243 . T) (-4242 . T) (-4245 . T)) NIL -(-1185 S -3539) +(-1185 S -3894) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136)))) -(-1186 -3539) +(-1186 -3894) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 94f9b9eb..2bd895b7 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,14 +1,14 @@ -(142548 . 3416412006) -(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) #0#) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) +(142548 . 3417125214) +(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) #0#) |has| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (-286 (-2 (|:| -2402 |#1|) (|:| -2746 |#2|))))) (((|#2| |#2|) . T)) ((((-523)) . T)) -((($ $) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) ((|#2| |#2|) . T) ((#0=(-383 (-523)) #0#) |has| |#2| (-37 (-383 (-523))))) +((($ $) -3255 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) ((|#2| |#2|) . T) ((#0=(-383 (-523)) #0#) |has| |#2| (-37 (-383 (-523))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (((|#2|) . T)) -((($) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) ((|#2|) . T) (((-383 (-523))) |has| |#2| (-37 (-383 (-523))))) +((($) -3255 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) ((|#2|) . T) (((-383 (-523))) |has| |#2| (-37 (-383 (-523))))) (|has| |#1| (-840)) ((((-794)) . T)) ((((-794)) . T)) @@ -23,28 +23,28 @@ ((((-203)) . T) (((-794)) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#1|) . T)) -(-3172 (|has| |#1| (-21)) (|has| |#1| (-784))) -((($ $) . T) ((#0=(-383 (-523)) #0#) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1| |#1|) . T)) -(-3172 (|has| |#1| (-759)) (|has| |#1| (-786))) +(-3255 (|has| |#1| (-21)) (|has| |#1| (-784))) +((($ $) . T) ((#0=(-383 (-523)) #0#) -3255 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1| |#1|) . T)) +(-3255 (|has| |#1| (-759)) (|has| |#1| (-786))) ((((-383 (-523))) |has| |#1| (-964 (-383 (-523)))) (((-523)) |has| |#1| (-964 (-523))) ((|#1|) . T)) ((((-794)) . T)) ((((-794)) . T)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-515))) (|has| |#1| (-784)) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#1| |#2| |#3|) . T)) (((|#4|) . T)) -((($) . T) (((-383 (-523))) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) +((($) . T) (((-383 (-523))) -3255 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) ((((-794)) . T)) ((((-794)) |has| |#1| (-1016))) (((|#1|) . T) ((|#2|) . T)) (((|#1|) . T) (((-523)) |has| |#1| (-964 (-523))) (((-383 (-523))) |has| |#1| (-964 (-383 (-523))))) -(-3172 (|has| |#2| (-158)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) -(-3172 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) -(((|#2| (-456 (-2810 |#1|) (-710))) . T)) +(-3255 (|has| |#2| (-158)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +(-3255 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(((|#2| (-456 (-1271 |#1|) (-710))) . T)) (((|#1| (-495 (-1087))) . T)) (((#0=(-801 |#1|) #0#) . T) ((#1=(-383 (-523)) #1#) . T) (($ $) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) (|has| |#4| (-344)) (|has| |#3| (-344)) (((|#1|) . T)) @@ -54,10 +54,10 @@ (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-515)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-515))) ((($) . T)) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) ((((-499)) |has| |#1| (-564 (-499)))) ((($) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((|#1|) . T)) ((($) . T)) @@ -66,59 +66,59 @@ ((((-794)) . T)) ((((-794)) . T)) ((((-383 (-523))) . T) (($) . T)) -((((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (((-1161 |#1| |#2| |#3|)) |has| |#1| (-339)) (($) . T) ((|#1|) . T)) +((((-383 (-523))) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (((-1161 |#1| |#2| |#3|)) |has| |#1| (-339)) (($) . T) ((|#1|) . T)) ((((-794)) . T)) ((((-794)) . T)) ((((-794)) . T)) (((|#1|) . T)) -(((|#1|) . T) (((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) . T)) +(((|#1|) . T) (((-383 (-523))) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) . T)) (((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523)))) (($) . T)) -(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3255 (|has| |#1| (-786)) (|has| |#1| (-1016))) (((|#1| |#2|) . T)) ((((-794)) . T)) (((|#1|) . T)) -(((#0=(-383 (-523)) #0#) |has| |#2| (-37 (-383 (-523)))) ((|#2| |#2|) . T) (($ $) -3172 (|has| |#2| (-158)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) +(((#0=(-383 (-523)) #0#) |has| |#2| (-37 (-383 (-523)))) ((|#2| |#2|) . T) (($ $) -3255 (|has| |#2| (-158)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) (((|#1|) . 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T)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) -(-3172 (|has| |#4| (-732)) (|has| |#4| (-784))) -(-3172 (|has| |#4| (-732)) (|has| |#4| (-784))) -(-3172 (|has| |#3| (-732)) (|has| |#3| (-784))) -(-3172 (|has| |#3| (-732)) (|has| |#3| (-784))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3255 (|has| |#4| (-732)) (|has| |#4| (-784))) +(-3255 (|has| |#4| (-732)) (|has| |#4| (-784))) +(-3255 (|has| |#3| (-732)) (|has| |#3| (-784))) +(-3255 (|has| |#3| (-732)) (|has| |#3| (-784))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-1016)) @@ -132,21 +132,21 @@ ((((-523)) . T)) ((((-523)) . T)) (((|#1|) . T)) -(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3255 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) (((|#1| (-710)) . T)) (|has| |#2| (-732)) -(-3172 (|has| |#2| (-732)) (|has| |#2| (-784))) +(-3255 (|has| |#2| (-732)) (|has| |#2| (-784))) (|has| |#2| (-784)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) ((((-1070) |#1|) . T)) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) (((|#1|) . T)) (((|#3| (-710)) . T)) (|has| |#1| (-136)) (|has| |#1| (-134)) -(-3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) -(-3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) (|has| |#1| (-1016)) ((((-383 (-523))) . T) (((-523)) . T)) ((((-1087) |#2|) |has| |#2| (-484 (-1087) |#2|)) ((|#2| |#2|) |has| |#2| (-286 |#2|))) @@ -154,7 +154,7 @@ (((|#1|) . T) (($) . T)) ((((-523)) . T)) ((((-523)) . 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T)) (((|#1|) . T)) ((((-383 (-523))) |has| |#1| (-964 (-383 (-523)))) (((-523)) |has| |#1| (-964 (-523))) ((|#1|) . T)) (((|#1|) . T) (((-523)) |has| |#1| (-585 (-523)))) -(((|#2|) . T) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2402 (-1070)) (|:| -2746 |#1|))) . T)) (|has| |#1| (-515)) (|has| |#1| (-515)) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) -(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3255 (|has| |#1| (-786)) (|has| |#1| (-1016))) (((|#1|) . T)) (|has| |#1| (-515)) (|has| |#1| (-515)) @@ -218,11 +218,11 @@ (((|#2|) . T) (($) . T) (((-383 (-523))) . T)) (-12 (|has| |#1| (-1016)) (|has| |#2| (-1016))) ((($) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((|#1|) . 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T) (((-203)) . T) (((-355)) . T) (((-823 (-355))) . T)) ((((-794)) . T)) -(-3172 (|has| |#1| (-21)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) +(-3255 (|has| |#1| (-21)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) (((|#1|) |has| |#1| (-158))) (((|#1| $) |has| |#1| (-263 |#1| |#1|))) ((((-794)) . T)) @@ -256,13 +256,13 @@ (|has| |#1| (-786)) (|has| |#1| (-1016)) (((|#1|) . T)) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) ((((-499)) |has| |#1| (-564 (-499)))) -((((-383 (-523))) |has| |#2| (-37 (-383 (-523)))) ((|#2|) |has| |#2| (-158)) (($) -3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) -((($) -3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) -((($) -3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((((-383 (-523))) |has| |#2| (-37 (-383 (-523)))) ((|#2|) |has| |#2| (-158)) (($) -3255 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) +((($) -3255 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($) -3255 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (|has| |#1| (-211)) -((($) -3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($) -3255 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (((|#1| (-495 (-757 (-1087)))) . T)) (((|#1| (-900)) . T)) (((#0=(-801 |#1|) $) |has| #0# (-263 #0# #0#))) @@ -271,7 +271,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1063)) -((((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) +((((-2 (|:| -2402 (-1070)) (|:| -2746 |#1|))) . T)) (|has| (-1155 |#1| |#2| |#3| |#4|) (-134)) (|has| (-1155 |#1| |#2| |#3| |#4|) (-136)) (|has| |#1| (-134)) @@ -288,20 +288,20 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-973))) ((((-794)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) #0#) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) #0#) |has| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (-286 (-2 (|:| -2402 |#1|) (|:| -2746 |#2|))))) (((|#1|) . 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T) ((#0=(-383 (-523)) #0#) |has| |#1| (-37 (-383 (-523))))) +((($ $) -3255 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1| |#1|) . T) ((#0=(-383 (-523)) #0#) |has| |#1| (-37 (-383 (-523))))) ((($) . T)) ((($) . T)) ((($) . T)) -((($) -3172 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($) -3255 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) ((((-794)) . T)) ((((-794)) . T)) (|has| (-1154 |#2| |#3| |#4|) (-136)) @@ -312,16 +312,16 @@ ((((-794)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3172 (|has| |#1| (-21)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) +(-3255 (|has| |#1| (-21)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) (((|#1|) . T)) ((((-523) |#1|) . 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T) (($) -3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) (((-383 (-523))) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339)))) (((|#3|) |has| |#3| (-973))) -((($) -3172 (|has| |#1| (-158)) (|has| |#1| (-515))) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($) -3255 (|has| |#1| (-158)) (|has| |#1| (-515))) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (|has| |#1| (-1016)) (((|#2| (-758 |#1|)) . T)) (((|#1|) . T)) @@ -381,37 +381,37 @@ ((((-133)) . T)) (((|#3|) |has| |#3| (-1016)) (((-523)) -12 (|has| |#3| (-964 (-523))) (|has| |#3| (-1016))) (((-383 (-523))) -12 (|has| |#3| (-964 (-383 (-523)))) (|has| |#3| (-1016)))) ((((-794)) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) (((|#1|) . 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T)) ((((-794)) . T)) @@ -653,22 +653,22 @@ (|has| |#1| (-1016)) (((|#2|) . T)) ((((-499)) |has| |#2| (-564 (-499))) (((-823 (-355))) |has| |#2| (-564 (-823 (-355)))) (((-823 (-523))) |has| |#2| (-564 (-823 (-523))))) -(((|#4|) -3172 (|has| |#4| (-158)) (|has| |#4| (-339)))) -(((|#3|) -3172 (|has| |#3| (-158)) (|has| |#3| (-339)))) +(((|#4|) -3255 (|has| |#4| (-158)) (|has| |#4| (-339)))) +(((|#3|) -3255 (|has| |#3| (-158)) (|has| |#3| (-339)))) ((((-794)) . T)) (((|#1|) . T)) -(-3172 (|has| |#2| (-427)) (|has| |#2| (-840))) -(-3172 (|has| |#1| (-427)) (|has| |#1| (-840))) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-840))) +(-3255 (|has| |#2| (-427)) (|has| |#2| (-840))) +(-3255 (|has| |#1| (-427)) (|has| |#1| (-840))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-840))) ((($ $) . T) ((#0=(-1087) $) |has| |#1| (-211)) ((#0# |#1|) |has| |#1| (-211)) ((#1=(-757 (-1087)) |#1|) . T) ((#1# $) . T)) -(-3172 (|has| |#1| (-427)) (|has| |#1| (-840))) +(-3255 (|has| |#1| (-427)) (|has| |#1| (-840))) ((((-523) |#2|) . T)) ((((-794)) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) -((($) -3172 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) ((|#3|) -3172 (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-973)))) +((($) -3255 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) ((|#3|) -3255 (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-973)))) ((((-523) |#1|) . T)) (|has| (-383 |#2|) (-136)) (|has| (-383 |#2|) (-134)) @@ -681,21 +681,21 @@ (|has| |#1| (-515)) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) ((((-794)) . T)) -((((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) +((((-2 (|:| -2402 (-1070)) (|:| -2746 |#1|))) . T)) (|has| |#1| (-37 (-383 (-523)))) -((((-364) (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) +((((-364) (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|))) . T)) (|has| |#1| (-37 (-383 (-523)))) (|has| |#2| (-1063)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-515))) (((|#1|) . T)) ((((-364) (-1070)) . T)) (|has| |#1| (-515)) ((((-112 |#1|)) . T)) ((((-523) |#1|) . T)) -(-3172 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3255 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) (((|#2|) . T)) ((((-794)) . T)) ((((-758 |#1|)) . T)) @@ -708,7 +708,7 @@ (((|#1|) |has| |#1| (-158))) ((((-794)) . T)) ((((-499)) |has| |#1| (-564 (-499)))) -(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3255 (|has| |#1| (-786)) (|has| |#1| (-1016))) (((|#2|) |has| |#2| (-286 |#2|))) (((#0=(-523) #0#) . T) ((#1=(-383 (-523)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -718,7 +718,7 @@ (((#0=(-523) #0#) . T) ((#1=(-383 (-523)) #1#) . T) (($ $) . T)) ((($) . T) (((-523)) . T) (((-383 (-523))) . T)) (|has| |#2| (-344)) -(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3255 (|has| |#1| (-786)) (|has| |#1| (-1016))) (((|#1|) . T) (((-383 (-523))) . T) (($) . T)) (((|#1|) . T) (((-383 (-523))) . T) (($) . T)) (((|#1|) . T) (((-383 (-523))) . T) (($) . T)) @@ -729,9 +729,9 @@ ((((-1085 |#1| |#2| |#3|) $) -12 (|has| (-1085 |#1| |#2| |#3|) (-263 (-1085 |#1| |#2| |#3|) (-1085 |#1| |#2| |#3|))) (|has| |#1| (-339))) (($ $) . T)) ((((-794)) . T)) ((((-794)) . T)) -((($) . T) (((-383 (-523))) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) +((($) . T) (((-383 (-523))) -3255 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) ((((-499)) |has| |#1| (-564 (-499)))) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) ((($ $) . T)) ((($ $) . T)) ((((-794)) . T)) @@ -741,12 +741,12 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($) -3255 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) ((((-383 (-523))) . T) (((-523)) . T)) ((((-523) (-133)) . T)) ((((-133)) . T)) (((|#1|) . T)) -(-3172 (|has| |#1| (-21)) (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-515)) (|has| |#1| (-973))) +(-3255 (|has| |#1| (-21)) (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-515)) (|has| |#1| (-973))) ((((-108)) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) ((((-108)) . T)) @@ -754,38 +754,38 @@ ((((-499)) |has| |#1| (-564 (-499))) (((-203)) . #0=(|has| |#1| (-949))) (((-355)) . #0#)) ((((-794)) . T)) (|has| |#1| (-759)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) (|has| |#1| (-786)) -(-3172 (|has| |#1| (-158)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-158)) (|has| |#1| (-515))) (|has| |#1| (-515)) (|has| |#1| (-840)) (((|#1|) . T)) (|has| |#1| (-1016)) ((((-794)) . 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T)) -(-3172 (|has| |#2| (-732)) (|has| |#2| (-784))) -(-3172 (|has| |#2| (-732)) (|has| |#2| (-784))) +(-3255 (|has| |#2| (-732)) (|has| |#2| (-784))) +(-3255 (|has| |#2| (-732)) (|has| |#2| (-784))) (-12 (|has| |#1| (-448)) (|has| |#2| (-448))) -(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) -(-3172 (-12 (|has| |#1| (-448)) (|has| |#2| (-448))) (-12 (|has| |#1| (-666)) (|has| |#2| (-666)))) +(-3255 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3255 (-12 (|has| |#1| (-448)) (|has| |#2| (-448))) (-12 (|has| |#1| (-666)) (|has| |#2| (-666)))) (((|#1|) . T)) (|has| |#2| (-732)) -(-3172 (|has| |#2| (-732)) (|has| |#2| (-784))) +(-3255 (|has| |#2| (-732)) (|has| |#2| (-784))) (((|#1| |#2|) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (|has| |#2| (-784)) @@ -800,7 +800,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-383 (-523))) . T) (($) . T)) -((($) . T) (((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) ((|#1|) . T)) +((($) . T) (((-383 (-523))) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) ((|#1|) . T)) (|has| |#1| (-767)) ((((-383 (-523))) |has| |#1| (-964 (-383 (-523)))) (((-523)) |has| |#1| (-964 (-523))) ((|#1|) . T)) (|has| |#1| (-1016)) @@ -811,8 +811,8 @@ (((|#3|) |has| |#3| (-1016))) (|has| |#3| (-344)) (((|#1|) . T) (((-794)) . T)) -((((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3172 (|has| |#1| (-339)) (|has| |#1| (-515))) (((-1161 |#1| |#2| |#3|)) |has| |#1| (-339)) ((|#1|) |has| |#1| (-158))) -(((|#1|) |has| |#1| (-158)) (((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3172 (|has| |#1| (-339)) (|has| |#1| (-515)))) +((((-383 (-523))) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3255 (|has| |#1| (-339)) (|has| |#1| (-515))) (((-1161 |#1| |#2| |#3|)) |has| |#1| (-339)) ((|#1|) |has| |#1| (-158))) +(((|#1|) |has| |#1| (-158)) (((-383 (-523))) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3255 (|has| |#1| (-339)) (|has| |#1| (-515)))) ((((-794)) . T)) ((($) |has| |#1| (-515)) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (((|#2|) . T)) @@ -822,30 +822,30 @@ (((|#1|) . T)) (((|#1|) |has| |#1| (-158))) ((((-383 (-523))) . T) (((-523)) . 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T)) -(-3172 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-515)) (|has| |#1| (-973))) +(-3255 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-515)) (|has| |#1| (-973))) (|has| $ (-136)) (|has| $ (-136)) (|has| |#1| (-1016)) ((((-794)) . T)) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-448)) (|has| |#1| (-515)) (|has| |#1| (-973)) (|has| |#1| (-1028))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-448)) (|has| |#1| (-515)) (|has| |#1| (-973)) (|has| |#1| (-1028))) ((($ $) |has| |#1| (-263 $ $)) ((|#1| $) |has| |#1| (-263 |#1| |#1|))) (((|#1| (-383 (-523))) . T)) (((|#1|) . T)) ((((-1087)) . T)) (|has| |#1| (-515)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-515))) (|has| |#1| (-515)) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) @@ -856,7 +856,7 @@ (|has| |#1| (-136)) (|has| |#1| (-134)) (|has| |#4| (-784)) -(((|#2| (-218 (-2810 |#1|) (-710)) (-796 |#1|)) . T)) +(((|#2| (-218 (-1271 |#1|) (-710)) (-796 |#1|)) . T)) (|has| |#3| (-784)) (((|#1| (-495 |#3|) |#3|) . T)) (|has| |#1| (-136)) @@ -870,21 +870,21 @@ (|has| |#1| (-134)) ((((-383 (-523))) |has| |#2| (-339)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) -(-3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) -(-3172 (|has| |#1| (-325)) (|has| |#1| (-344))) +(-3255 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +(-3255 (|has| |#1| (-325)) (|has| |#1| (-344))) ((((-1054 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-158)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-211)) (|has| |#2| (-973))) -(((|#2|) . T) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) -(-3172 (|has| |#3| (-732)) (|has| |#3| (-784))) -(-3172 (|has| |#3| (-732)) (|has| |#3| (-784))) +(((|#2|) . T) (((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) +(-3255 (|has| |#3| (-732)) (|has| |#3| (-784))) +(-3255 (|has| |#3| (-732)) (|has| |#3| (-784))) ((((-794)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) . T) (($) . T)) ((((-638)) . T)) -(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3255 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) (|has| |#1| (-515)) (((|#1|) . T)) (((|#1|) . T)) @@ -906,10 +906,10 @@ (((|#1| (-383 (-523))) . T)) (((|#3|) . T) (((-562 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) ((($ $) . T) ((|#2| $) . T)) (((|#1|) . T) (((-383 (-523))) . T) (($) . T)) (((#0=(-1085 |#1| |#2| |#3|) #0#) -12 (|has| (-1085 |#1| |#2| |#3|) (-286 (-1085 |#1| |#2| |#3|))) (|has| |#1| (-339))) (((-1087) #0#) -12 (|has| (-1085 |#1| |#2| |#3|) (-484 (-1087) (-1085 |#1| |#2| |#3|))) (|has| |#1| (-339)))) @@ -917,8 +917,8 @@ ((((-794)) . T)) ((((-794)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) -(((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016))) (((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) |has| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (-286 (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))))) +(((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) (((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) |has| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (-286 (-2 (|:| -2402 |#1|) (|:| -2746 |#2|))))) +(((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016))) (((-2 (|:| -2402 (-1070)) (|:| -2746 |#1|))) |has| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (-286 (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|))))) ((((-794)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -929,10 +929,10 @@ ((($ $) . T) ((#0=(-796 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-767)) (|has| |#1| (-1016)) -(((|#2| |#2|) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-973))) (($ $) |has| |#2| (-158))) -(((|#2|) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)))) -((((-523) (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-973))) (($) |has| |#2| (-158))) +(((|#2| |#2|) -3255 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-973))) (($ $) |has| |#2| (-158))) +(((|#2|) -3255 (|has| |#2| (-158)) (|has| |#2| (-339)))) +((((-523) (-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -3255 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-973))) (($) |has| |#2| (-158))) ((((-710)) . T)) ((((-523)) . T)) (|has| |#1| (-515)) @@ -945,29 +945,29 @@ ((((-112 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-136)) -(-3172 (|has| |#1| (-158)) (|has| |#1| (-515))) -(-3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) -(-3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) -(-3172 (|has| |#1| (-158)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-158)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-158)) (|has| |#1| (-515))) ((((-823 (-523))) . T) (((-823 (-355))) . T) (((-499)) . T) (((-1087)) . T)) ((((-794)) . T)) -(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3255 (|has| |#1| (-786)) (|has| |#1| (-1016))) ((($) . T)) ((((-794)) . T)) -(-3172 (|has| |#2| (-158)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +(-3255 (|has| |#2| (-158)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) (((|#2|) |has| |#2| (-158))) -((($) -3172 (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) ((|#2|) |has| |#2| (-158)) (((-383 (-523))) |has| |#2| (-37 (-383 (-523))))) +((($) -3255 (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) ((|#2|) |has| |#2| (-158)) (((-383 (-523))) |has| |#2| (-37 (-383 (-523))))) ((((-801 |#1|)) . T)) -(-3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) +(-3255 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) (-12 (|has| |#3| (-211)) (|has| |#3| (-973))) (|has| |#2| (-1063)) -(((#0=(-51)) . T) (((-2 (|:| -3772 (-1087)) (|:| -2482 #0#))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -2402 (-1087)) (|:| -2746 #0#))) . T)) (((|#1| |#2|) . T)) -(-3172 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) +(-3255 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) (((|#1| (-523) (-1001)) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#1| (-383 (-523)) (-1001)) . T)) -((($) -3172 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325)) (|has| |#1| (-515))) (((-383 (-523))) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) +((($) -3255 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325)) (|has| |#1| (-515))) (((-383 (-523))) -3255 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) ((((-523) |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) @@ -975,37 +975,37 @@ (-12 (|has| |#1| (-344)) (|has| |#2| (-344))) ((((-794)) . T)) ((((-1087) |#1|) |has| |#1| (-484 (-1087) |#1|)) ((|#1| |#1|) |has| |#1| (-286 |#1|))) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-344))) (((|#1|) . 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T)) -(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) #0#) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) #0#) |has| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (-286 (-2 (|:| -2402 |#1|) (|:| -2746 |#2|))))) (|has| |#1| (-515)) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) ((((-794)) . T)) (((|#1| |#2|) . T)) -(-3172 (|has| |#2| (-427)) (|has| |#2| (-840))) -(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) -(-3172 (|has| |#1| (-427)) (|has| |#1| (-840))) +(-3255 (|has| |#2| (-427)) (|has| |#2| (-840))) +(-3255 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3255 (|has| |#1| (-427)) (|has| |#1| (-840))) ((((-383 (-523))) . T) (((-523)) . T)) ((((-523)) . T)) -((((-383 (-523))) |has| |#2| (-37 (-383 (-523)))) ((|#2|) |has| |#2| (-158)) (($) -3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) +((((-383 (-523))) |has| |#2| (-37 (-383 (-523)))) ((|#2|) |has| |#2| (-158)) (($) -3255 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) ((($) . T)) ((((-794)) . T)) (((|#1|) . T)) ((((-801 |#1|)) . T) (($) . T) (((-383 (-523))) . T)) ((((-794)) . T)) -(((|#3| |#3|) -3172 (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-973))) (($ $) |has| |#3| (-158))) +(((|#3| |#3|) -3255 (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-973))) (($ $) |has| |#3| (-158))) (|has| |#1| (-949)) ((((-794)) . T)) -(((|#3|) -3172 (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-973))) (($) |has| |#3| (-158))) +(((|#3|) -3255 (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-973))) (($) |has| |#3| (-158))) ((((-523) (-108)) . T)) (((|#1|) |has| |#1| (-286 |#1|))) (|has| |#1| (-344)) @@ -1013,31 +1013,31 @@ (|has| |#1| (-344)) ((((-1087) $) |has| |#1| (-484 (-1087) $)) (($ $) |has| |#1| (-286 $)) ((|#1| |#1|) |has| |#1| (-286 |#1|)) (((-1087) |#1|) |has| |#1| (-484 (-1087) |#1|))) ((((-1087)) |has| |#1| (-831 (-1087)))) -(-3172 (-12 (|has| |#1| (-211)) (|has| |#1| (-339))) (|has| |#1| (-325))) +(-3255 (-12 (|has| |#1| (-211)) (|has| |#1| (-339))) (|has| |#1| (-325))) ((((-364) (-1034)) . T)) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-364) |#1|) . T)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-325))) (|has| |#1| (-1016)) ((((-794)) . T)) ((((-794)) . T)) ((((-841 |#1|)) . T)) -((((-383 (-523))) |has| |#2| (-37 (-383 (-523)))) ((|#2|) |has| |#2| (-158)) (($) -3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) -((((-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((|#1|) |has| |#1| (-158)) (($) -3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840)))) +((((-383 (-523))) |has| |#2| (-37 (-383 (-523)))) ((|#2|) |has| |#2| (-158)) (($) -3255 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) +((((-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((|#1|) |has| |#1| (-158)) (($) -3255 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840)))) (((|#1| |#2|) . T)) ((($) . T)) (((|#1| |#1|) . T)) (((#0=(-801 |#1|)) |has| #0# (-286 #0#))) (((|#1| |#2|) . T)) -(-3172 (|has| |#2| (-732)) (|has| |#2| (-784))) -(-3172 (|has| |#2| (-732)) (|has| |#2| (-784))) +(-3255 (|has| |#2| (-732)) (|has| |#2| (-784))) +(-3255 (|has| |#2| (-732)) (|has| |#2| (-784))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732))) (((|#1|) . T)) (-12 (|has| |#1| (-732)) (|has| |#2| (-732))) -(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3255 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) (|has| |#1| (-1109)) (((#0=(-523) #0#) . T) ((#1=(-383 (-523)) #1#) . T) (($ $) . T)) ((((-383 (-523))) . T) (($) . T)) @@ -1048,8 +1048,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-383 (-523)) #0#) . T)) (|has| |#1| (-339)) ((((-523)) . T) (((-383 (-523))) . T) (($) . T)) -((($ $) . T) ((#0=(-383 (-523)) #0#) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1| |#1|) . T)) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((($ $) . T) ((#0=(-383 (-523)) #0#) -3255 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1| |#1|) . T)) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) (((|#1|) . T) (($) . T) (((-383 (-523))) . T)) ((((-794)) . T)) ((((-794)) . T)) @@ -1064,14 +1064,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-784)) (|has| |#1| (-784)) -((($) . T) (((-383 (-523))) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) -(-3172 (|has| |#1| (-158)) (|has| |#1| (-515))) -(((#0=(-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) #0#) |has| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (-286 (-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))))) +((($) . T) (((-383 (-523))) -3255 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) +(-3255 (|has| |#1| (-158)) (|has| |#1| (-515))) +(((#0=(-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) #0#) |has| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (-286 (-2 (|:| -2402 (-1087)) (|:| -2746 (-51)))))) ((($) . T)) (|has| |#2| (-786)) ((($) . T)) (((|#2|) |has| |#2| (-1016))) -((((-794)) -3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-563 (-794))) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) (((-1169 |#2|)) . T)) +((((-794)) -3255 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-563 (-794))) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) (((-1169 |#2|)) . T)) (|has| |#1| (-786)) (|has| |#1| (-786)) ((((-1070) (-51)) . T)) @@ -1079,10 +1079,10 @@ ((((-794)) . T)) ((((-523)) |has| #0=(-383 |#2|) (-585 (-523))) ((#0#) . T)) ((((-523) (-133)) . T)) -((((-523) (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T) ((|#1| |#2|) . T)) +((((-523) (-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T) ((|#1| |#2|) . T)) ((((-383 (-523))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) ((((-794)) . T)) ((((-841 |#1|)) . T)) (|has| |#1| (-339)) @@ -1107,31 +1107,31 @@ ((($) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-158))) -((((-523) (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T) ((|#1| |#2|) . T)) +((((-523) (-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) ((($) |has| |#1| (-515)) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#3|) . T)) (((|#1|) |has| |#1| (-158))) -((((-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((|#1|) |has| |#1| (-158)) (($) -3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840)))) -((($) -3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((((-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((|#1|) |has| |#1| (-158)) (($) -3255 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840)))) +((($) -3255 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (((|#1|) . T)) (((|#1|) . T)) ((((-499)) |has| |#1| (-564 (-499))) (((-823 (-355))) |has| |#1| (-564 (-823 (-355)))) (((-823 (-523))) |has| |#1| (-564 (-823 (-523))))) ((((-794)) . T)) -(((|#2|) . T) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) (|has| |#2| (-784)) (-12 (|has| |#2| (-211)) (|has| |#2| (-973))) (|has| |#1| (-515)) (|has| |#1| (-1063)) ((((-1070) |#1|) . T)) -(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) -(((#0=(-383 (-523)) #0#) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($ $) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) ((|#1| |#1|) . T)) +(-3255 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(((#0=(-383 (-523)) #0#) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($ $) -3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) ((|#1| |#1|) . T)) ((((-383 (-523))) |has| |#1| (-964 (-523))) (((-523)) |has| |#1| (-964 (-523))) (((-1087)) |has| |#1| (-964 (-1087))) ((|#1|) . T)) ((((-523) |#2|) . T)) ((((-383 (-523))) |has| |#1| (-964 (-383 (-523)))) (((-523)) |has| |#1| (-964 (-523))) ((|#1|) . T)) ((((-523)) |has| |#1| (-817 (-523))) (((-355)) |has| |#1| (-817 (-355)))) -((((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) ((|#1|) . T)) +((((-383 (-523))) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) ((|#1|) . T)) (((|#1|) . T)) ((((-589 |#4|)) . T) (((-794)) . T)) ((((-499)) |has| |#4| (-564 (-499)))) @@ -1144,17 +1144,17 @@ (((|#1|) . T)) (((|#2|) . T)) ((((-1087)) |has| (-383 |#2|) (-831 (-1087)))) -(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) #0#) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) #0#) |has| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (-286 (-2 (|:| -2402 |#1|) (|:| -2746 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-794)) -3172 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-563 (-794))) (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-344)) (|has| |#3| (-732)) (|has| |#3| (-784)) (|has| |#3| (-973)) (|has| |#3| (-1016))) (((-1169 |#3|)) . T)) +((((-794)) -3255 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-563 (-794))) (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-344)) (|has| |#3| (-732)) (|has| |#3| (-784)) (|has| |#3| (-973)) (|has| |#3| (-1016))) (((-1169 |#3|)) . T)) ((((-523) |#2|) . T)) -(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) -(((|#2| |#2|) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-973))) (($ $) |has| |#2| (-158))) +(-3255 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(((|#2| |#2|) -3255 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-973))) (($ $) |has| |#2| (-158))) ((((-794)) . T)) ((((-794)) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T) ((|#2|) . T)) ((((-794)) . T)) ((((-794)) . T)) ((((-1070) (-1087) (-523) (-203) (-794)) . T)) @@ -1189,8 +1189,8 @@ (|has| |#1| (-37 (-383 (-523)))) ((((-794)) . T)) ((((-499)) |has| |#1| (-564 (-499)))) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) -(((|#2|) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-973))) (($) |has| |#2| (-158))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +(((|#2|) -3255 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-973))) (($) |has| |#2| (-158))) (|has| $ (-136)) ((((-383 |#2|)) . T)) ((((-383 (-523))) |has| #0=(-383 |#2|) (-964 (-383 (-523)))) (((-523)) |has| #0# (-964 (-523))) ((#0#) . T)) @@ -1201,11 +1201,11 @@ (((|#3|) |has| |#3| (-158))) (|has| |#1| (-136)) (|has| |#1| (-134)) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-344))) (|has| |#1| (-136)) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-344))) (|has| |#1| (-136)) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-344))) (|has| |#1| (-136)) (((|#1|) . T)) (((|#2|) . T)) @@ -1236,7 +1236,7 @@ ((((-927 |#1|)) . T) ((|#1|) . T)) ((((-794)) . T)) ((((-794)) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) ((((-383 (-523))) . T) (((-383 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1083 |#1|)) . T)) ((((-523)) . T) (($) . T) (((-383 (-523))) . T)) @@ -1244,9 +1244,9 @@ (|has| |#1| (-786)) (((|#2|) . T)) ((((-523)) . T) (($) . T) (((-383 (-523))) . T)) -((((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) +((((-2 (|:| -2402 (-1070)) (|:| -2746 |#1|))) . T)) ((((-523) |#2|) . T)) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) (((|#2|) . T)) ((((-523) |#3|) . T)) (((|#2|) . T)) @@ -1261,7 +1261,7 @@ (((|#3|) -12 (|has| |#3| (-286 |#3|)) (|has| |#3| (-1016)))) (((|#2|) . T)) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) #0#) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) #0#) |has| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (-286 (-2 (|:| -2402 |#1|) (|:| -2746 |#2|))))) (((|#2| |#2|) . T)) (|has| |#2| (-339)) (((|#2|) . T) (((-523)) |has| |#2| (-964 (-523))) (((-383 (-523))) |has| |#2| (-964 (-383 (-523))))) @@ -1291,19 +1291,19 @@ (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#1| |#2|) . T)) ((((-523) (-133)) . T)) -(((#0=(-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) #0#) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) -((($) -3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +(((#0=(-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) #0#) |has| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (-286 (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) +((($) -3255 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (|has| |#1| (-786)) (((|#2| (-710) (-1001)) . T)) (((|#1| |#2|) . T)) -(-3172 (|has| |#1| (-158)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-158)) (|has| |#1| (-515))) (|has| |#1| (-730)) (((|#1|) |has| |#1| (-158))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-3172 (|has| |#1| (-136)) (-12 (|has| |#1| (-339)) (|has| |#2| (-136)))) -(-3172 (|has| |#1| (-134)) (-12 (|has| |#1| (-339)) (|has| |#2| (-134)))) +(-3255 (|has| |#1| (-136)) (-12 (|has| |#1| (-339)) (|has| |#2| (-136)))) +(-3255 (|has| |#1| (-134)) (-12 (|has| |#1| (-339)) (|has| |#2| (-134)))) (((|#4|) . T)) (|has| |#1| (-134)) ((((-1070) |#1|) . T)) @@ -1316,10 +1316,10 @@ (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#3|) . T)) ((((-1161 |#1| |#2| |#3|)) |has| |#1| (-339))) -(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3255 (|has| |#1| (-786)) (|has| |#1| (-1016))) (((|#1|) . T)) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016))) (((-888 |#1|)) . T)) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016))) (((-888 |#1|)) . T)) (|has| |#1| (-784)) (|has| |#1| (-784)) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) @@ -1332,8 +1332,8 @@ ((($) . T)) ((((-364) (-1070)) . T)) ((($) |has| |#1| (-515)) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) -((((-794)) -3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-563 (-794))) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) (((-1169 |#2|)) . T)) -(((#0=(-51)) . T) (((-2 (|:| -3772 (-1070)) (|:| -2482 #0#))) . T)) +((((-794)) -3255 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-563 (-794))) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) (((-1169 |#2|)) . T)) +(((#0=(-51)) . T) (((-2 (|:| -2402 (-1070)) (|:| -2746 #0#))) . T)) (((|#1|) . T)) ((((-794)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) @@ -1341,7 +1341,7 @@ (|has| |#2| (-134)) (|has| |#2| (-136)) (|has| |#1| (-448)) -(-3172 (|has| |#1| (-448)) (|has| |#1| (-666)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) +(-3255 (|has| |#1| (-448)) (|has| |#1| (-666)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) (|has| |#1| (-339)) ((((-794)) . T)) (|has| |#1| (-37 (-383 (-523)))) @@ -1350,8 +1350,8 @@ (|has| |#1| (-784)) (|has| |#1| (-784)) ((((-794)) . T)) -((((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3172 (|has| |#1| (-339)) (|has| |#1| (-515))) (((-1161 |#1| |#2| |#3|)) |has| |#1| (-339)) ((|#1|) |has| |#1| (-158))) -(((|#1|) |has| |#1| (-158)) (((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3172 (|has| |#1| (-339)) (|has| |#1| (-515)))) +((((-383 (-523))) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3255 (|has| |#1| (-339)) (|has| |#1| (-515))) (((-1161 |#1| |#2| |#3|)) |has| |#1| (-339)) ((|#1|) |has| |#1| (-158))) +(((|#1|) |has| |#1| (-158)) (((-383 (-523))) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3255 (|has| |#1| (-339)) (|has| |#1| (-515)))) ((($) |has| |#1| (-515)) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (((|#1| |#2|) . T)) ((((-1087)) |has| |#1| (-831 (-1087)))) @@ -1359,7 +1359,7 @@ ((((-794)) . T)) ((((-794)) . T)) (|has| |#1| (-1016)) -(((|#2| (-456 (-2810 |#1|) (-710)) (-796 |#1|)) . T)) +(((|#2| (-456 (-1271 |#1|) (-710)) (-796 |#1|)) . T)) ((((-383 (-523))) . #0=(|has| |#2| (-339))) (($) . #0#)) (((|#1| (-495 (-1087)) (-1087)) . T)) (((|#1|) . T)) @@ -1379,16 +1379,16 @@ (|has| |#1| (-136)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) -((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) . T)) +(((|#1|) . T) (((-2 (|:| -2402 (-1070)) (|:| -2746 |#1|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) +((((-2 (|:| -2402 (-1087)) (|:| -2746 (-51)))) . T)) ((((-1085 |#1| |#2| |#3|)) |has| |#1| (-339))) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) ((((-1087) (-51)) . T)) ((($ $) . T)) (((|#1| (-523)) . T)) ((((-841 |#1|)) . T)) -(((|#1|) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-973))) (($) -3172 (|has| |#1| (-831 (-1087))) (|has| |#1| (-973)))) +(((|#1|) -3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-973))) (($) -3255 (|has| |#1| (-831 (-1087))) (|has| |#1| (-973)))) (((|#1|) . T) (((-523)) |has| |#1| (-964 (-523))) (((-383 (-523))) |has| |#1| (-964 (-383 (-523))))) (|has| |#1| (-786)) (|has| |#1| (-786)) @@ -1403,13 +1403,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-286 |#4|)) (|has| |#4| (-1016)))) (((|#1|) |has| |#1| (-158))) (((|#4| |#4|) -12 (|has| |#4| (-286 |#4|)) (|has| |#4| (-1016)))) -(((|#3|) -3172 (|has| |#3| (-158)) (|has| |#3| (-339)))) +(((|#3|) -3255 (|has| |#3| (-158)) (|has| |#3| (-339)))) (|has| |#2| (-786)) (|has| |#1| (-786)) -(-3172 (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-840))) +(-3255 (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-840))) ((($ $) . T) ((#0=(-383 (-523)) #0#) . T)) ((((-523) |#2|) . T)) -(((|#2|) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)))) +(((|#2|) -3255 (|has| |#2| (-158)) (|has| |#2| (-339)))) (|has| |#1| (-325)) (((|#3| |#3|) -12 (|has| |#3| (-286 |#3|)) (|has| |#3| (-1016)))) ((($) . T) (((-383 (-523))) . T)) @@ -1417,7 +1417,7 @@ (|has| |#1| (-759)) (|has| |#1| (-759)) (((|#1|) . T)) -(-3172 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3255 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325))) (|has| |#1| (-784)) (|has| |#1| (-784)) (|has| |#1| (-784)) @@ -1426,13 +1426,13 @@ ((((-523)) . T) (($) . T) (((-383 (-523))) . T)) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-325))) (|has| |#1| (-37 (-383 (-523)))) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) ((((-1087)) |has| |#1| (-831 (-1087))) (((-1001)) . T)) (((|#1|) . T)) (|has| |#1| (-784)) -(((#0=(-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) #0#) |has| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (-286 (-2 (|:| -3772 (-1070)) (|:| -2482 (-51)))))) +(((#0=(-2 (|:| -2402 (-1070)) (|:| -2746 (-51))) #0#) |has| (-2 (|:| -2402 (-1070)) (|:| -2746 (-51))) (-286 (-2 (|:| -2402 (-1070)) (|:| -2746 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (|has| |#1| (-1016)) (((|#1|) . T)) @@ -1450,7 +1450,7 @@ (((|#1|) . T)) ((((-133)) . T)) (((|#2|) |has| |#2| (-158))) -(-3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) +(-3255 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) (((|#1|) . T)) (|has| |#1| (-134)) (|has| |#1| (-136)) @@ -1472,32 +1472,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016))) ((#0=(-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) #0#) |has| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (-286 (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))))) -(-3172 (|has| |#2| (-427)) (|has| |#2| (-840))) -(-3172 (|has| |#1| (-427)) (|has| |#1| (-840))) +(((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016))) ((#0=(-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) #0#) |has| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (-286 (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|))))) +(-3255 (|has| |#2| (-427)) (|has| |#2| (-840))) +(-3255 (|has| |#1| (-427)) (|has| |#1| (-840))) (((|#1|) . T) (($) . T)) (((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) (((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(((|#3|) -3172 (|has| |#3| (-158)) (|has| |#3| (-339)))) +(((|#3|) -3255 (|has| |#3| (-158)) (|has| |#3| (-339)))) (|has| |#1| (-786)) (|has| |#1| (-515)) ((((-536 |#1|)) . T)) ((($) . T)) (((|#2|) . T)) -(-3172 (-12 (|has| |#1| (-339)) (|has| |#2| (-759))) (-12 (|has| |#1| (-339)) (|has| |#2| (-786)))) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (-12 (|has| |#1| (-339)) (|has| |#2| (-759))) (-12 (|has| |#1| (-339)) (|has| |#2| (-786)))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-515))) ((((-841 |#1|)) . T)) (((|#1| (-467 |#1| |#3|) (-467 |#1| |#2|)) . T)) (((|#1| |#4| |#5|) . T)) (((|#1| (-710)) . T)) ((((-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((|#1|) |has| |#1| (-158)) (($) |has| |#1| (-515))) -((((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3172 (|has| |#1| (-339)) (|has| |#1| (-515))) (((-1085 |#1| |#2| |#3|)) |has| |#1| (-339)) ((|#1|) |has| |#1| (-158))) -(((|#1|) |has| |#1| (-158)) (((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3172 (|has| |#1| (-339)) (|has| |#1| (-515)))) +((((-383 (-523))) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3255 (|has| |#1| (-339)) (|has| |#1| (-515))) (((-1085 |#1| |#2| |#3|)) |has| |#1| (-339)) ((|#1|) |has| |#1| (-158))) +(((|#1|) |has| |#1| (-158)) (((-383 (-523))) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3255 (|has| |#1| (-339)) (|has| |#1| (-515)))) ((($) |has| |#1| (-515)) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) -((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) . T)) +((((-2 (|:| -2402 (-1087)) (|:| -2746 (-51)))) . T)) ((((-383 |#2|)) . T) (((-383 (-523))) . T) (($) . T)) ((((-614 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1505,17 +1505,17 @@ ((((-794)) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) ((((-794)) . T)) -((((-383 (-523))) |has| |#2| (-37 (-383 (-523)))) ((|#2|) |has| |#2| (-158)) (($) -3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) +((((-383 (-523))) |has| |#2| (-37 (-383 (-523)))) ((|#2|) |has| |#2| (-158)) (($) -3255 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) ((((-794)) . T)) ((((-794)) . T)) ((((-794)) . T)) (((|#2|) . T)) -(-3172 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-344)) (|has| |#3| (-732)) (|has| |#3| (-784)) (|has| |#3| (-973)) (|has| |#3| (-1016))) -(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3255 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-344)) (|has| |#3| (-732)) (|has| |#3| (-784)) (|has| |#3| (-973)) (|has| |#3| (-1016))) +(-3255 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) ((((-383 (-523))) |has| |#1| (-964 (-383 (-523)))) (((-523)) |has| |#1| (-964 (-523))) ((|#1|) . T)) (|has| |#1| (-1109)) (|has| |#1| (-1109)) -(-3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) +(-3255 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) (|has| |#1| (-1109)) (|has| |#1| (-1109)) (((|#3| |#3|) . T)) @@ -1528,43 +1528,43 @@ (((|#1|) . T) (((-383 (-523))) . T) (($) . T)) ((((-1070) (-51)) . T)) (|has| |#1| (-1016)) -(-3172 (|has| |#2| (-759)) (|has| |#2| (-786))) +(-3255 (|has| |#2| (-759)) (|has| |#2| (-786))) (((|#1|) . T)) -((($) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) (((-383 (-523))) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) +((($) -3255 (|has| |#1| (-339)) (|has| |#1| (-325))) (((-383 (-523))) -3255 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) (((|#1|) |has| |#1| (-158)) (($) . T)) ((($) . T)) ((((-1085 |#1| |#2| |#3|)) -12 (|has| (-1085 |#1| |#2| |#3|) (-286 (-1085 |#1| |#2| |#3|))) (|has| |#1| (-339)))) ((((-794)) . T)) -(-3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +(-3255 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) ((($) . T)) -(-3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3255 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) ((((-794)) . T)) -(-3172 (|has| |#1| (-427)) (|has| |#1| (-840))) +(-3255 (|has| |#1| (-427)) (|has| |#1| (-840))) (|has| |#2| (-840)) (|has| |#1| (-339)) (((|#2|) |has| |#2| (-1016))) -(-3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3255 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((($) . T) ((|#2|) . T)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-840))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-840))) (|has| |#1| (-840)) (|has| |#1| (-840)) ((((-499)) . T) (((-383 (-1083 (-523)))) . T) (((-203)) . T) (((-355)) . T)) ((((-355)) . T) (((-203)) . T) (((-794)) . T)) (|has| |#1| (-840)) -(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3255 (|has| |#1| (-786)) (|has| |#1| (-1016))) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) ((($ $) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) ((($ $) . T)) ((((-523) (-108)) . T)) ((($) . T)) (((|#1|) . T)) ((((-523)) . T)) ((((-108)) . T)) -(-3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) (|has| |#1| (-37 (-383 (-523)))) (((|#1| (-523)) . T)) ((($) . T)) @@ -1586,7 +1586,7 @@ (((|#1| (-1133 |#1| |#2| |#3|)) . T)) (((|#1| (-710)) . T)) (((|#1|) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) ((((-794)) . T)) (|has| |#1| (-1016)) ((((-1070) |#1|) . T)) @@ -1606,18 +1606,18 @@ (((|#1|) . T)) ((((-523)) . T)) ((((-794)) . T)) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-325))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-325))) ((((-794)) . T)) (|has| |#1| (-136)) (((|#3|) . T)) -(-3172 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) +(-3255 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) ((((-794)) . T)) ((((-1154 |#2| |#3| |#4|)) . T) (((-1155 |#1| |#2| |#3| |#4|)) . T)) ((((-794)) . T)) -((((-47)) -12 (|has| |#1| (-515)) (|has| |#1| (-964 (-523)))) (((-562 $)) . T) ((|#1|) . T) (((-523)) |has| |#1| (-964 (-523))) (((-383 (-523))) -3172 (-12 (|has| |#1| (-515)) (|has| |#1| (-964 (-523)))) (|has| |#1| (-964 (-383 (-523))))) (((-383 (-883 |#1|))) |has| |#1| (-515)) (((-883 |#1|)) |has| |#1| (-973)) (((-1087)) . T)) +((((-47)) -12 (|has| |#1| (-515)) (|has| |#1| (-964 (-523)))) (((-562 $)) . T) ((|#1|) . T) (((-523)) |has| |#1| (-964 (-523))) (((-383 (-523))) -3255 (-12 (|has| |#1| (-515)) (|has| |#1| (-964 (-523)))) (|has| |#1| (-964 (-383 (-523))))) (((-383 (-883 |#1|))) |has| |#1| (-515)) (((-883 |#1|)) |has| |#1| (-973)) (((-1087)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-710)) . T)) -((($) -3172 (|has| |#1| (-339)) (|has| |#1| (-515))) (((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) ((|#1|) |has| |#1| (-158))) +((($) -3255 (|has| |#1| (-339)) (|has| |#1| (-515))) (((-383 (-523))) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) ((|#1|) |has| |#1| (-158))) (((|#1|) |has| |#1| (-286 |#1|))) ((((-1155 |#1| |#2| |#3| |#4|)) . T)) ((((-523)) |has| |#1| (-817 (-523))) (((-355)) |has| |#1| (-817 (-355)))) @@ -1625,14 +1625,14 @@ (|has| |#1| (-515)) (((|#1|) . T)) ((((-794)) . T)) -(((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) +(((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) (((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) |has| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (-286 (-2 (|:| -2402 |#1|) (|:| -2746 |#2|))))) (((|#1|) |has| |#1| (-158))) ((($) |has| |#1| (-515)) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) (((|#1|) . T)) (((|#3|) |has| |#3| (-1016))) -(((|#2|) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)))) +(((|#2|) -3255 (|has| |#2| (-158)) (|has| |#2| (-339)))) ((((-1154 |#2| |#3| |#4|)) . T)) ((((-108)) . T)) (|has| |#1| (-759)) @@ -1642,8 +1642,8 @@ (|has| |#1| (-784)) (|has| |#1| (-784)) (((|#1| (-523) (-1001)) . T)) -(-3172 (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +(-3255 (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) (((|#1| (-383 (-523)) (-1001)) . T)) (((|#1| (-710) (-1001)) . T)) (|has| |#1| (-786)) @@ -1659,28 +1659,28 @@ (((|#1|) . T)) (|has| |#1| (-1016)) ((((-523)) -12 (|has| |#1| (-339)) (|has| |#2| (-585 (-523)))) ((|#2|) |has| |#1| (-339))) -(-3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) +(-3255 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) (((|#2|) |has| |#2| (-158))) (((|#1|) |has| |#1| (-158))) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) -((((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) +((((-2 (|:| -2402 (-1070)) (|:| -2746 |#1|))) . T)) ((((-794)) . T)) (|has| |#3| (-784)) ((((-794)) . T)) ((((-1154 |#2| |#3| |#4|) (-295 |#2| |#3| |#4|)) . T)) ((((-794)) . T)) -(((|#1| |#1|) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-973)))) +(((|#1| |#1|) -3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-973)))) (((|#1|) . T)) ((((-523)) . T)) ((((-523)) . T)) -(((|#1|) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-973)))) +(((|#1|) -3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-973)))) (((|#2|) |has| |#2| (-339))) ((($) . T) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-339))) (|has| |#1| (-786)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) |has| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (-286 (-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))))) -(-3172 (|has| |#1| (-427)) (|has| |#1| (-840))) +((((-2 (|:| -2402 (-1087)) (|:| -2746 (-51)))) |has| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (-286 (-2 (|:| -2402 (-1087)) (|:| -2746 (-51)))))) +(-3255 (|has| |#1| (-427)) (|has| |#1| (-840))) (((|#2|) . T) (((-523)) |has| |#2| (-585 (-523)))) ((((-794)) . T)) ((((-794)) . T)) @@ -1714,18 +1714,18 @@ (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) (((|#1|) . T)) -(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3255 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) (((|#1| |#1|) . T) ((#0=(-383 (-523)) #0#) . T) (($ $) . T)) ((((-794)) . T)) (((|#1|) . T) (((-383 (-523))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) (|has| |#1| (-339)) (|has| |#1| (-339)) (|has| (-383 |#2|) (-211)) (|has| |#1| (-840)) (((|#2|) |has| |#2| (-973))) -(((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) +(((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) (((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) |has| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (-286 (-2 (|:| -2402 |#1|) (|:| -2746 |#2|))))) (|has| |#1| (-339)) (((|#1|) |has| |#1| (-158))) (((|#1| |#1|) . T)) @@ -1750,7 +1750,7 @@ (((|#1| (-383 (-523)) (-1001)) . T)) (((|#1| (-710) (-1001)) . T)) (((#0=(-383 |#2|) #0#) . T) ((#1=(-383 (-523)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-523)) -3172 (|has| (-383 (-523)) (-964 (-523))) (|has| |#1| (-964 (-523)))) (((-383 (-523))) . T)) +(((|#1|) . T) (((-523)) -3255 (|has| (-383 (-523)) (-964 (-523))) (|has| |#1| (-964 (-523)))) (((-383 (-523))) . T)) (((|#1| (-554 |#1| |#3|) (-554 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-158))) (((|#1|) . T)) @@ -1769,24 +1769,24 @@ ((((-638)) . T)) (((|#2|) |has| |#2| (-158))) (|has| |#2| (-784)) -((((-108)) |has| |#1| (-1016)) (((-794)) -3172 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-448)) (|has| |#1| (-666)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973)) (|has| |#1| (-1028)) (|has| |#1| (-1016)))) +((((-108)) |has| |#1| (-1016)) (((-794)) -3255 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-448)) (|has| |#1| (-666)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973)) (|has| |#1| (-1028)) (|has| |#1| (-1016)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3772 (-1070)) (|:| -2482 (-51)))) . T)) +((((-2 (|:| -2402 (-1070)) (|:| -2746 (-51)))) . T)) ((((-794)) . T)) ((((-523) |#1|) . T)) ((((-638)) . T) (((-383 (-523))) . T) (((-523)) . T)) (((|#1| |#1|) |has| |#1| (-158))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) +(((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) (((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) |has| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (-286 (-2 (|:| -2402 |#1|) (|:| -2746 |#2|))))) ((((-355)) . T)) ((((-638)) . T)) ((((-383 (-523))) . #0=(|has| |#2| (-339))) (($) . #0#)) (((|#1|) |has| |#1| (-158))) ((((-383 (-883 |#1|))) . T)) (((|#2| |#2|) . T)) -(-3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) -(-3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3255 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +(-3255 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) (((|#2|) . T)) (|has| |#2| (-786)) (((|#3|) |has| |#3| (-973))) @@ -1796,14 +1796,14 @@ (|has| |#1| (-786)) ((((-1087)) |has| |#2| (-831 (-1087)))) ((((-794)) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) ((((-383 (-523))) . T) (($) . T)) (|has| |#1| (-448)) (|has| |#1| (-344)) (|has| |#1| (-344)) (|has| |#1| (-344)) (|has| |#1| (-339)) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-448)) (|has| |#1| (-515)) (|has| |#1| (-973)) (|has| |#1| (-1028))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-448)) (|has| |#1| (-515)) (|has| |#1| (-973)) (|has| |#1| (-1028))) (|has| |#1| (-37 (-383 (-523)))) ((((-112 |#1|)) . T)) ((((-112 |#1|)) . T)) @@ -1824,11 +1824,11 @@ (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-786)) -((((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) +((((-2 (|:| -2402 (-1070)) (|:| -2746 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-136)) (|has| |#1| (-134)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)))) ((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) |has| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (-286 (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)))) ((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) (((|#2|) . T)) (((|#3|) . T)) ((((-112 |#1|)) . T)) @@ -1846,11 +1846,11 @@ ((((-499)) |has| |#1| (-564 (-499))) (((-823 (-523))) |has| |#1| (-564 (-823 (-523)))) (((-823 (-355))) |has| |#1| (-564 (-823 (-355)))) (((-355)) . #0=(|has| |#1| (-949))) (((-203)) . #0#)) (((|#1|) |has| |#1| (-339))) ((((-794)) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) ((($ $) . T) (((-562 $) $) . T)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-515))) ((($) . T) (((-1155 |#1| |#2| |#3| |#4|)) . T) (((-383 (-523))) . T)) -((($) -3172 (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-515)) (|has| |#1| (-973))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-515))) +((($) -3255 (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-515)) (|has| |#1| (-973))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-515))) (|has| |#1| (-339)) (|has| |#1| (-339)) (|has| |#1| (-339)) @@ -1861,11 +1861,11 @@ ((((-355)) . T)) (((|#3|) -12 (|has| |#3| (-286 |#3|)) (|has| |#3| (-1016)))) ((((-794)) . T)) -(-3172 (|has| |#2| (-427)) (|has| |#2| (-840))) +(-3255 (|has| |#2| (-427)) (|has| |#2| (-840))) (((|#1|) . T)) (|has| |#1| (-786)) (|has| |#1| (-786)) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) ((((-499)) |has| |#1| (-564 (-499)))) (((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) (|has| |#1| (-1016)) @@ -1874,13 +1874,13 @@ (|has| |#1| (-134)) (|has| |#1| (-136)) ((((-523)) . T)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-515))) (((#0=(-1154 |#2| |#3| |#4|)) . T) (((-383 (-523))) |has| #0# (-37 (-383 (-523)))) (($) . T)) ((((-523)) . T)) (|has| |#1| (-339)) -(-3172 (-12 (|has| (-1161 |#1| |#2| |#3|) (-136)) (|has| |#1| (-339))) (|has| |#1| (-136))) -(-3172 (-12 (|has| (-1161 |#1| |#2| |#3|) (-134)) (|has| |#1| (-339))) (|has| |#1| (-134))) +(-3255 (-12 (|has| (-1161 |#1| |#2| |#3|) (-136)) (|has| |#1| (-339))) (|has| |#1| (-136))) +(-3255 (-12 (|has| (-1161 |#1| |#2| |#3|) (-134)) (|has| |#1| (-339))) (|has| |#1| (-134))) (|has| |#1| (-339)) (|has| |#1| (-134)) (|has| |#1| (-136)) @@ -1897,18 +1897,18 @@ (((|#1| |#2|) . T)) (((|#1|) . T) (((-523)) |has| |#1| (-585 (-523)))) (((|#3|) |has| |#3| (-158))) -(-3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) +(-3255 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) ((((-523)) . T)) (((|#1| $) |has| |#1| (-263 |#1| |#1|))) ((((-383 (-523))) . T) (($) . T) (((-383 |#1|)) . T) ((|#1|) . T)) ((((-794)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -3172 (|has| |#1| (-267)) (|has| |#1| (-339))) ((#0=(-383 (-523)) #0#) |has| |#1| (-339))) -((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) . T)) +(((|#1| |#1|) . T) (($ $) -3255 (|has| |#1| (-267)) (|has| |#1| (-339))) ((#0=(-383 (-523)) #0#) |has| |#1| (-339))) +((((-2 (|:| -2402 (-1087)) (|:| -2746 (-51)))) . T)) ((($) . T)) ((((-523) |#1|) . T)) ((((-1087)) |has| (-383 |#2|) (-831 (-1087)))) -(((|#1|) . T) (($) -3172 (|has| |#1| (-267)) (|has| |#1| (-339))) (((-383 (-523))) |has| |#1| (-339))) +(((|#1|) . T) (($) -3255 (|has| |#1| (-267)) (|has| |#1| (-339))) (((-383 (-523))) |has| |#1| (-339))) ((((-499)) |has| |#2| (-564 (-499)))) ((((-629 |#2|)) . T) (((-794)) . T)) (((|#1|) . T)) @@ -1916,8 +1916,8 @@ (((|#4|) -12 (|has| |#4| (-286 |#4|)) (|has| |#4| (-1016)))) ((((-801 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) -(-3172 (|has| |#4| (-732)) (|has| |#4| (-784))) -(-3172 (|has| |#3| (-732)) (|has| |#3| (-784))) +(-3255 (|has| |#4| (-732)) (|has| |#4| (-784))) +(-3255 (|has| |#3| (-732)) (|has| |#3| (-784))) ((((-794)) . T)) ((((-794)) . T)) (((|#4|) -12 (|has| |#4| (-286 |#4|)) (|has| |#4| (-1016)))) @@ -1933,17 +1933,17 @@ ((((-383 (-523))) . T) (($) . T)) ((((-383 (-523))) . T) (($) . T)) ((((-383 (-523))) . T) (($) . T)) -(-3172 (|has| |#1| (-427)) (|has| |#1| (-1127))) +(-3255 (|has| |#1| (-427)) (|has| |#1| (-1127))) ((($) . T)) ((((-383 (-523))) |has| #0=(-383 |#2|) (-964 (-383 (-523)))) (((-523)) |has| #0# (-964 (-523))) ((#0#) . T)) (((|#2|) . T) (((-523)) |has| |#2| (-585 (-523)))) (((|#1| (-710)) . T)) (|has| |#1| (-786)) (((|#1|) . T) (((-523)) |has| |#1| (-585 (-523)))) -((($) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) (((-383 (-523))) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) +((($) -3255 (|has| |#1| (-339)) (|has| |#1| (-325))) (((-383 (-523))) -3255 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) ((((-523)) . T)) (|has| |#1| (-37 (-383 (-523)))) -((((-2 (|:| -3772 (-1070)) (|:| -2482 (-51)))) |has| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (-286 (-2 (|:| -3772 (-1070)) (|:| -2482 (-51)))))) +((((-2 (|:| -2402 (-1070)) (|:| -2746 (-51)))) |has| (-2 (|:| -2402 (-1070)) (|:| -2746 (-51))) (-286 (-2 (|:| -2402 (-1070)) (|:| -2746 (-51)))))) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (|has| |#1| (-784)) (|has| |#1| (-37 (-383 (-523)))) @@ -1968,24 +1968,24 @@ (((|#1| |#2|) . T)) ((((-133)) . T)) ((((-719 |#1| (-796 |#2|))) . T)) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) (|has| |#1| (-1109)) (((|#1|) . T)) -(-3172 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-344)) (|has| |#3| (-732)) (|has| |#3| (-784)) (|has| |#3| (-973)) (|has| |#3| (-1016))) +(-3255 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-344)) (|has| |#3| (-732)) (|has| |#3| (-784)) (|has| |#3| (-973)) (|has| |#3| (-1016))) ((((-1087) |#1|) |has| |#1| (-484 (-1087) |#1|))) (((|#2|) . T)) -((($ $) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1| |#1|) . T) ((#0=(-383 (-523)) #0#) |has| |#1| (-37 (-383 (-523))))) -((($) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($ $) -3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1| |#1|) . T) ((#0=(-383 (-523)) #0#) |has| |#1| (-37 (-383 (-523))))) +((($) -3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) ((((-841 |#1|)) . T)) ((($) . T)) ((((-383 (-883 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) ((((-499)) |has| |#4| (-564 (-499)))) ((((-794)) . T) (((-589 |#4|)) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-784)) -(((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016))) (((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) |has| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (-286 (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))))) +(((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016))) (((-2 (|:| -2402 (-1070)) (|:| -2746 |#1|))) |has| (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|)) (-286 (-2 (|:| -2402 (-1070)) (|:| -2746 |#1|))))) (|has| |#1| (-1016)) (|has| |#1| (-339)) (|has| |#1| (-786)) @@ -1993,16 +1993,16 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-383 (-523))) . T)) -((($) -3172 (|has| |#1| (-339)) (|has| |#1| (-515))) (((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) ((|#1|) |has| |#1| (-158))) +((($) -3255 (|has| |#1| (-339)) (|has| |#1| (-515))) (((-383 (-523))) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) ((|#1|) |has| |#1| (-158))) (|has| |#1| (-134)) (|has| |#1| (-136)) -(-3172 (-12 (|has| (-1085 |#1| |#2| |#3|) (-136)) (|has| |#1| (-339))) (|has| |#1| (-136))) -(-3172 (-12 (|has| (-1085 |#1| |#2| |#3|) (-134)) (|has| |#1| (-339))) (|has| |#1| (-134))) +(-3255 (-12 (|has| (-1085 |#1| |#2| |#3|) (-136)) (|has| |#1| (-339))) (|has| |#1| (-136))) +(-3255 (-12 (|has| (-1085 |#1| |#2| |#3|) (-134)) (|has| |#1| (-339))) (|has| |#1| (-134))) (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-136)) (|has| |#1| (-134)) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) ((((-1161 |#1| |#2| |#3|)) |has| |#1| (-339))) (|has| |#1| (-784)) (((|#1| |#2|) . T)) @@ -2025,9 +2025,9 @@ ((((-794)) . T)) ((((-794)) . T)) ((((-499)) |has| |#1| (-564 (-499)))) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) ((((-1087) |#1|) |has| |#1| (-484 (-1087) |#1|)) ((|#1| |#1|) |has| |#1| (-286 |#1|))) -(((|#1|) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)))) +(((|#1|) -3255 (|has| |#1| (-158)) (|has| |#1| (-339)))) ((((-292 |#1|)) . T)) (((|#2|) |has| |#2| (-339))) (((|#2|) . T)) @@ -2048,14 +2048,14 @@ (|has| |#1| (-134)) (|has| |#1| (-136)) ((($ $) . T)) -(-3172 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-448)) (|has| |#1| (-666)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973)) (|has| |#1| (-1028)) (|has| |#1| (-1016))) +(-3255 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-448)) (|has| |#1| (-666)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973)) (|has| |#1| (-1028)) (|has| |#1| (-1016))) (|has| |#1| (-515)) (((|#2|) . T)) ((((-523)) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-515)) (|has| |#1| (-973))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-515)) (|has| |#1| (-973))) ((((-536 |#1|)) . T)) ((($) . T)) (((|#1| (-57 |#1|) (-57 |#1|)) . T)) @@ -2080,12 +2080,12 @@ (((|#1| |#2|) . T)) ((((-1087) |#1|) . T)) (((|#4|) . T)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-325))) ((((-1087) (-51)) . T)) ((((-1154 |#2| |#3| |#4|) (-295 |#2| |#3| |#4|)) . T)) ((((-383 (-523))) |has| |#1| (-964 (-383 (-523)))) (((-523)) |has| |#1| (-964 (-523))) ((|#1|) . T)) ((((-794)) . T)) -(-3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) +(-3255 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) (((#0=(-1155 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-383 (-523)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-158)) ((#0=(-383 (-523)) #0#) |has| |#1| (-515)) (($ $) |has| |#1| (-515))) (((|#1|) . T) (($) . T) (((-383 (-523))) . T)) @@ -2104,14 +2104,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) (((|#2| |#3|) . T)) -(-3172 (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +(-3255 (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) (((|#1| (-495 |#2|)) . T)) (((|#1| (-710)) . T)) (((|#1| (-495 (-1006 (-1087)))) . T)) (((|#1|) |has| |#1| (-158))) (((|#1|) . T)) (|has| |#2| (-840)) -(-3172 (|has| |#2| (-732)) (|has| |#2| (-784))) +(-3255 (|has| |#2| (-732)) (|has| |#2| (-784))) ((((-794)) . T)) ((($ $) . T) ((#0=(-1154 |#2| |#3| |#4|) #0#) . T) ((#1=(-383 (-523)) #1#) |has| #0# (-37 (-383 (-523))))) ((((-841 |#1|)) . T)) @@ -2120,13 +2120,13 @@ ((($) . T)) ((($) . T)) (|has| |#1| (-339)) -(-3172 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325)) (|has| |#1| (-515))) (|has| |#1| (-339)) ((($) . T) ((#0=(-1154 |#2| |#3| |#4|)) . T) (((-383 (-523))) |has| #0# (-37 (-383 (-523))))) (((|#1| |#2|) . T)) ((((-1085 |#1| |#2| |#3|)) |has| |#1| (-339))) -(-3172 (-12 (|has| |#1| (-284)) (|has| |#1| (-840))) (|has| |#1| (-339)) (|has| |#1| (-325))) -(-3172 (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) +(-3255 (-12 (|has| |#1| (-284)) (|has| |#1| (-840))) (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3255 (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) ((((-523)) |has| |#1| (-585 (-523))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-794)) . T)) @@ -2158,27 +2158,27 @@ (((|#1|) |has| |#1| (-158))) ((((-794)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-286 |#4|)) (|has| |#4| (-1016)))) -(((|#2|) -3172 (|has| |#2| (-6 (-4250 "*"))) (|has| |#2| (-158)))) -(-3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) -(-3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(((|#2|) -3255 (|has| |#2| (-6 (-4250 "*"))) (|has| |#2| (-158)))) +(-3255 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +(-3255 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) (|has| |#2| (-786)) (|has| |#2| (-840)) (|has| |#1| (-840)) (((|#2|) |has| |#2| (-158))) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) ((((-1161 |#1| |#2| |#3|)) |has| |#1| (-339))) ((((-794)) . T)) ((((-794)) . T)) ((((-499)) . T) (((-523)) . T) (((-823 (-523))) . T) (((-355)) . T) (((-203)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) -((((-2 (|:| -3772 (-1070)) (|:| -2482 (-51)))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) +((((-2 (|:| -2402 (-1070)) (|:| -2746 (-51)))) . T)) (((|#1|) . T)) ((((-794)) . T)) (((|#1| |#2|) . T)) (((|#1| (-383 (-523))) . T)) (((|#1|) . T)) -(-3172 (|has| |#1| (-267)) (|has| |#1| (-339))) +(-3255 (|has| |#1| (-267)) (|has| |#1| (-339))) ((((-133)) . T)) ((((-383 |#2|)) . T) (((-383 (-523))) . T) (($) . T)) (|has| |#1| (-784)) @@ -2193,7 +2193,7 @@ ((((-383 (-523))) . T) (($) . T)) ((((-794)) . T)) ((((-794)) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-794)) . T)) ((((-794)) . T)) @@ -2204,7 +2204,7 @@ (((|#1|) . T)) ((((-589 (-133))) . T) (((-1070)) . T)) ((((-794)) . T)) -((((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) +((((-2 (|:| -2402 (-1070)) (|:| -2746 |#1|))) . T)) ((((-1087) |#1|) |has| |#1| (-484 (-1087) |#1|)) ((|#1| |#1|) |has| |#1| (-286 |#1|))) (|has| |#1| (-786)) ((((-794)) . T)) @@ -2216,16 +2216,16 @@ ((((-794)) . T) (((-589 |#4|)) . T)) (((|#2|) . T)) ((((-841 |#1|)) . T) (((-383 (-523))) . T) (($) . T)) -(-3172 (|has| |#4| (-158)) (|has| |#4| (-784)) (|has| |#4| (-973))) -(-3172 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) +(-3255 (|has| |#4| (-158)) (|has| |#4| (-784)) (|has| |#4| (-973))) +(-3255 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) ((((-1087) (-51)) . T)) -(-3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3255 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) -(-3172 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3255 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3255 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-784)) (|has| |#2| (-973))) (|has| |#1| (-840)) (|has| |#1| (-840)) (((|#2|) . T)) @@ -2240,12 +2240,12 @@ (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) (|has| |#1| (-759)) (((#0=(-841 |#1|) #0#) . T) (($ $) . T) ((#1=(-383 (-523)) #1#) . T)) ((((-383 |#2|)) . T)) (|has| |#1| (-784)) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) (((|#1| |#1|) . T) ((#0=(-383 (-523)) #0#) . T) ((#1=(-523) #1#) . T) (($ $) . T)) ((((-841 |#1|)) . T) (($) . T) (((-383 (-523))) . T)) (((|#2|) |has| |#2| (-973)) (((-523)) -12 (|has| |#2| (-585 (-523))) (|has| |#2| (-973)))) @@ -2255,25 +2255,25 @@ (|has| |#1| (-134)) (((|#2|) . T)) ((((-794)) . T)) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) -((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) . T)) -(((#0=(-51)) . T) (((-2 (|:| -3772 (-1087)) (|:| -2482 #0#))) . T)) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-344))) +((((-2 (|:| -2402 (-1087)) (|:| -2746 (-51)))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -2402 (-1087)) (|:| -2746 #0#))) . T)) (|has| |#1| (-325)) ((((-523)) . T)) ((((-794)) . T)) (((#0=(-1155 |#1| |#2| |#3| |#4|) $) |has| #0# (-263 #0# #0#))) (|has| |#1| (-339)) (((#0=(-1001) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-325))) (((#0=(-383 (-523)) #0#) . T) ((#1=(-638) #1#) . T) (($ $) . T)) ((((-292 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-383 (-523))) |has| |#1| (-339))) (|has| |#1| (-1016)) (((|#1|) . T)) -(((|#1|) -3172 (|has| |#2| (-343 |#1|)) (|has| |#2| (-393 |#1|)))) -(((|#1|) -3172 (|has| |#2| (-343 |#1|)) (|has| |#2| (-393 |#1|)))) +(((|#1|) -3255 (|has| |#2| (-343 |#1|)) (|has| |#2| (-393 |#1|)))) +(((|#1|) -3255 (|has| |#2| (-343 |#1|)) (|has| |#2| (-393 |#1|)))) (((|#2|) . T)) ((((-383 (-523))) . T) (((-638)) . T) (($) . T)) (((|#3| |#3|) . T)) @@ -2292,7 +2292,7 @@ (((|#2|) . T)) (((|#1|) . T)) ((((-523)) . T)) -(-3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) (((|#2|) . T) (((-523)) |has| |#2| (-585 (-523)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2329,7 +2329,7 @@ (|has| |#2| (-949)) ((($) . T)) (|has| |#1| (-840)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2337,24 +2337,24 @@ ((($) . T)) (|has| |#1| (-339)) ((((-841 |#1|)) . T)) -((($) -3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($) -3255 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) ((($ $) . T) ((#0=(-383 (-523)) #0#) . T)) -(-3172 (|has| |#1| (-344)) (|has| |#1| (-786))) +(-3255 (|has| |#1| (-344)) (|has| |#1| (-786))) (((|#1|) . T)) ((((-794)) . T)) ((((-1087)) -12 (|has| |#1| (-15 * (|#1| (-383 (-523)) |#1|))) (|has| |#1| (-831 (-1087))))) ((((-383 |#2|) |#3|) . T)) ((($) . T) (((-383 (-523))) . T)) ((((-710) |#1|) . T)) -(((|#2| (-218 (-2810 |#1|) (-710))) . T)) +(((|#2| (-218 (-1271 |#1|) (-710))) . T)) (((|#1| (-495 |#3|)) . T)) ((((-383 (-523))) . T)) -(-3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3255 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((((-794)) . T)) -(((#0=(-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) #0#) |has| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (-286 (-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))))) +(((#0=(-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) #0#) |has| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (-286 (-2 (|:| -2402 (-1087)) (|:| -2746 (-51)))))) (|has| |#1| (-840)) (|has| |#2| (-339)) -(-3172 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3255 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) ((((-155 (-355))) . T) (((-203)) . T) (((-355)) . T)) ((((-794)) . T)) (((|#1|) . T)) @@ -2371,11 +2371,11 @@ (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) -(-3172 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3255 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325))) (|has| |#1| (-37 (-383 (-523)))) (-12 (|has| |#1| (-508)) (|has| |#1| (-767))) ((((-794)) . T)) -((((-1087)) -3172 (-12 (|has| |#1| (-15 * (|#1| (-523) |#1|))) (|has| |#1| (-831 (-1087)))) (-12 (|has| |#1| (-339)) (|has| |#2| (-831 (-1087)))))) +((((-1087)) -3255 (-12 (|has| |#1| (-15 * (|#1| (-523) |#1|))) (|has| |#1| (-831 (-1087)))) (-12 (|has| |#1| (-339)) (|has| |#2| (-831 (-1087)))))) (|has| |#1| (-339)) ((((-1087)) -12 (|has| |#1| (-15 * (|#1| (-383 (-523)) |#1|))) (|has| |#1| (-831 (-1087))))) (|has| |#1| (-339)) @@ -2385,7 +2385,7 @@ (((|#1|) . T)) (((|#2|) |has| |#1| (-339))) (((|#2|) |has| |#1| (-339))) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-158))) (((|#1|) . T)) @@ -2408,31 +2408,31 @@ (((|#2|) |has| |#1| (-339))) ((((-355)) -12 (|has| |#1| (-339)) (|has| |#2| (-817 (-355)))) (((-523)) -12 (|has| |#1| (-339)) (|has| |#2| (-817 (-523))))) (|has| |#1| (-339)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-515))) (|has| |#1| (-339)) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-515))) (|has| |#1| (-339)) (|has| |#1| (-515)) (((|#4| |#4|) -12 (|has| |#4| (-286 |#4|)) (|has| |#4| (-1016)))) (((|#3|) . T)) (((|#1|) . T)) -(-3172 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3255 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) (((|#2|) . T)) (((|#2|) . T)) -(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) -((((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +(-3255 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) +((((-2 (|:| -2402 (-1070)) (|:| -2746 |#1|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) (|has| |#1| (-37 (-383 (-523)))) (((|#1| |#2|) . T)) (|has| |#1| (-37 (-383 (-523)))) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-344))) (|has| |#1| (-136)) ((((-1070) |#1|) . T)) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-344))) (|has| |#1| (-136)) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-344))) (|has| |#1| (-136)) ((((-536 |#1|)) . T)) ((($) . T)) @@ -2440,7 +2440,7 @@ (|has| |#1| (-515)) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-325))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-325))) (|has| |#1| (-136)) ((((-794)) . T)) ((($) . T)) @@ -2465,7 +2465,7 @@ (|has| |#1| (-730)) (|has| |#1| (-730)) ((((-499)) |has| |#1| (-564 (-499)))) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) ((((-110)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2486,7 +2486,7 @@ ((((-523)) . T)) ((((-794)) . T)) ((((-523)) . T)) -(-3172 (|has| |#2| (-732)) (|has| |#2| (-784))) +(-3255 (|has| |#2| (-732)) (|has| |#2| (-784))) ((((-155 (-355))) . T) (((-203)) . T) (((-355)) . T)) ((((-794)) . T)) ((((-794)) . T)) @@ -2498,9 +2498,9 @@ (((|#1|) . T) (($) . T) (((-383 (-523))) . T)) (|has| |#1| (-339)) (|has| |#1| (-339)) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) -(-3172 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-448)) (|has| |#1| (-666)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973)) (|has| |#1| (-1028)) (|has| |#1| (-1016))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +(-3255 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-448)) (|has| |#1| (-666)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973)) (|has| |#1| (-1028)) (|has| |#1| (-1016))) (|has| |#1| (-1063)) ((((-523) |#1|) . T)) (((|#1|) . T)) @@ -2518,8 +2518,8 @@ (((|#1|) . T)) (|has| |#1| (-515)) ((((-383 |#2|)) . T) (((-383 (-523))) . T) (($) . T)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-515))) ((((-355)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2528,7 +2528,7 @@ (|has| |#1| (-515)) (|has| |#1| (-1016)) ((((-719 |#1| (-796 |#2|))) |has| (-719 |#1| (-796 |#2|)) (-286 (-719 |#1| (-796 |#2|))))) -(-3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +(-3255 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) (((|#1|) . T)) (((|#2| |#3|) . T)) (|has| |#2| (-840)) @@ -2538,12 +2538,12 @@ (|has| |#1| (-211)) (((|#1| (-495 (-1006 (-1087)))) . T)) (|has| |#2| (-339)) -((((-2 (|:| -3772 (-1070)) (|:| -2482 (-51)))) . T)) +((((-2 (|:| -2402 (-1070)) (|:| -2746 (-51)))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) ((((-794)) . T)) ((((-794)) . T)) -(-3172 (|has| |#3| (-732)) (|has| |#3| (-784))) +(-3255 (|has| |#3| (-732)) (|has| |#3| (-784))) ((((-794)) . T)) ((((-794)) . T)) (((|#1|) . T)) @@ -2552,8 +2552,8 @@ ((((-523)) . T)) (((|#3|) . T)) ((((-794)) . T)) -(-3172 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325))) -(-3172 (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-515)) (|has| |#1| (-973))) +(-3255 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3255 (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-515)) (|has| |#1| (-973))) (((#0=(-536 |#1|) #0#) . T) (($ $) . T) ((#1=(-383 (-523)) #1#) . T)) ((($ $) . T) ((#0=(-383 (-523)) #0#) . T)) (((|#1|) |has| |#1| (-158))) @@ -2566,7 +2566,7 @@ (((|#1|) . T)) ((((-794)) |has| |#1| (-563 (-794)))) ((((-271 |#3|)) . T)) -(((#0=(-383 (-523)) #0#) |has| |#2| (-37 (-383 (-523)))) ((|#2| |#2|) . T) (($ $) -3172 (|has| |#2| (-158)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) +(((#0=(-383 (-523)) #0#) |has| |#2| (-37 (-383 (-523)))) ((|#2| |#2|) . T) (($ $) -3255 (|has| |#2| (-158)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-383 (-523))) |has| |#2| (-37 (-383 (-523)))) ((|#2|) . T)) @@ -2574,20 +2574,20 @@ (((|#1|) . T) (((-383 (-523))) . T) (($) . T)) (((|#1|) . T) (((-383 (-523))) . T) (($) . T)) (((|#1|) . T) (((-383 (-523))) . T) (($) . T)) -((($ $) -3172 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1| |#1|) . T) ((#0=(-383 (-523)) #0#) |has| |#1| (-37 (-383 (-523))))) -((($ $) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1| |#1|) . 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T) ((#0=(-383 (-523)) #0#) |has| |#1| (-37 (-383 (-523))))) +((($ $) -3255 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1| |#1|) . T) ((#0=(-383 (-523)) #0#) |has| |#1| (-37 (-383 (-523))))) ((((-794)) . T)) -((($) -3172 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) -((($) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($) -3255 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($) -3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (|has| |#2| (-840)) (|has| |#1| (-840)) -((($) -3172 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($) -3255 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (((|#1|) . T)) -((((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) +((((-2 (|:| -2402 (-1070)) (|:| -2746 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) @@ -2601,10 +2601,10 @@ (((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) (((#0=(-383 (-523)) #0#) . T)) ((((-383 (-523))) . 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T) (($ $) -3172 (|has| |#1| (-158)) (|has| |#1| (-515)))) +((($) . T) (((-383 (-523))) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) ((|#1|) . T)) +(((#0=(-383 (-523)) #0#) |has| |#1| (-37 (-383 (-523)))) ((|#1| |#1|) . T) (($ $) -3255 (|has| |#1| (-158)) (|has| |#1| (-515)))) ((($) . T) (((-383 (-523))) . T)) (((|#1|) . T) (((-383 (-523))) . T) (((-523)) . T) (($) . T)) (((|#2|) |has| |#2| (-973)) (((-523)) -12 (|has| |#2| (-585 (-523))) (|has| |#2| (-973)))) -((((-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((|#1|) . T) (($) -3172 (|has| |#1| (-158)) (|has| |#1| (-515)))) +((((-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((|#1|) . T) (($) -3255 (|has| |#1| (-158)) (|has| |#1| (-515)))) (|has| |#1| (-515)) (((|#1|) |has| |#1| (-339))) ((((-523)) . T)) @@ -2642,8 +2642,8 @@ ((((-794)) . T)) (|has| |#2| (-759)) (|has| |#2| (-759)) -((((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) ((|#2|) |has| |#1| (-339)) (($) . T) ((|#1|) . T)) -(((|#1|) . 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T)) -(-3172 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-732)) (|has| |#3| (-784)) (|has| |#3| (-973))) -(-3172 (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-784)) (|has| |#3| (-973))) +(-3255 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-732)) (|has| |#3| (-784)) (|has| |#3| (-973))) +(-3255 (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-784)) (|has| |#3| (-973))) ((((-794)) . T)) (((|#1|) . T)) -(-3172 (|has| |#2| (-732)) (|has| |#2| (-784))) -(-3172 (-12 (|has| |#1| (-732)) (|has| |#2| (-732))) (-12 (|has| |#1| (-786)) (|has| |#2| (-786)))) +(-3255 (|has| |#2| (-732)) (|has| |#2| (-784))) +(-3255 (-12 (|has| |#1| (-732)) (|has| |#2| (-732))) (-12 (|has| |#1| (-786)) (|has| |#2| (-786)))) ((((-801 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-344)) @@ -2700,7 +2700,7 @@ (((|#1|) . T)) ((((-794)) . T)) (|has| |#2| (-840)) -((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) . T)) +((((-2 (|:| -2402 (-1087)) (|:| -2746 (-51)))) . T)) ((((-499)) |has| |#2| (-564 (-499))) (((-823 (-355))) |has| |#2| (-564 (-823 (-355)))) (((-823 (-523))) |has| |#2| (-564 (-823 (-523))))) ((((-794)) . T)) ((((-794)) . T)) @@ -2733,11 +2733,11 @@ ((((-383 |#2|) |#3|) . T)) (((|#1|) . T)) (|has| |#1| (-1016)) -(((|#2| (-456 (-2810 |#1|) (-710))) . T)) +(((|#2| (-456 (-1271 |#1|) (-710))) . T)) ((((-523) |#1|) . T)) (((|#2| |#2|) . T)) (((|#1| (-495 (-1087))) . T)) -(-3172 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3255 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) ((((-523)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -2747,9 +2747,9 @@ ((($) . T) (((-383 (-523))) . T)) ((($) . T)) ((($) . T)) -(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3255 (|has| |#1| (-786)) (|has| |#1| (-1016))) (((|#1|) . 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T) (((-383 (-523))) . T) (($) . T)) ((($ $) . T) ((#0=(-383 (-523)) #0#) . T)) @@ -2822,14 +2822,14 @@ (((|#2|) |has| |#2| (-973)) (((-523)) -12 (|has| |#2| (-585 (-523))) (|has| |#2| (-973)))) (((|#1|) . T)) (|has| |#2| (-339)) -(((#0=(-383 (-523)) #0#) |has| |#2| (-37 (-383 (-523)))) ((|#2| |#2|) . T) (($ $) -3172 (|has| |#2| (-158)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) -((($ $) -3172 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1| |#1|) . T) ((#0=(-383 (-523)) #0#) |has| |#1| (-37 (-383 (-523))))) +(((#0=(-383 (-523)) #0#) |has| |#2| (-37 (-383 (-523)))) ((|#2| |#2|) . T) (($ $) -3255 (|has| |#2| (-158)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) +((($ $) -3255 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1| |#1|) . T) ((#0=(-383 (-523)) #0#) |has| |#1| (-37 (-383 (-523))))) (((|#1| |#1|) . T) (($ $) . T) ((#0=(-383 (-523)) #0#) . T)) (((|#1| |#1|) . 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T)) @@ -2848,25 +2848,25 @@ (((|#1|) |has| |#2| (-393 |#1|))) (((|#1|) |has| |#2| (-393 |#1|))) ((((-841 |#1|)) . T) (((-383 (-523))) . T) (($) . T)) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) ((((-499)) |has| |#1| (-564 (-499)))) ((((-794)) . T)) -((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) |has| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (-286 (-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))))) -(-3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +((((-2 (|:| -2402 (-1087)) (|:| -2746 (-51)))) |has| (-2 (|:| -2402 (-1087)) (|:| -2746 (-51))) (-286 (-2 (|:| -2402 (-1087)) (|:| -2746 (-51)))))) +(-3255 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) ((((-523) |#1|) . T)) ((((-523) |#1|) . T)) ((((-523) |#1|) . 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T)) +(((#0=(-383 (-523)) #0#) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($ $) -3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) ((|#1| |#1|) . T)) ((((-523) |#1|) . T)) ((((-292 |#1|)) . T)) (((#0=(-638) (-1083 #0#)) . T)) -((((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) ((|#1|) . T)) +((((-383 (-523))) -3255 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3255 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) ((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . T)) (|has| |#1| (-784)) ((($ $) . T) ((#0=(-796 |#1|) $) . T) ((#0# |#2|) . T)) @@ -2899,12 +2899,12 @@ (((#0=(-1155 |#1| |#2| |#3| |#4|)) |has| #0# (-286 #0#))) ((($) . T)) (((|#1|) . 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T)) -(-3172 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) -(-3172 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-124)) (|has| |#2| (-124))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) +(-3255 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3255 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-124)) (|has| |#2| (-124))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) ((((-1161 |#1| |#2| |#3|)) |has| |#1| (-339))) ((($) . T) (((-801 |#1|)) . T) (((-383 (-523))) . T)) ((((-1161 |#1| |#2| |#3|)) |has| |#1| (-339))) @@ -2941,15 +2941,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-383 |#2|)) . T)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-325))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) ((((-499)) |has| |#1| (-564 (-499)))) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) ((((-499)) |has| |#1| (-564 (-499)))) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) ((((-499)) |has| |#1| (-564 (-499)))) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) (((|#1|) . T)) (((|#2| |#2|) . T) ((#0=(-383 (-523)) #0#) . T) (($ $) . T)) ((((-523)) . T)) @@ -2978,32 +2978,32 @@ ((((-1161 |#1| |#2| |#3|)) |has| |#1| (-339))) ((((-1087)) . T) (((-794)) . T)) (|has| |#1| (-339)) -((((-383 (-523))) |has| |#2| (-37 (-383 (-523)))) ((|#2|) |has| |#2| (-158)) (($) -3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) +((((-383 (-523))) |has| |#2| (-37 (-383 (-523)))) ((|#2|) |has| |#2| (-158)) (($) -3255 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-383 (-523))) |has| |#2| (-37 (-383 (-523)))) ((|#2|) . T)) -((($) -3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) -((($) -3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($) -3255 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($) -3255 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) ((((-1020)) . T)) ((((-794)) . T)) ((($) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((|#1|) . T)) ((($) . T)) -((($) -3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($) -3255 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (|has| |#2| (-840)) (|has| |#1| (-840)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-158))) ((((-638)) . T)) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) (((|#1|) |has| |#1| (-158))) (((|#1|) |has| |#1| (-158))) ((((-383 (-523))) . T) (($) . T)) (((|#1| (-523)) . T)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-325))) (|has| |#1| (-339)) (|has| |#1| (-339)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) -(-3172 (|has| |#1| (-158)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3255 (|has| |#1| (-158)) (|has| |#1| (-515))) (((|#1| (-523)) . T)) (((|#1| (-383 (-523))) . T)) (((|#1| (-710)) . T)) @@ -3018,16 +3018,16 @@ ((((-823 (-355))) . T) (((-823 (-523))) . T) (((-1087)) . T) (((-499)) . T)) (((|#1|) . T)) ((((-794)) . T)) -(-3172 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) -(-3172 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-124)) (|has| |#2| (-124))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) +(-3255 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3255 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-124)) (|has| |#2| (-124))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) ((((-523)) . T)) ((((-523)) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3255 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) ((((-1087)) -12 (|has| |#2| (-831 (-1087))) (|has| |#2| (-973)))) -(-3172 (-12 (|has| |#1| (-448)) (|has| |#2| (-448))) (-12 (|has| |#1| (-666)) (|has| |#2| (-666)))) +(-3255 (-12 (|has| |#1| (-448)) (|has| |#2| (-448))) (-12 (|has| |#1| (-666)) (|has| |#2| (-666)))) (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-339)) @@ -3051,7 +3051,7 @@ ((((-1070) (-1087) (-523) (-203) (-794)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) -(-3172 (|has| |#1| (-325)) (|has| |#1| (-344))) +(-3255 (|has| |#1| (-325)) (|has| |#1| (-344))) (((|#1| |#2|) . T)) ((($) . T) ((|#1|) . T)) ((((-794)) . T)) @@ -3059,7 +3059,7 @@ ((($) . T) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (((|#2|) |has| |#2| (-1016)) (((-523)) -12 (|has| |#2| (-964 (-523))) (|has| |#2| (-1016))) (((-383 (-523))) -12 (|has| |#2| (-964 (-383 (-523)))) (|has| |#2| (-1016)))) ((((-499)) |has| |#1| (-564 (-499)))) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) ((($) . T) (((-383 (-523))) . T)) (|has| |#1| (-840)) (|has| |#1| (-840)) @@ -3068,14 +3068,14 @@ ((((-794)) . T)) (((|#2| |#2|) . T)) (((|#1| |#1|) |has| |#1| (-158))) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) -(-3172 (|has| |#1| (-21)) (|has| |#1| (-784))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3255 (|has| |#1| (-21)) (|has| |#1| (-784))) (((|#2|) . T)) -(-3172 (|has| |#1| (-21)) (|has| |#1| (-784))) +(-3255 (|has| |#1| (-21)) (|has| |#1| (-784))) (((|#1|) |has| |#1| (-158))) (((|#1|) . T)) (((|#1|) . T)) -((((-794)) -3172 (-12 (|has| |#1| (-563 (-794))) (|has| |#2| (-563 (-794)))) (-12 (|has| |#1| (-1016)) (|has| |#2| (-1016))))) +((((-794)) -3255 (-12 (|has| |#1| (-563 (-794))) (|has| |#2| (-563 (-794)))) (-12 (|has| |#1| (-1016)) (|has| |#2| (-1016))))) ((((-383 |#2|) |#3|) . T)) ((((-383 (-523))) . T) (($) . T)) (|has| |#1| (-37 (-383 (-523)))) @@ -3087,17 +3087,17 @@ (((|#1|) . T) (((-383 (-523))) . T) (((-523)) . T) (($) . T)) (((#0=(-523) #0#) . T)) ((($) . T) (((-383 (-523))) . T)) -(-3172 (|has| |#4| (-158)) (|has| |#4| (-784)) (|has| |#4| (-973))) -(-3172 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) +(-3255 (|has| |#4| (-158)) (|has| |#4| (-784)) (|has| |#4| (-973))) +(-3255 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) (|has| |#4| (-732)) -(-3172 (|has| |#4| (-732)) (|has| |#4| (-784))) +(-3255 (|has| |#4| (-732)) (|has| |#4| (-784))) (|has| |#4| (-784)) (|has| |#3| (-732)) -(-3172 (|has| |#3| (-732)) (|has| |#3| (-784))) +(-3255 (|has| |#3| (-732)) (|has| |#3| (-784))) (|has| |#3| (-784)) ((((-523)) . T)) (((|#2|) . T)) -((((-1087)) -3172 (-12 (|has| (-1085 |#1| |#2| |#3|) (-831 (-1087))) (|has| |#1| (-339))) (-12 (|has| |#1| (-15 * (|#1| (-523) |#1|))) (|has| |#1| (-831 (-1087)))))) +((((-1087)) -3255 (-12 (|has| (-1085 |#1| |#2| |#3|) (-831 (-1087))) (|has| |#1| (-339))) (-12 (|has| |#1| (-15 * (|#1| (-523) |#1|))) (|has| |#1| (-831 (-1087)))))) ((((-1087)) -12 (|has| |#1| (-15 * (|#1| (-383 (-523)) |#1|))) (|has| |#1| (-831 (-1087))))) ((((-1087)) -12 (|has| |#1| (-15 * (|#1| (-710) |#1|))) (|has| |#1| (-831 (-1087))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3112,11 +3112,11 @@ ((((-1085 |#1| |#2| |#3|)) |has| |#1| (-339))) ((((-1085 |#1| |#2| |#3|)) |has| |#1| (-339))) ((((-1052 |#1| |#2|)) . T)) -(((|#2|) . T) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) -((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) +((((-2 (|:| -2402 (-1087)) (|:| -2746 (-51)))) . T)) ((($) . T)) (|has| |#1| (-949)) -(((|#2|) . T) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) ((((-794)) . T)) ((((-499)) |has| |#2| (-564 (-499))) (((-823 (-523))) |has| |#2| (-564 (-823 (-523)))) (((-823 (-355))) |has| |#2| (-564 (-823 (-355)))) (((-355)) . #0=(|has| |#2| (-949))) (((-203)) . #0#)) ((((-1087) (-51)) . T)) @@ -3128,15 +3128,15 @@ ((((-1085 |#1| |#2| |#3|)) . T)) ((((-1085 |#1| |#2| |#3|)) . T) (((-1078 |#1| |#2| |#3|)) . T)) ((((-794)) . T)) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) ((((-523) |#1|) . T)) ((((-1085 |#1| |#2| |#3|)) |has| |#1| (-339))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-339)) -(((|#3|) . T) ((|#2|) . T) (($) -3172 (|has| |#4| (-158)) (|has| |#4| (-784)) (|has| |#4| (-973))) ((|#4|) -3172 (|has| |#4| (-158)) (|has| |#4| (-339)) (|has| |#4| (-973)))) -(((|#2|) . T) (($) -3172 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) ((|#3|) -3172 (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-973)))) +(((|#3|) . T) ((|#2|) . T) (($) -3255 (|has| |#4| (-158)) (|has| |#4| (-784)) (|has| |#4| (-973))) ((|#4|) -3255 (|has| |#4| (-158)) (|has| |#4| (-339)) (|has| |#4| (-973)))) +(((|#2|) . T) (($) -3255 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) ((|#3|) -3255 (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-973)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-339)) @@ -3148,37 +3148,37 @@ ((((-794)) . T)) ((((-794)) . T)) (((|#1|) . T)) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) ((((-523) |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-339)) (|has| |#2| (-263 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-840))) -(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-840))) +(-3255 (|has| |#1| (-786)) (|has| |#1| (-1016))) ((((-794)) . T)) ((((-794)) . T)) ((((-794)) . T)) (((|#1| (-495 |#2|)) . T)) -((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) . T)) +((((-2 (|:| -2402 (-1087)) (|:| -2746 (-51)))) . T)) (((|#1| (-523)) . T)) (((|#1| (-383 (-523))) . T)) (((|#1| (-710)) . T)) ((((-112 |#1|)) . T) (($) . T) (((-383 (-523))) . T)) -(-3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) -(-3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3255 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +(-3255 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((($) . T)) (((|#2| (-495 (-796 |#1|))) . T)) ((((-523) |#1|) . T)) (((|#2|) . T)) (((|#2| (-710)) . T)) -((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3255 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) (((|#1|) . T)) (((|#1| |#2|) . T)) ((((-1070) |#1|) . T)) ((((-383 |#2|)) . T)) -((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -2402 |#1|) (|:| -2746 |#2|))) . T)) (|has| |#1| (-515)) (|has| |#1| (-515)) ((($) . T) ((|#2|) . T)) @@ -3186,12 +3186,12 @@ (((|#1| |#2|) . T)) (((|#2| $) |has| |#2| (-263 |#2| |#2|))) (((|#1| (-589 |#1|)) |has| |#1| (-784))) -(-3172 (|has| |#1| (-211)) (|has| |#1| (-325))) -(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3255 (|has| |#1| (-211)) (|has| |#1| (-325))) +(-3255 (|has| |#1| (-339)) (|has| |#1| (-325))) (|has| |#1| (-1016)) (((|#1|) . T)) ((((-383 (-523))) . T) (($) . T)) -((((-927 |#1|)) . T) ((|#1|) . T) (((-523)) -3172 (|has| (-927 |#1|) (-964 (-523))) (|has| |#1| (-964 (-523)))) (((-383 (-523))) -3172 (|has| (-927 |#1|) (-964 (-383 (-523)))) (|has| |#1| (-964 (-383 (-523)))))) +((((-927 |#1|)) . T) ((|#1|) . T) (((-523)) -3255 (|has| (-927 |#1|) (-964 (-523))) (|has| |#1| (-964 (-523)))) (((-383 (-523))) -3255 (|has| (-927 |#1|) (-964 (-383 (-523)))) (|has| |#1| (-964 (-383 (-523)))))) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) @@ -3202,9 +3202,9 @@ (((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1052 |#1| |#2|) #0#) |has| (-1052 |#1| |#2|) (-286 (-1052 |#1| |#2|)))) -(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) #0#) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) #0#) |has| (-2 (|:| -2402 |#1|) (|:| -2746 |#2|)) (-286 (-2 (|:| -2402 |#1|) (|:| -2746 |#2|))))) (((#0=(-112 |#1|)) |has| #0# (-286 #0#))) -(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3255 (|has| |#1| (-786)) (|has| |#1| (-1016))) ((($ $) . T)) ((($ $) . T) ((#0=(-796 |#1|) $) . T) ((#0# |#2|) . T)) ((($ $) . T) ((|#2| $) |has| |#1| (-211)) ((|#2| |#1|) |has| |#1| (-211)) ((|#3| |#1|) . T) ((|#3| $) . T)) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 3ec04b2a..18141eb1 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3416411995) +(30 . 3417125207) (4251 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -460,649 +460,652 @@ |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |cosIfCan| |elliptic| |mergeFactors| |identityMatrix| - |readLineIfCan!| |aLinear| |mapdiv| |imagj| |infLex?| |squareFreePrim| - |direction| |clipWithRanges| |front| |semicolonSeparate| |close| - |s19abf| |ode2| |localReal?| |coercePreimagesImages| |t| - |retractIfCan| |cyclic?| |commonDenominator| |rightNorm| - |palgintegrate| |cCot| |localAbs| |resultantnaif| |s17aef| |mathieu24| - |e02ddf| |rename!| |setColumn!| |leftRankPolynomial| |kmax| |f07aef| - |lifting| |e02dff| |certainlySubVariety?| |display| |updatD| - |OMputEndError| |csubst| |oblateSpheroidal| |chineseRemainder| - |cyclicSubmodule| |getGraph| |dilog| |logIfCan| |column| - |symmetricPower| |expressIdealMember| |compdegd| |taylorRep| - |eigenvalues| |keys| |OMlistSymbols| |/\\| |rowEchLocal| - |OMencodingUnknown| |sin| |acschIfCan| |rk4| |univariatePolynomials| - |rootOf| |gbasis| |equiv?| |monomial| F2FG |\\/| |resetVariableOrder| - |exQuo| |primitivePart| |constantRight| |cos| |getStream| |callForm?| - |virtualDegree| |perfectNthRoot| |pureLex| |multivariate| - |listOfMonoms| |d01anf| |indicialEquation| - |removeRedundantFactorsInPols| |tan| |rombergo| |insertTop!| - |upperCase?| |subNodeOf?| |reduceBasisAtInfinity| - |rewriteIdealWithRemainder| |variables| |inspect| |f01mcf| |cot| - |numerator| |infix| |oddInfiniteProduct| |input| |rightTrim| - |monicRightDivide| |bubbleSort!| |distribute| |octon| |simpleBounds?| - |OMgetVariable| |rightRecip| |real?| |sec| |leastMonomial| |satisfy?| - |df2mf| |leftTrim| |library| |abelianGroup| |discriminantEuclidean| - |vectorise| |setnext!| |logical?| |factorList| |simplifyExp| |csc| - |super| |option| |factorsOfDegree| |categoryFrame| |reduction| |cAsec| - |setScreenResolution3D| |createNormalPoly| |factorFraction| |c06fuf| - |randomR| |asin| |setStatus!| |internalSubQuasiComponent?| |e02bbf| - |invertibleElseSplit?| |genericRightTrace| |c05pbf| |realElementary| - |fortranLogical| Y |weierstrass| |map| |acos| |pointData| - |basisOfRightNucloid| |subst| |edf2ef| |removeSquaresIfCan| |nthr| - |lowerCase!| |properties| |taylor| |characteristicPolynomial| |nrows| - |iitanh| |tab| |makeVariable| |pointPlot| |iibinom| |lflimitedint| - |partitions| |set| |uncouplingMatrices| |deref| |submod| |laurent| - |ncols| |translate| |saturate| |diagonals| |sncndn| |boundOfCauchy| - |rischNormalize| |hasHi| |inverseIntegralMatrix| |moduleSum| |puiseux| - |cAcosh| |ramified?| |halfExtendedSubResultantGcd2| - |cyclotomicFactorization| |pol| |constantOperator| - |setLegalFortranSourceExtensions| |frst| |e02adf| |and?| |d01bbf| - |OMputEndBVar| |iisqrt2| |movedPoints| |listYoungTableaus| |inv| |qqq| - |setright!| |exprHasAlgebraicWeight| |convert| |atan| |inR?| - |unprotectedRemoveRedundantFactors| |rightAlternative?| |objects| |sn| - |typeLists| |ground?| |rowEch| |hspace| |pastel| |genericLeftNorm| - |acot| |minPoly| |setPosition| |base| |factorPolynomial| |less?| - |ground| |setleaves!| |asec| |clipSurface| |LiePoly| |aCubic| - |fortranCarriageReturn| |reverse!| |leadingMonomial| |summation| - |repSq| |zag| |acsc| |resize| |ideal| |mapMatrixIfCan| |sumSquares| - |selectfirst| |leadingCoefficient| |iisech| |removeConstantTerm| - |OMreadFile| |sinh| |viewport2D| |copy!| |recip| |sumOfDivisors| - |invertible?| |primitiveMonomials| |withPredicates| |leadingBasisTerm| - |evaluateInverse| |li| |c05adf| |cosh| |powerAssociative?| - |linearAssociatedLog| |show| |reductum| |removeZeroes| |rur| - |clikeUniv| |e04naf| |tanh| |prinb| |bright| |viewPhiDefault| - |selectOptimizationRoutines| |hitherPlane| |inverseColeman| - |polynomialZeros| |untab| |coth| |deepestTail| |failed?| |logpart| - |exponent| |simplifyLog| |trace| |c06ebf| |extendedIntegrate| - |perfectNthPower?| |sech| |mainForm| |selectsecond| |OMgetError| - |groebner?| |endOfFile?| |setvalue!| |leftRank| |idealSimplify| - |lintgcd| |vspace| |exprToGenUPS| |internalIntegrate| - |collectQuasiMonic| |void| |branchPointAtInfinity?| |OMputEndAtp| - UTS2UP |delete| |revert| |radicalOfLeftTraceForm| |someBasis| - |rightExtendedGcd| |showSummary| |splitDenominator| - |stoseInvertibleSetsqfreg| |makeMulti| |nlde| |quartic| |critBonD| - |physicalLength| |mantissa| |rule| |basisOfLeftAnnihilator| |f07fdf| - |operation| |badValues| |option?| |OMsupportsSymbol?| |enumerate| - |f01bsf| |setsubMatrix!| |previous| |patternMatch| |dmpToHdmp| - |extractProperty| |showAttributes| |interpolate| |algebraicDecompose| - |lazyGintegrate| |viewThetaDefault| |completeHermite| - |repeatUntilLoop| |padicallyExpand| |iicsch| |subResultantsChain| - |innerint| |swap| |reducedForm| |traverse| |genericLeftDiscriminant| - |coerceImages| |monic?| |fprindINFO| |palgextint0| |symbolTableOf| - |baseRDE| |rangeIsFinite| |flagFactor| |adaptive3D?| |leftOne| |terms| - |squareTop| |isOp| |fortranDoubleComplex| |comparison| - |tableForDiscreteLogarithm| |normalizedDivide| |OMconnInDevice| - |cyclicCopy| |complexExpand| |useSingleFactorBound| |startTableGcd!| - |subscriptedVariables| |OMread| |delta| |pmintegrate| |reverseLex| - |c06ekf| |radicalSolve| |ravel| |argument| |iidprod| - |algebraicVariables| |reducedQPowers| |depth| |or?| |e02dcf| - |internal?| |twoFactor| |sort| |toseLastSubResultant| |reshape| - |members| |changeNameToObjf| |conditionsForIdempotents| |yCoordinates| - |rightRank| |double?| |pile| |collect| |selectNonFiniteRoutines| - |derivative| |cCosh| |removeRedundantFactors| |tubePointsDefault| - |Nul| |setValue!| |sh| |prefix| |leftRemainder| |log10| |components| - |complexZeros| |linearAssociatedExp| |mainCoefficients| |green| - |atanhIfCan| |f04faf| |wholeRagits| |resultant| |leftTraceMatrix| - |leftRegularRepresentation| |createNormalElement| |critM| |iiasec| - |getIdentifier| |content| |SturmHabichtMultiple| |size?| |generator| - |cos2sec| |jacobian| |scopes| |mapUnivariateIfCan| |restorePrecision| - |generalLambert| |relationsIdeal| |semiSubResultantGcdEuclidean1| - |scanOneDimSubspaces| |random| |sort!| |iisinh| |flexible?| - |fortranCompilerName| |fibonacci| |explogs2trigs| |Ei| - |radicalEigenvalues| |bivariatePolynomials| |sturmSequence| - |shanksDiscLogAlgorithm| |mr| |deepestInitial| |basicSet| |exprToUPS| - |debug| |mesh| |zeroDim?| |factor1| |leftQuotient| |choosemon| - |digit?| |paraboloidal| |delete!| |nextsubResultant2| - |screenResolution| |f04adf| |bfKeys| |contains?| RF2UTS |removeSinSq| - |ran| |nextSubsetGray| |minRowIndex| |normalizeAtInfinity| |tanSum| - |OMUnknownSymbol?| |stoseInvertible?reg| |internalZeroSetSplit| - |jordanAdmissible?| |cTan| |factorOfDegree| |recur| |leftAlternative?| - |bitTruth| |iiacsc| |rowEchelon| |iflist2Result| ~= |orbit| |rational| - |s15aef| |OMgetFloat| |palgint| |addMatchRestricted| |d03eef| - |lexGroebner| |viewpoint| |elementary| |coerce| |alphabetic?| - |sts2stst| |replace| |integralLastSubResultant| |goodPoint| |dihedral| - |particularSolution| |expintegrate| |aQuadratic| |leaves| |lo| - |optpair| |construct| |computePowers| |stopMusserTrials| |s21bcf| - |factorSquareFreePolynomial| |zero| |clearTable!| |alternating| - |phiCoord| |palglimint| |incr| |startTableInvSet!| |karatsubaDivide| - |att2Result| |charpol| |true| |legendre| |f04jgf| |rightUnit| - |sequences| |LazardQuotient2| |hi| |bitCoef| |fortranLinkerArgs| - |f04arf| |relativeApprox| |lowerPolynomial| |And| - |standardBasisOfCyclicSubmodule| |moebiusMu| |definingEquations| - |leftDivide| |iipow| |fixedDivisor| |bumprow| |RemainderList| |f01maf| - |weights| |Or| |modTree| |discriminant| |impliesOperands| - |closedCurve| |algebraic?| |integralRepresents| |bringDown| |wrregime| - |digit| |Not| |basisOfRightAnnihilator| |pdf2df| - |reciprocalPolynomial| |homogeneous?| |symbolIfCan| - |modularGcdPrimitive| |stosePrepareSubResAlgo| |zCoord| - |leviCivitaSymbol| |useEisensteinCriterion| |wronskianMatrix| - |setPredicates| |clip| |primitive?| |duplicates| |overbar| |notelem| - |palgint0| |d01aqf| |numberOfComponents| |exprHasLogarithmicWeights| - |removeRoughlyRedundantFactorsInContents| |integerIfCan| - |irreducible?| |empty?| |bat1| |s17dhf| |mdeg| |outputForm| |subspace| - |stoseInvertibleSet| |s13adf| |modularGcd| |signAround| |pow| |mkPrim| - |numberOfMonomials| |selectAndPolynomials| |ODESolve| - |reducedDiscriminant| |merge!| |setProperties!| |numberOfVariables| - |measure| |splitConstant| |setMinPoints| |leaf?| |rotatex| |bumptab| - |explimitedint| |lazyEvaluate| |rewriteIdealWithHeadRemainder| - |f04axf| |wholeRadix| |qroot| |sech2cosh| |setchildren!| |iicot| - |changeName| |highCommonTerms| |prinshINFO| |showTheSymbolTable| - |ldf2lst| |cyclotomicDecomposition| |tensorProduct| - |basisOfRightNucleus| |Ci| |closeComponent| |generators| - |numberOfImproperPartitions| |deepExpand| |PDESolve| |ratpart| - |regime| |genericPosition| |tanintegrate| |alphanumeric| |inf| - |showTheFTable| |next| |possiblyInfinite?| |stop| |nullity| |c06eaf| - |pdct| |generate| |leftFactorIfCan| |createRandomElement| |atoms| - |hypergeometric0F1| |block| |constant?| |cCsc| |bat| |alphabetic| - |probablyZeroDim?| |setelt| |curryLeft| |leadingExponent| |maxrank| - |append| |fortranCharacter| |firstSubsetGray| |null| |monomRDE| - |mapUnivariate| |incrementBy| |point?| |limit| |key?| |norm| |node| - |d02kef| |mainMonomials| |cycleEntry| |case| |iExquo| |expand| |parts| - |complexIntegrate| |plusInfinity| |copy| |copies| |bsolve| - |totalDegree| |printStatement| |Zero| |semiResultantEuclidean2| - |quasiRegular| |mainDefiningPolynomial| |filterWhile| - |trailingCoefficient| |hyperelliptic| |gcdprim| |isQuotient| - |identitySquareMatrix| |genericRightDiscriminant| |dec| |One| - |stoseInternalLastSubResultant| |setImagSteps| |filterUntil| - |enterPointData| |algebraicOf| |pushdterm| |outputAsTex| |lhs| - |argumentList!| |subResultantGcdEuclidean| |completeSmith| |select| - |unexpand| |putColorInfo| |isAbsolutelyIrreducible?| |doubleRank| - |quadratic| |rhs| |generalTwoFactor| |equiv| |lllip| |hessian| - |separant| |FormatRoman| |padicFraction| |getMeasure| - |limitedIntegrate| |endSubProgram| |stoseSquareFreePart| - |computeBasis| |iiacos| |rst| |printHeader| |hdmpToDmp| |cyclic| - |f02akf| |read!| |d02bhf| |nonQsign| |generic?| - |countRealRootsMultiple| |height| |e| |froot| |genericRightTraceForm| - |elt| |polygon| |structuralConstants| |setFieldInfo| |noLinearFactor?| - |charthRoot| |minrank| |externalList| |createPrimitivePoly| - |solveLinearPolynomialEquationByRecursion| |primeFactor| |equation| - |KrullNumber| |rightRegularRepresentation| |rCoord| |sylvesterMatrix| - |simpson| |light| |makeRecord| |diagonal?| |decrease| - |stripCommentsAndBlanks| |bindings| |polygamma| - |halfExtendedSubResultantGcd1| |definingInequation| |exactQuotient!| - |eigenvectors| |mirror| |complement| |df2ef| |f01qef| - |dimensionOfIrreducibleRepresentation| |primlimintfrac| |denomRicDE| - |makeGraphImage| |nthRoot| |coerceL| |functionIsFracPolynomial?| - |testDim| |sinhIfCan| |associative?| |scalarMatrix| |split| - |repeating| |factorSquareFree| |parent| |curveColorPalette| - |branchIfCan| |assign| |findBinding| |rootSplit| |c06gbf| |listLoops| - |laurentIfCan| |presuper| |setScreenResolution| |createThreeSpace| - |ScanFloatIgnoreSpaces| |dim| |times!| |f02adf| |noKaratsuba| |qelt| - |concat!| |cAsin| |asechIfCan| |internalSubPolSet?| |iisqrt3| - |initializeGroupForWordProblem| |differentialVariables| |droot| - |Frobenius| |resultantEuclidean| |evenInfiniteProduct| |constDsolve| - |euclideanNormalForm| |OMgetString| |xRange| |list?| - |parabolicCylindrical| |d01akf| |perfectSqrt| |e04fdf| UP2UTS - |schwerpunkt| |algint| |getSyntaxFormsFromFile| |yRange| |s18dcf| - |setfirst!| |symbol?| |overset?| |getRef| |property| |latex| |open?| - |postfix| |zRange| |usingTable?| |lazyIrreducibleFactors| |fortran| - |frobenius| |partialQuotients| |mapExponents| |oddlambert| |map!| - |s17dgf| |dfRange| |wholePart| |realZeros| |subCase?| |OMgetEndApp| - |alternative?| |createLowComplexityNormalBasis| |lowerCase| |qsetelt!| - |OMgetEndAtp| |paren| |topPredicate| |negative?| |subSet| - |rightTraceMatrix| |lookup| |units| |primextintfrac| |tan2cot| - |incrementKthElement| |leftUnits| |c06fqf| |mesh?| |setVariableOrder| - |internalIntegrate0| |radicalSimplify| |redPo| - |purelyAlgebraicLeadingMonomial?| - |rewriteIdealWithQuasiMonicGenerators| |OMclose| |cycleSplit!| - |writable?| |maxPoints3D| |bfEntry| |getlo| |setRow!| |jacobi| - |minColIndex| |divide| |coefficient| |leftDiscriminant| - |resultantReduit| |tanIfCan| |selectODEIVPRoutines| |lyndonIfCan| - |sin2csc| |mapSolve| |e02baf| |coth2tanh| |OMsetEncoding| |implies?| - |lowerCase?| |normalise| |removeSinhSq| |colorDef| |extendedEuclidean| - |d02gbf| |acsch| |polyRDE| |lift| |exactQuotient| |mapmult| |e02gaf| - |code| |lazyPquo| |mapExpon| |OMwrite| |comment| |mapBivariate| - |cot2tan| |PollardSmallFactor| |reduce| |gderiv| |coth2trigh| - |substring?| |drawCurves| |rotatey| |selectMultiDimensionalRoutines| - |subQuasiComponent?| |HermiteIntegrate| |SFunction| |corrPoly| |polar| - |log2| |pToHdmp| |arg1| |squareMatrix| |generalizedEigenvector| - |s17akf| |arguments| |simplifyPower| |irreducibleFactor| |queue| - |lfintegrate| |numberOfComputedEntries| |identity| |suffix?| |f2df| - |arg2| |makeTerm| |setPoly| |computeCycleLength| |laplace| |mathieu23| - |fractRagits| |predicate| |extensionDegree| |solveRetract| |interval| - |skewSFunction| |e01sef| |shift| |getProperty| - |createMultiplicationMatrix| |OMserve| |script| - |showFortranOutputStack| |e04dgf| |eigenvector| |prefix?| |second| - |groebgen| |conditions| |e01bgf| |magnitude| |numberOfFactors| - |laguerreL| |subset?| |nthCoef| |currentSubProgram| |idealiserMatrix| - |third| |multinomial| |match| |complex?| |changeVar| |rk4qc| - |perfectSquare?| |expint| |d01apf| |getCurve| |messagePrint| - |polygon?| |branchPoint?| |laguerre| |internalAugment| - |semiIndiceSubResultantEuclidean| |triangular?| |tex| - |multiEuclideanTree| |normalDeriv| |operators| |pop!| - |selectOrPolynomials| |shiftRight| |numeric| |extractPoint| - |modifyPoint| |LowTriBddDenomInv| - |generalizedContinuumHypothesisAssumed?| |setOrder| |iiGamma| |s17adf| - |semiSubResultantGcdEuclidean2| |linearPolynomials| |radical| |wreath| - |nthFactor| |plotPolar| |nullary?| |equivOperands| |processTemplate| - |rootKerSimp| |diagonalProduct| |stronglyReduced?| |style| |graeffe| - |rk4f| |exists?| |parametersOf| |infix?| |insertMatch| |tail| |mix| - |reorder| |numFunEvals3D| |factorSquareFreeByRecursion| |limitedint| - |returnTypeOf| |iiatanh| |addPointLast| |mask| |leftPower| |stirling1| - |integralDerivationMatrix| |OMputEndObject| |parameters| - |rightCharacteristicPolynomial| |reducedSystem| - |resultantReduitEuclidean| |internalLastSubResultant| |connect| - |binaryFunction| |supRittWu?| |weakBiRank| - |stiffnessAndStabilityFactor| |tryFunctionalDecomposition?| - |bombieriNorm| |compBound| |index?| |pair?| - |removeIrreducibleRedundantFactors| |idealiser| |clearTheFTable| - |ratDsolve| |f01ref| |rightRemainder| |tubeRadiusDefault| |e01sbf| - |var1StepsDefault| |algSplitSimple| |expextendedint| |eq?| - |numericalOptimization| |say| |rk4a| |adaptive| |e01sff| - |indiceSubResultant| |geometric| |eigenMatrix| |characteristicSet| - |routines| |lquo| |flatten| |subscript| |radix| |currentCategoryFrame| - |dmpToP| |chiSquare1| |precision| |isobaric?| |exp1| |forLoop| - |graphImage| |formula| |iisec| |s18def| |controlPanel| |tubeRadius| - |getOperator| |d02raf| |readable?| |doublyTransitive?| |setFormula!| - |zeroMatrix| |list| |linkToFortran| |infRittWu?| |binarySearchTree| - |coerceS| |csch| |denomLODE| |any?| |over| |child| |character?| |car| - |log| |rightUnits| |deriv| |setButtonValue| |f02aff| |asinh| |rules| - |triangularSystems| |ode1| |printCode| |minset| |predicates| |cdr| - |curveColor| |ptFunc| |s20acf| |nextLatticePermutation| |acosh| - |createIrreduciblePoly| |OMlistCDs| |leastPower| |setCondition!| - |setDifference| |minPoints| |decimal| |createMultiplicationTable| - |bipolarCylindrical| |cyclicEqual?| |atanh| |tracePowMod| |label| - |monicRightFactorIfCan| |unit| |adjoint| |setIntersection| |pushdown| - |extractBottom!| |quickSort| |arrayStack| FG2F |acoth| - |functionIsContinuousAtEndPoints| |complexNumeric| |trivialIdeal?| - |scalarTypeOf| |moreAlgebraic?| |outerProduct| |setUnion| - |cyclicGroup| |totalLex| |bernoulli| |semiResultantEuclidean1| |ode| - |asech| |antiCommutative?| |viewPosDefault| |binaryTournament| - |digamma| |generalSqFr| |apply| |ffactor| |term| |ref| - |makeViewport2D| |generalizedInverse| |kernels| |prinpolINFO| - |algintegrate| |seriesToOutputForm| |solve1| |changeBase| |shade| - |anfactor| |e04ycf| |int| |linears| |univariate| |doubleDisc| - |showTheRoutinesTable| |parabolic| |colorFunction| |concat| |size| - |printInfo| |comp| |shallowCopy| |OMputInteger| |rotate| |s21baf| - |title| |shuffle| |f01rcf| |outputAsScript| |setErrorBound| - |drawComplex| |getMultiplicationMatrix| |An| |coordinate| - 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|indicialEquationAtInfinity| |complete| |destruct| |initiallyReduced?| - |palginfieldint| |OMgetSymbol| |nary?| |rootNormalize| - |genericLeftMinimalPolynomial| |integralBasis| |rightLcm| - |defineProperty| |stiffnessAndStabilityOfODEIF| - |removeRoughlyRedundantFactorsInPol| |constant| - |numberOfFractionalTerms| |contract| |sinIfCan| ** |shrinkable| - |removeRedundantFactorsInContents| |viewSizeDefault| |find| - |flexibleArray| |internalInfRittWu?| |var2Steps| |autoCoerce| |remove| - |s17def| |imagi| |normalizedAssociate| |dimensions| |tanQ| |optional?| - |shellSort| |tryFunctionalDecomposition| |univariatePolynomialsGcds| - |bandedHessian| |padecf| |iiexp| |unrankImproperPartitions0| - |mainVariable?| |unary?| |implies| EQ |setOfMinN| |erf| |addPoint2| - |last| |indices| |e01bhf| |makeEq| |consnewpol| |power!| |iomode| - |gethi| |curryRight| |xor| |unitNormal| |assoc| |modulus| |color| - |e01baf| |mainCharacterization| |createZechTable| |prindINFO| |maxint| - |OMopenString| |iCompose| |prepareSubResAlgo| |tan2trig| |lazyPrem| - |axes| |c06gcf| |OMUnknownCD?| |prolateSpheroidal| |reset| - |viewport3D| |powerSum| |constantToUnaryFunction| |maxIndex| |middle| - |headReduced?| |nonSingularModel| |symmetricProduct| |commutative?| - |top!| |addiag| |lyndon| |diff| |mainKernel| |harmonic| |condition| - |write| |push!| |cycleTail| |slash| |integerBound| |finiteBound| - |f02xef| |primPartElseUnitCanonical| |prefixRagits| |pole?| - |rootRadius| |zeroSetSplit| |meatAxe| |conditionP| |tValues| - |specialTrigs| |sinh2csch| |getZechTable| |interReduce| |call| |mat| - |stoseInvertible?| ~ |zero?| |polyPart| |normalized?| |lfextendedint| - |purelyTranscendental?| |OMputAttr| |enterInCache| |elRow1!| - |roughBase?| |children| |mkIntegral| |OMputSymbol| - |sizeMultiplication| |length| |BasicMethod| - |primPartElseUnitCanonical!| |smith| |inRadical?| |reindex| |setlast!| - |build| |torsionIfCan| |scripts| |factorset| |plot| |hconcat| - |string?| |Hausdorff| |relerror| |lazyIntegrate| |entry?| |varList| - |iiacosh| |realEigenvalues| |setAdaptive3D| |element?| |e02def| - |degree| |subMatrix| |OMputBVar| |rightExactQuotient| |quadraticForm| - |nodeOf?| |graphState| |open| |splitNodeOf!| |cardinality| - |fortranLiteralLine| |Lazard| |getOperands| |rspace| - |stoseLastSubResultant| |ldf2vmf| |toseInvertibleSet| |extension| - |result| |wordsForStrongGenerators| |coleman| |ord| - |getMultiplicationTable| |integral| |doubleResultant| |coefChoose| - |cyclicEntries| |close!| |s19adf| |term?| |leftNorm| - |factorGroebnerBasis| |rationalPoint?| |radicalRoots| |write!| - |f04qaf| |match?| |generalPosition| |fortranDouble| |matrixConcat3D| - |ranges| |characteristicSerie| |eyeDistance| |LyndonCoordinates| - |coord| |expr| |symFunc| |leftExactQuotient| |bitLength| |nextColeman| - |increase| |reseed| |e04ucf| |localUnquote| |has?| |abs| |uniform| - |OMputApp| |errorKind| |makeResult| |B1solve| |reduceLODE| |s14aaf| - |startPolynomial| |monomial?| |repeating?| |normal?| - |pointColorDefault| |genericLeftTraceForm| |mainVariables| |cscIfCan| - |OMgetEndAttr| |collectUpper| |LazardQuotient| |functionIsOscillatory| - |outputList| |pleskenSplit| |stronglyReduce| |conjug| - |transcendentalDecompose| |infiniteProduct| |red| |normalize| - |sumOfKthPowerDivisors| |variable| |OMgetEndObject| |numberOfCycles| - |bivariateSLPEBR| |iidsum| |totalDifferential| |bivariate?| - |mathieu22| |s17ahf| |floor| |rootsOf| |resetBadValues| |determinant| - |leadingIdeal| |nextItem| |biRank| |groebSolve| |algDsolve| - |collectUnder| |optimize| |vark| |SturmHabicht| |create3Space| - |normalDenom| |continuedFraction| |computeInt| |s17dcf| |realRoots| - |complexForm| |e01bff| |represents| |symmetricRemainder| |s01eaf| - |sylvesterSequence| |plus| |inconsistent?| |associator| - |bezoutDiscriminant| |definingPolynomial| |outputGeneral| |hexDigit| - |coshIfCan| |rootPoly| |quasiRegular?| |resetNew| |one?| |OMgetBind| - |airyBi| |showArrayValues| |init| |iicos| |nextNormalPrimitivePoly| - |algebraicCoefficients?| |graphs| |leftUnit| |monicLeftDivide| - |changeThreshhold| |head| |f01rdf| |OMReadError?| |cycleLength| - |balancedBinaryTree| |pushucoef| |sizeLess?| |iifact| - 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|diagonalMatrix| |updateStatus!| |width| |euler| |returns| |powers| - |numericIfCan| |extractClosed| |makeFR| |d01ajf| |redPol| - |listConjugateBases| |janko2| |iisin| |OMunhandledSymbol| |qPot| - |lexico| |minimalPolynomial| |op| |triangulate| |unitNormalize| - |evenlambert| |commutator| |createPrimitiveElement| |safeCeiling| - |iiacot| |meshPar2Var| |headReduce| |evaluate| |oneDimensionalArray| - |nthExponent| |level| |spherical| |moduloP| |pushNewContour| - |integralCoordinates| |coordinates| |reducedContinuedFraction| - |ellipticCylindrical| D |eulerPhi| |nextPartition| |insert| - |acothIfCan| |pointColorPalette| |compound?| |gcdcofact| |normalForm| - |cSec| |central?| |rightTrace| |LyndonBasis| |exp| |optional| - |rischDEsys| |solveid| |c02agf| |regularRepresentation| |s17agf| - |imagK| |rightDivide| |domainOf| |nodes| |supDimElseRittWu?| - |alphanumeric?| |s21bdf| |fTable| |cCoth| |printingInfo?| - |fortranInteger| |hex| |refine| |numerators| |nonLinearPart| - |lighting| |palgextint| |setClosed| |operator| |hasTopPredicate?| - 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|setMaxPoints3D| |rquo| |ratPoly| |insertBottom!| |atanIfCan| - |normFactors| |point| OR |lastSubResultant| |unit?| |makeViewport3D| - |c06gqf| |torsion?| |createGenericMatrix| |brillhartIrreducible?| - |charClass| |leastAffineMultiple| AND |contours| |directSum| - |rdregime| |status| |atom?| |antisymmetricTensors| |packageCall| - |yCoord| |cAsinh| |makeSeries| |orbits| |jacobiIdentity?| |imagJ| - |intersect| |useNagFunctions| |belong?| |series| |lagrange| |e02ahf| - |Si| |cross| |outputSpacing| |s19acf| |semiResultantReduitEuclidean| - |pointLists| |iiasech| |complexLimit| |infinite?| |mapUp!| - |divideIfCan| |sqfree| |trim| |quatern| |baseRDEsys| |dmp2rfi| - |henselFact| |subHeight| |groebnerFactorize| |clearTheIFTable| - |newReduc| |linearDependenceOverZ| |internalDecompose| - |leadingSupport| |rootOfIrreduciblePoly| |f02aaf| |stFuncN| |digits| - |nullary| |maxRowIndex| |c06ecf| |atrapezoidal| |interpret| |sincos| - |palgRDE0| |lyndon?| |mathieu12| |min| |rationalApproximation| - |laplacian| |dimensionsOf| |patternMatchTimes| |upDateBranches| - 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|OMsupportsCD?| |se2rfi| |associatedEquations| |increment| |anticoord| - |strongGenerators| |schema| |OMgetAtp| |prod| |reify| |f02abf| - |multisect| |f02ajf| |nextSublist| |stFunc1| |fillPascalTriangle| - |cAcsch| |dequeue!| |cycleElt| |lists| |sparsityIF| |matrixGcd| - |ratDenom| |var1Steps| |aspFilename| |rightDiscriminant| - |systemCommand| |e02aef| |htrigs| |checkPrecision| |changeMeasure| - |tower| |gradient| |whileLoop| |GospersMethod| |leftTrace| |matrix| - |minPol| |fixedPoint| |doubleFloatFormat| |pack!| - |lazyPremWithDefault| |antiCommutator| |bandedJacobian| |ReduceOrder| - |solid?| |integralMatrixAtInfinity| |minusInfinity| |expandPower| - |mindeg| |universe| |e04mbf| |cAtan| |primitiveElement| |getConstant| - |prologue| |basisOfLeftNucloid| |leftScalarTimes!| |generateIrredPoly| - |normal| |drawStyle| |sPol| |localIntegralBasis| |node?| |finite?| - |trapezoidal| |cschIfCan| |extendedint| |surface| |duplicates?| - |mindegTerm| |s20adf| |autoReduced?| |pquo| |OMgetEndBind| |setref| - |linear| |OMreadStr| |integer?| |permutationGroup| |listOfLists| - |objectOf| |arity| |midpoints| |exponents| |id| |OMputError| - |buildSyntax| |reverse| |sec2cos| |optAttributes| |select!| BY - |rationalPower| |leftZero| |fmecg| |accuracyIF| |s18aef| |center| - |cond| |positive?| |inverse| |polynomial| |lastSubResultantElseSplit| - |subresultantVector| |e02zaf| |squareFreePart| |setProperty| - |changeWeightLevel| |goto| |exprHasWeightCosWXorSinWX| |table| - |nilFactor| |graphCurves| |modifyPointData| |type| |getCode| |e02bcf| - |firstUncouplingMatrix| |nextPrimitivePoly| |resultantEuclideannaif| - |new| |permutations| |symmetric?| |rotatez| |sechIfCan| |c02aff| |is?| - |ignore?| |intChoose| |constantKernel| |insertRoot!| |doubleComplex?| - |inHallBasis?| |zeroDimensional?| |fullPartialFraction| - |topFortranOutputStack| |antisymmetric?| |bottom!| |f02bjf| |iiacoth| - |normalElement| |cyclePartition| |asecIfCan| |convergents| |isList| - |basisOfMiddleNucleus| |normInvertible?| |basis| |lazyResidueClass| - |inc| |mainSquareFreePart| |totalfract| |fi2df| |distance| - |LyndonWordsList1| |romberg| |orOperands| LODO2FUN |matrixDimensions| - |key| |create| |basisOfLeftNucleus| |cot2trig| |youngGroup| - |minPoints3D| |symbolTable| |float?| |merge| |top| - |complexNumericIfCan| |bumptab1| |divergence| |options| |kovacic| - |partialDenominators| |mainValue| |besselJ| - |semiLastSubResultantEuclidean| |dioSolve| |parametric?| |continue| - |lp| |OMmakeConn| |dihedralGroup| |d01gbf| |squareFreeLexTriangular| - |rectangularMatrix| |tanh2trigh| |divideExponents| |measure2Result| - |OMputVariable| |pushFortranOutputStack| |makeSUP| |linearMatrix| - |filename| |currentEnv| |ceiling| |selectFiniteRoutines| |shiftLeft| - |mapDown!| |popFortranOutputStack| |closed?| |OMgetApp| |Is| |augment| - |karatsuba| |coefficients| |null?| |palglimint0| |psolve| - |lazyPseudoRemainder| |exprToXXP| |useSingleFactorBound?| - |outputAsFortran| |showTheIFTable| |approximants| |realEigenvectors| - |basisOfCentroid| |not?| |bracket| |minimize| |s21bbf| |declare| - |dark| |polCase| |semiResultantEuclideannaif| |dot| |gcdcofactprim| - |iteratedInitials| |meshPar1Var| |parse| |left| |unitVector| - |intPatternMatch| |points| |halfExtendedResultant1| - |numberOfIrreduciblePoly| |multMonom| |component| |printInfo!| - |genericRightMinimalPolynomial| |presub| |right| |cartesian| - |cRationalPower| |stopTableGcd!| |unmakeSUP| |odd?| |critpOrder| - |npcoef| |e02bef| |s17ajf| |initial| |stopTable!| |cPower| - |setAttributeButtonStep| |critMTonD1| |e02daf| |debug3D| |lSpaceBasis| - |iicsc| |axesColorDefault| |gcdPrimitive| |stopTableInvSet!| - |elliptic?| |principal?| |zeroOf| |singleFactorBound| |complexSolve| - |possiblyNewVariety?| |iiacsch| |hdmpToP| |viewDefaults| |radPoly| - |imaginary| |opeval| |closedCurve?| |countable?| |ParCond| - |decreasePrecision| |diophantineSystem| |test| |ScanArabic| |cap| - |palgLODE| |f04mbf| |OMgetObject| |round| |groebner| |pattern| - |lfextlimint| |extendedSubResultantGcd| |integral?| |seed| - |selectPDERoutines| |recolor| |swapColumns!| |cAcos| |putGraph| - |getButtonValue| |monicDecomposeIfCan| |lieAdmissible?| |f01qcf| - |curry| |firstNumer| |useEisensteinCriterion?| |lepol| |redpps| - |constantIfCan| |intensity| |composite| |unvectorise| |isMult| - |uniform01| |rightRankPolynomial| |mulmod| |s19aaf| |output| - |screenResolution3D| |semiDegreeSubResultantEuclidean| |external?| - |pmComplexintegrate| |ipow| |OMencodingSGML| |shallowExpand| - |pointSizeDefault| |morphism| |leadingTerm| = |linGenPos| |nsqfree| - |stFunc2| |testModulus| |cubic| |radicalEigenvector| |compactFraction| - |tRange| |preprocess| |hash| |equality| |neglist| |s14baf| |qinterval| - |monomialIntPoly| |brillhartTrials| |lllp| |tree| |poisson| - |complexElementary| |e02bdf| |var2StepsDefault| |fortranComplex| - |e04jaf| < |vector| |getOrder| |remainder| |quasiAlgebraicSet| - |iiperm| |divisors| |entries| |push| |toroidal| |problemPoints| - |count| |alternatingGroup| |cothIfCan| > |primaryDecomp| - |linearlyDependentOverZ?| |linearDependence| |differentiate| - |ocf2ocdf| |replaceKthElement| |setLabelValue| |d01alf| - |hasPredicate?| |rightFactorIfCan| |ramifiedAtInfinity?| - |getVariableOrder| <= |leader| |ScanRoman| |cLog| |indicialEquations| - |zeroSquareMatrix| |pseudoDivide| |cCsch| |deleteRoutine!| - |roughUnitIdeal?| |unrankImproperPartitions1| |partialNumerators| - |transpose| >= |exquo| |mightHaveRoots| |associatedSystem| - |eisensteinIrreducible?| |ddFact| |quotientByP| |index| - |factorSFBRlcUnit| |quasiMonic?| |sup| |leftGcd| - |clearFortranOutputStack| |s15adf| |div| |representationType| |prime| - |oddintegers| |powmod| |maximumExponent| |OMputFloat| - |rightScalarTimes!| |overlabel| |tube| |generic| |decomposeFunc| |quo| - |root?| |applyRules| |rationalFunction| |binding| |edf2df| - |outlineRender| |body| |asinIfCan| |lifting1| |extractSplittingLeaf| - |f02bbf| |rarrow| + |newLine| |minimumDegree| |fullDisplay| |e02akf| - |asimpson| |clearCache| |pair| |wordInStrongGenerators| |s17acf| - |s18adf| |Beta| |hMonic| |stoseIntegralLastSubResultant| |rem| - - |roman| |cAsech| |csc2sin| |OMParseError?| |cfirst| - |combineFeatureCompatibility| |lazyVariations| |compile| |nil| - |OMencodingBinary| |pr2dmp| |OMbindTCP| |graphStates| / - |groebnerIdeal| |solveInField| |viewWriteDefault| |socf2socdf| - |insertionSort!| |df2fi| |vertConcat| |chebyshevT| - |completeEchelonBasis| |rotate!| |zoom| |OMputEndAttr| |constantLeft| - |radicalEigenvectors| |toScale| |rootBound| |ksec| - |expandTrigProducts| |irreducibleRepresentation| |sub| |zeroDimPrime?| - |partition| |leftRecip| |numberOfNormalPoly| |quote| |rootPower| - |dAndcExp| |heap| |integralMatrix| |infinityNorm| |d02bbf| - |laurentRep| |s18acf| |approximate| |getGoodPrime| |fractionPart| - |trunc| |iicosh| |scripted?| |d03faf| |complex| |rdHack1| - |clearDenominator| |lambert| |xn| |showAllElements| |crest| - |makeSketch| |sin?| |imagk| |gramschmidt| |pToDmp| |addPoint| - |trapezoidalo| |ridHack1| |squareFreePolynomial| |elements| - |nextsousResultant2| |outputFloating| |unitsColorDefault| |tubePlot| - |OMconnectTCP| |removeCosSq| |elColumn2!| |palgRDE| - |degreeSubResultant| |fill!| |multiset| |outputFixed| - |raisePolynomial| |setEpilogue!| |nextIrreduciblePoly| |cosSinInfo| - |inrootof| |message| |obj| |OMgetBVar| |c06frf| |solveLinearlyOverQ| - |qfactor| |OMgetInteger| |OMputBind| |cTanh| |subResultantChain| - |vedf2vef| |removeDuplicates!| |rubiksGroup| |orthonormalBasis| - |cache| |diag| |stoseInvertibleSetreg| |copyInto!| - |constantCoefficientRicDE| |seriesSolve| |HenselLift| |f02aef| - |leadingIndex| |blankSeparate| |const| |makeUnit| |primextendedint| - |prevPrime| |linearlyDependent?| |rename| |not| |iiabs| - |permutationRepresentation| |cosh2sech| |linearAssociatedOrder| |scan| - |char| |exptMod| |perspective| |curve?| |sample| |makeCos| |swap!| - |acoshIfCan| |invmod| |trigs2explogs| |palgLODE0| |cotIfCan| |updatF| - |name| |symmetricDifference| |unravel| |nthFlag| |monomialIntegrate| - |csch2sinh| |subTriSet?| |critT| |hasoln| |horizConcat| |composites| - |fixPredicate| |float| |f02agf| |integralAtInfinity?| |mainVariable| - |makeop| |wordInGenerators| |search| |principalIdeal| |crushedSet| - |lprop| |setProperty!| |newTypeLists| |pomopo!| |stack| |minordet| - |trueEqual| |squareFree| |e01daf| |midpoint| |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| |primitive?| |d02ejf| |coordinate| |cSinh| + |withPredicates| |setRow!| |bivariateSLPEBR| |duplicates| |quadratic?| + |inverseIntegralMatrixAtInfinity| + |solveLinearPolynomialEquationByFractions| |leadingBasisTerm| |jacobi| + |iidsum| |overbar| |bipolar| |beauzamyBound| |fglmIfCan| + |evaluateInverse| |minColIndex| |totalDifferential| |match?| |notelem| + |primintegrate| |mkAnswer| |OMcloseConn| |c05adf| |divide| |cond| + |bivariate?| |palgint0| |hclf| |linear?| |normDeriv2| |coefficient| + |mathieu22| |d01aqf| |width| |f04atf| |indiceSubResultantEuclidean| + |separateDegrees| |real?| |leftDiscriminant| |s17ahf| + |numberOfComponents| |bag| |curve| |univariatePolynomial| + |leastMonomial| |resultantReduit| |floor| |exprHasLogarithmicWeights| + |generate| |largest| |scale| |weight| |satisfy?| |tanIfCan| |rootsOf| + |logGamma| |ricDsolve| |module| |df2mf| |selectODEIVPRoutines| + |resetBadValues| |mesh| |incrementBy| |OMopenFile| |OMencodingXML| + |sortConstraints| |abelianGroup| |#| |lyndonIfCan| |determinant| + |zeroDim?| |optional| |expand| |checkRur| |besselI| |jordanAlgebra?| + |discriminantEuclidean| |sin2csc| |leadingIdeal| |factor1| + |filterWhile| |degreePartition| |weighted| |LiePolyIfCan| |vectorise| + |nextItem| |leftQuotient| |filterUntil| |leftCharacteristicPolynomial| + |binary| |fortranTypeOf| |setnext!| + |dimensionOfIrreducibleRepresentation| |biRank| |choosemon| |select| + |f04asf| |power| |readIfCan!| |logical?| |varList| |primlimintfrac| + |groebSolve| |paraboloidal| |conjugate| |loopPoints| |rational?| + |factorList| |denomRicDE| |algDsolve| |delete!| |nthRootIfCan| + |simplifyExp| |makeGraphImage| |collectUnder| |nextsubResultant2| + |exp1| |mathieu12| |extract!| |super| |nthRoot| |vark| |forLoop| + |screenResolution| |rationalApproximation| |rule| |prime?| + |factorsOfDegree| |coerceL| |SturmHabicht| |f04adf| |graphImage| + |laplacian| |secIfCan| |categoryFrame| |functionIsFracPolynomial?| + |bfKeys| |iisec| |makeRecord| |dimensionsOf| |more?| |reduction| + |testDim| |factorset| |member?| |eval| |contains?| |s18def| + |patternMatchTimes| |monicDivide| |cAsec| |sinhIfCan| |scaleRoots| + |plot| RF2UTS |upDateBranches| |controlPanel| |extend| + |setScreenResolution3D| |associative?| |hconcat| |pseudoRemainder| + |removeSinSq| |tubeRadius| |extractIndex| |createNormalPoly| + |scalarMatrix| |expIfCan| |string?| |ran| |approxNthRoot| + |FormatArabic| |getOperator| |pair| |nodes| |factorFraction| |split| + |e01saf| |Hausdorff| |nextSubsetGray| |d02raf| |acosIfCan| |e01bef| + |supDimElseRittWu?| |c06fuf| |repeating| |Aleph| |relerror| + |minRowIndex| |leftMinimalPolynomial| |readable?| |alphanumeric?| + |checkForZero| |randomR| |factorSquareFree| |lazyIntegrate| + |interpretString| |null| |normalizeAtInfinity| |doublyTransitive?| + |leftExtendedGcd| |s21bdf| |viewDeltaYDefault| |append| |plus| + |setStatus!| |entry?| |parent| |squareFreeLexTriangular| |firstDenom| + |createGenericMatrix| |case| |tanSum| |setFormula!| |cSin| + |primeFrobenius| |fTable| |brillhartIrreducible?| + |internalSubQuasiComponent?| |curveColorPalette| |iiacosh| |t| + |numberOfChildren| |rectangularMatrix| |Zero| |OMUnknownSymbol?| + |zeroMatrix| |nil?| |cCoth| |f01brf| |e02bbf| |charClass| + |branchIfCan| |realEigenvalues| |generalInfiniteProduct| |tanh2trigh| + |One| |stoseInvertible?reg| |linkToFortran| |unparse| |OMsupportsCD?| + |printingInfo?| |invertibleElseSplit?| |assign| |leftMult| + |setAdaptive3D| |leastAffineMultiple| |divideExponents| + |internalZeroSetSplit| |OMgetEndError| |infRittWu?| |fortranInteger| + |se2rfi| |d01alf| |genericRightTrace| |times| |findBinding| |credPol| + |element?| |measure2Result| |contours| |iroot| |jordanAdmissible?| + |associatedEquations| |binarySearchTree| |hex| |message| + |hasPredicate?| |c05pbf| |rootSplit| |e02def| |binomial| |directSum| + |OMputVariable| |cTan| |coerceS| |d02cjf| |increment| |refine| + |rightFactorIfCan| |realElementary| |c06gbf| |s14abf| |degree| + |rdregime| |makeSUP| |factorOfDegree| |solveLinear| |denomLODE| + |numerators| |anticoord| |ramifiedAtInfinity?| |fortranLogical| + |linearMatrix| |listLoops| |subMatrix| |order| |atom?| |elt| + |linearlyDependent?| |recur| |any?| |quoByVar| |nonLinearPart| + |strongGenerators| |getVariableOrder| |weierstrass| |monom| + |laurentIfCan| |OMputBVar| |OMgetAttr| |antisymmetricTensors| + |ceiling| |rename| |createPrimitiveNormalPoly| |leftAlternative?| + |over| |schema| |name| |lighting| |ScanRoman| |pointData| |presuper| + |rightExactQuotient| |chainSubResultants| |packageCall| + |selectFiniteRoutines| |iiabs| |char| |bitTruth| |pascalTriangle| + |child| |palgextint| |OMgetAtp| |cLog| |basisOfRightNucloid| + |setScreenResolution| |quadraticForm| |expandLog| |yCoord| |shiftLeft| + |permutationRepresentation| |iiacsc| |numberOfPrimitivePoly| + |character?| |prod| |setClosed| |indicialEquations| |edf2ef| |common| + |createThreeSpace| |nodeOf?| |realSolve| |mapDown!| |cAsinh| + |cosh2sech| |reify| |rowEchelon| |mapCoef| |rightUnits| |operator| + |float| |zeroSquareMatrix| |removeSquaresIfCan| + |ScanFloatIgnoreSpaces| |singRicDE| |graphState| |makeSeries| + |closed?| |linearAssociatedOrder| |iflist2Result| |f07fef| |deriv| + |f02abf| |hasTopPredicate?| |pseudoDivide| |nthr| |times!| |sdf2lst| + |splitNodeOf!| |OMgetApp| |orbits| |scan| |orbit| |setButtonValue| + |listRepresentation| |reopen!| |multisect| |cCsch| |lowerCase!| + |f02adf| |setProperties| |cardinality| |jacobiIdentity?| |Is| + |exptMod| |rational| |drawComplexVectorField| |f02aff| |f02ajf| + |makeYoungTableau| |deleteRoutine!| |characteristicPolynomial| + |noKaratsuba| |fortranLiteralLine| |integers| |imagJ| |augment| |keys| + |perspective| |s15aef| |getBadValues| |triangularSystems| |myDegree| + |nextSublist| |roughUnitIdeal?| |iitanh| |operation| |concat!| + |OMputString| |Lazard| |intersect| |karatsuba| |curve?| |OMgetFloat| + |position!| |ode1| |numberOfDivisors| |stFunc1| + |unrankImproperPartitions1| |tab| |cAsin| |algebraicSort| + |getOperands| |useNagFunctions| |coefficients| |sample| |palgint| + |printCode| |primintfldpoly| |fillPascalTriangle| |companionBlocks| + |partialNumerators| |makeVariable| |asechIfCan| |minGbasis| |rspace| + |belong?| |null?| |makeCos| |addMatchRestricted| |meshFun2Var| + |minset| |setleft!| |cAcsch| |transpose| |pointPlot| + |internalSubPolSet?| |stoseLastSubResultant| |clearTheSymbolTable| + |palglimint0| |lagrange| |swap!| |d03eef| |vconcat| |predicates| + |partialFraction| |dequeue!| GE |mightHaveRoots| |iibinom| |iisqrt3| + |sayLength| |ldf2vmf| |e02ahf| |psolve| |acoshIfCan| |cycleElt| + |lexGroebner| |curveColor| |makeSin| |setStatus| GT |associatedSystem| + |lflimitedint| |initializeGroupForWordProblem| |singular?| + |toseInvertibleSet| |Si| |lazyPseudoRemainder| |invmod| |sparsityIF| + |viewpoint| |ptFunc| |characteristic| |linearPart| LE + |eisensteinIrreducible?| |partitions| |differentialVariables| + |extension| |delay| |exprToXXP| |cross| |trigs2explogs| + |resetAttributeButtons| |elementary| |traceMatrix| |s20acf| + |matrixGcd| LT |ddFact| |uncouplingMatrices| |droot| + |derivationCoordinates| |wordsForStrongGenerators| |outputSpacing| + |useSingleFactorBound?| |palgLODE0| |ravel| |alphabetic?| + |getProperties| |nextLatticePermutation| |ratDenom| |initiallyReduce| + |quotientByP| |lp| |deref| |Frobenius| |trace2PowMod| |coleman| + |s19acf| |showTheIFTable| |basisOfCommutingElements| |cotIfCan| + |reshape| |sts2stst| |createIrreduciblePoly| |c06fpf| |var1Steps| + |fortran| |factorSFBRlcUnit| |submod| |eq| |resultantEuclidean| |ord| + |sizePascalTriangle| |approximants| |semiResultantReduitEuclidean| + |updatF| |integralLastSubResultant| |OMlistCDs| |truncate| |s17dlf| + |aspFilename| |quasiMonic?| |saturate| |iter| |evenInfiniteProduct| + |factorial| |getMultiplicationTable| |pointLists| |realEigenvectors| + |symmetricDifference| |goodPoint| |safetyMargin| |leastPower| + |dictionary| |rightDiscriminant| |sup| |diagonals| |constDsolve| + |ListOfTerms| |integral| |basisOfCentroid| |iiasech| |unravel| + |dihedral| |cn| |chiSquare| |setCondition!| |e02aef| |eulerE| + |leftGcd| |sncndn| |euclideanNormalForm| |doubleResultant| |imagE| + |complexLimit| |bracket| |nthFlag| |particularSolution| + |explicitEntries?| |minPoints| |minIndex| |htrigs| + |clearFortranOutputStack| |boundOfCauchy| |OMgetString| |coefChoose| + |simplify| |minimize| |infinite?| |decimal| |monomialIntegrate| + |expintegrate| |update| |outputArgs| |selectSumOfSquaresRoutines| + |changeMeasure| |clearCache| |s15adf| |lift| |rischNormalize| |list?| + |setClipValue| |cyclicEntries| |mapUp!| |s21bbf| |csch2sinh| + |aQuadratic| |createMultiplicationTable| |ScanFloatIgnoreSpacesIfCan| + |createNormalPrimitivePoly| |gradient| |representationType| |reduce| + |hasHi| |parabolicCylindrical| |close!| |e02agf| |dark| |divideIfCan| + |subTriSet?| |bipolarCylindrical| |optpair| |whileLoop| + |commaSeparate| |associatorDependence| |function| |prime| + |inverseIntegralMatrix| |d01akf| |exp| |s19adf| |legendreP| |polCase| + |sqfree| |critT| |computePowers| |e04gcf| |cyclicEqual?| + |GospersMethod| |xCoord| |arguments| |oddintegers| |moduleSum| + |perfectSqrt| |term?| |selectPolynomials| |semiResultantEuclideannaif| + |trim| |hasoln| |stopMusserTrials| |tracePowMod| |remove!| |leftTrace| + |OMputAtp| |powmod| |cAcosh| |e04fdf| |isQuotient| |leftNorm| + |critMonD1| |quatern| |dot| |horizConcat| |s21bcf| |lexTriangular| + |monicRightFactorIfCan| |minPol| |OMconnOutDevice| |maximumExponent| + UP2UTS |factorGroebnerBasis| |monomRDEsys| |gcdcofactprim| + |baseRDEsys| |composites| |factorSquareFreePolynomial| |position| + |unit| |showRegion| |fixedPoint| |addBadValue| |certainlySubVariety?| + |OMputFloat| |schwerpunkt| |rationalPoint?| |transform| |dmp2rfi| + |iteratedInitials| |fixPredicate| |doubleFloatFormat| |clearTable!| + |cExp| |adjoint| |innerEigenvectors| |script| |updatD| + |rightScalarTimes!| |algint| |headRemainder| |radicalRoots| + |meshPar1Var| |henselFact| |f02agf| |alternating| |cAcot| |pushdown| + |pack!| |OMputEndApp| |OMputEndError| |overlabel| + |getSyntaxFormsFromFile| |write!| |minus!| |subHeight| |unitVector| + |integralAtInfinity?| |extractBottom!| |plenaryPower| |retractable?| + |lazyPremWithDefault| |csubst| |tube| |stop| |s18dcf| |height| D + |f04qaf| |getExplanations| |groebnerFactorize| |intPatternMatch| + |conditionsForIdempotents| |mainVariable| |quickSort| |s17aff| + |antiCommutator| |roughBasicSet| |tex| |oblateSpheroidal| |generic| + |setfirst!| |generalPosition| |plus!| |clearTheIFTable| |points| + |yCoordinates| |makeop| |arrayStack| |setEmpty!| |numberOfHues| + |bandedJacobian| |chineseRemainder| |decomposeFunc| |rightRank| + |fortranDouble| |symbol?| |isPlus| |symbolTable| |newReduc| + |halfExtendedResultant1| FG2F |wordInGenerators| |identification| + |systemCommand| |d01asf| |constant| |ReduceOrder| |string| + |cyclicSubmodule| |root?| |matrixConcat3D| |squareFreeFactors| + |numberOfIrreduciblePoly| |linearDependenceOverZ| |double?| + |principalIdeal| |applyRules| |balancedFactorisation| + |functionIsContinuousAtEndPoints| |retract| |solid?| |expt| |getGraph| + |brace| |doubleRank| |pushFortranOutputStack| |ranges| + |primitivePart!| |multMonom| |internalDecompose| |pile| |crushedSet| + |integralMatrixAtInfinity| |LyndonWordsList| |trivialIdeal?| |lcm| + |f02wef| |logIfCan| |rationalFunction| |quadratic| |binding| + |popFortranOutputStack| |OMgetEndBVar| |characteristicSerie| + |component| |leadingSupport| |collect| |lprop| |next| + |increasePrecision| |scalarTypeOf| |erf| |hermiteH| |expandPower| + |normal| |column| |generalTwoFactor| |outputAsFortran| |sign| + |eyeDistance| |rootOfIrreduciblePoly| |printInfo!| |setProperty!| + |selectNonFiniteRoutines| |discreteLog| |mindeg| |edf2df| + |symmetricPower| |equiv| |divisor| |LyndonCoordinates| + |genericRightMinimalPolynomial| |f02aaf| |derivative| |newTypeLists| + |error| |parametersOf| |universe| |fortranReal| |gcd| + |expressIdealMember| |value| |outlineRender| |lllip| |comment| |log| + |coord| |f02fjf| |presub| |stFuncN| |pomopo!| |cCosh| |insertMatch| + |expintfldpoly| |compdegd| |e04mbf| |union| |assert| |asinIfCan| + |hessian| |basisOfCenter| |symFunc| |cartesian| |digits| + |removeRedundantFactors| |minordet| |mix| |false| |iprint| |cAtan| + |lifting1| |taylorRep| |separant| |interpret| |cRationalPower| + |nullary| |trueEqual| |tubePointsDefault| |reorder| |hasSolution?| + |primitiveElement| |eigenvalues| |extractSplittingLeaf| |FormatRoman| + |viewport3D| |maxRowIndex| |stopTableGcd!| |Nul| |squareFree| + |numFunEvals3D| |getConstant| |square?| |f02bbf| |OMlistSymbols| + |padicFraction| |leaves| |powerSum| |c06ecf| |unmakeSUP| |e01daf| + |setValue!| |factorSquareFreeByRecursion| |rightMinimalPolynomial| + |prologue| |rowEchLocal| |rarrow| |getMeasure| + |constantToUnaryFunction| |atrapezoidal| |odd?| |sh| |midpoint| + |limitedint| |newLine| |OMencodingUnknown| |limitedIntegrate| + |maxIndex| |critpOrder| |sincos| |leftRemainder| |returnTypeOf| + |leftLcm| |acschIfCan| |minimumDegree| |endSubProgram| |inc| |middle| + |palgRDE0| |npcoef| |components| |iiatanh| |diagonalMatrix| + |fullDisplay| |rk4| |stoseSquareFreePart| |headReduced?| |lyndon?| + |e02bef| |complexZeros| |addPointLast| |updateStatus!| |e02akf| + |univariatePolynomials| |computeBasis| |nonSingularModel| |directory| + |linearAssociatedExp| |numer| |leftPower| |euler| |rootOf| |asimpson| + |iiacos| |symmetricProduct| |denom| |mainCoefficients| |stirling1| + |returns| |gbasis| |wordInStrongGenerators| |rst| |commutative?| + |green| |integralDerivationMatrix| |powers| |call| |s17acf| |equiv?| + |printHeader| |top!| |atanhIfCan| |pi| |OMputEndObject| |numericIfCan| + F2FG |hdmpToDmp| |addiag| |f04faf| |infinity| + |rightCharacteristicPolynomial| |extractClosed| |resetVariableOrder| + |cyclic| |lyndon| |wholeRagits| |datalist| |reducedSystem| |true| + |makeFR| |exQuo| |f02akf| |diff| |result| |resultant| + |resultantReduitEuclidean| |d01ajf| |primitivePart| |read!| + |mainKernel| |leftTraceMatrix| |kernel| |internalLastSubResultant| + |redPol| |constantRight| |d02bhf| |harmonic| |lambert| |draw| + |leftRegularRepresentation| |connect| |listConjugateBases| |getStream| + |nonQsign| |push!| |remove| |xn| |createNormalElement| + |binaryFunction| |janko2| |callForm?| |generic?| |cycleTail| |lhs| + |showAllElements| |critM| |supRittWu?| |iisin| |virtualDegree| + |countRealRootsMultiple| |slash| |last| |rhs| |crest| |iiasec| + |weakBiRank| |OMunhandledSymbol| |perfectNthRoot| |froot| |assoc| + |integerBound| |makeSketch| |makeObject| |getIdentifier| + |stiffnessAndStabilityFactor| |qPot| |rank| |pureLex| + |genericRightTraceForm| |finiteBound| |sin?| |content| + |tryFunctionalDecomposition?| |lexico| |listOfMonoms| |polygon| + |f02xef| |imagk| |SturmHabichtMultiple| |coef| |bombieriNorm| + |minimalPolynomial| |d01anf| |structuralConstants| + |primPartElseUnitCanonical| |gramschmidt| |size?| |compBound| + |triangulate| |indicialEquation| |setFieldInfo| |prefixRagits| + |pToDmp| |cos2sec| |index?| |unitNormalize| + |removeRedundantFactorsInPols| |noLinearFactor?| |pole?| |addPoint| + |jacobian| |pair?| |leader| |evenlambert| |rombergo| |charthRoot| + |rootRadius| |trapezoidalo| |scopes| + |removeIrreducibleRedundantFactors| |commutator| |optimize| + |insertTop!| |lists| |minrank| |zeroSetSplit| |ridHack1| + |mapUnivariateIfCan| |idealiser| |createPrimitiveElement| |upperCase?| + |externalList| |meatAxe| |squareFreePolynomial| |restorePrecision| + |clearTheFTable| |safeCeiling| |id| |subNodeOf?| |createPrimitivePoly| + |conditionP| |plusInfinity| |elements| |generalLambert| |ratDsolve| + |iiacot| |reduceBasisAtInfinity| + |solveLinearPolynomialEquationByRecursion| |tValues| |minusInfinity| + |nextsousResultant2| |relationsIdeal| |f01ref| |meshPar2Var| |table| + |rewriteIdealWithRemainder| |primeFactor| |specialTrigs| + |outputFloating| |semiSubResultantGcdEuclidean1| |rightRemainder| + |headReduce| |new| |inspect| |KrullNumber| |sinh2csch| + |unitsColorDefault| |scanOneDimSubspaces| |variable| + |tubeRadiusDefault| |evaluate| |f01mcf| |rightRegularRepresentation| + |getZechTable| |tubePlot| |sort!| |e01sbf| |oneDimensionalArray| + |numerator| |rCoord| |interReduce| |OMconnectTCP| |iisinh| + |var1StepsDefault| |nthExponent| |infix| |sylvesterMatrix| |mat| + |removeCosSq| |flexible?| |algSplitSimple| |spherical| + |oddInfiniteProduct| |simpson| |stoseInvertible?| |type| |elColumn2!| + |fortranCompilerName| |expextendedint| |moduloP| |monicRightDivide| + |light| |zero?| |palgRDE| |fibonacci| |eq?| |pushNewContour| + |bubbleSort!| |tower| |diagonal?| |polyPart| |degreeSubResultant| + |printInfo| |explogs2trigs| |numericalOptimization| + |integralCoordinates| |key| |body| |distribute| |decrease| |ruleset| + |normalized?| |fill!| |Ei| |rk4a| |coordinates| |options| |octon| + |stripCommentsAndBlanks| |lfextendedint| |multiset| + |radicalEigenvalues| |adaptive| |reducedContinuedFraction| + |simpleBounds?| |bindings| |purelyTranscendental?| |outputFixed| + |bivariatePolynomials| |e01sff| |ellipticCylindrical| |filename| + |left| |OMgetVariable| |suchThat| |polygamma| |OMputAttr| + |raisePolynomial| |sturmSequence| |hash| |indiceSubResultant| + |eulerPhi| |right| |rightRecip| |halfExtendedSubResultantGcd1| + |enterInCache| |setEpilogue!| |shanksDiscLogAlgorithm| |geometric| + |not?| |nextPartition| |definingInequation| |zero| |elRow1!| + |nextIrreduciblePoly| |deepestInitial| |count| |eigenMatrix| + |acothIfCan| |parse| |exactQuotient!| |roughBase?| |cosSinInfo| + |basicSet| |characteristicSet| |pointColorPalette| |eigenvectors| + |And| |children| |inrootof| |exprToUPS| |routines| |compound?| |exquo| + |condition| |mirror| |Or| |mkIntegral| |OMgetBVar| |lquo| |gcdcofact| + |div| |obj| |complement| |Not| |OMputSymbol| |c06frf| |patternMatch| + |subscript| |normalForm| |quo| |df2ef| |cache| |sizeMultiplication| + |dmpToHdmp| |solveLinearlyOverQ| |radix| |cSec| |f01qef| |BasicMethod| + |qfactor| |extractProperty| |currentCategoryFrame| |central?| |nil| + |rem| |currentEnv| |primPartElseUnitCanonical!| |interpolate| + |OMgetInteger| |dmpToP| |rightTrace| |inf| |failed| |smith| ** + |algebraicDecompose| |OMputBind| |chiSquare1| |LyndonBasis| |/\\| + |showTheFTable| |inRadical?| |cTanh| |lazyGintegrate| |search| + |isobaric?| |approximate| |rischDEsys| |digit?| |\\/| + |possiblyInfinite?| |reindex| |viewThetaDefault| |subResultantChain| + |complex| |solveid| EQ |nullity| |setlast!| |vedf2vef| + |completeHermite| |OMserve| |c02agf| |c06eaf| |build| + |repeatUntilLoop| |removeDuplicates!| |showFortranOutputStack| + |regularRepresentation| |pdct| |torsionIfCan| |rubiksGroup| + |padicallyExpand| |dilog| |e04dgf| |s17agf| |leftFactorIfCan| |iicsch| + |orthonormalBasis| |eigenvector| |index| |imagK| |parameters| + |createRandomElement| |rightLcm| |irreducibleFactors| |diag| + |subResultantsChain| |groebgen| |rightDivide| |atoms| |s18aff| + |defineProperty| |innerint| |stoseInvertibleSetreg| |e01bgf| ^ + |domainOf| |not| |hypergeometric0F1| |stiffnessAndStabilityOfODEIF| + |rroot| |swap| |copyInto!| |magnitude| |block| |d01fcf| + |removeRoughlyRedundantFactorsInPol| |reducedForm| |numberOfFactors| + |constantCoefficientRicDE| |sin| |rightTrim| |d03edf| |tanAn| + |constant?| |numberOfFractionalTerms| |extendIfCan| |seriesSolve| + |laguerreL| |traverse| |cos| |leftTrim| |iilog| |userOrdered?| |cCsc| + |contract| |setTex!| |genericLeftDiscriminant| |HenselLift| |subset?| + |tan| |tubePoints| |totolex| |bat| |d01gaf| |sinIfCan| |f02aef| + |coerceImages| |nthCoef| |cot| |infieldIntegrate| |rowEchelonLocal| + |cosIfCan| |alphabetic| |shrinkable| |omError| |symmetric?| + |contractSolve| |leadingIndex| |monic?| |currentSubProgram| |sec| + |variationOfParameters| |dominantTerm| |elliptic| |probablyZeroDim?| + |removeRedundantFactorsInContents| |high| |rotatez| |imagI| + |fprindINFO| |blankSeparate| |idealiserMatrix| |csc| |innerSolve1| + |normalizeIfCan| |max| |mergeFactors| |curryLeft| |cAcoth| + |viewSizeDefault| |outputMeasure| |sechIfCan| |palgextint0| |li| + |const| |multinomial| |asin| |binomThmExpt| |drawToScale| + |identityMatrix| |leadingExponent| |find| |hermite| |completeHensel| + |c02aff| |makeUnit| |symbolTableOf| |complex?| |acos| + |complexEigenvectors| |integrate| |composite| |readLineIfCan!| + |maxrank| |expenseOfEvaluation| |flexibleArray| |commutativeEquality| + |is?| |primextendedint| |baseRDE| |changeVar| |atan| |solid| + |normal01| |unvectorise| |aLinear| |fortranCharacter| |OMputEndBind| + |internalInfRittWu?| |ignore?| |bernoulliB| |rangeIsFinite| + |prevPrime| |rk4qc| |singularAtInfinity?| |mvar| |isMult| |mapdiv| + |firstSubsetGray| |chvar| |var2Steps| |intChoose| |gcdPolynomial| + |flagFactor| |perfectSquare?| |knownInfBasis| |mpsode| |uniform01| + |imagj| |monomRDE| |s17def| |countRealRoots| |constantKernel| + |monicCompleteDecompose| |adaptive3D?| |expint| |complexRoots| |tanNa| + |rightRankPolynomial| |infLex?| |mapUnivariate| |every?| |imagi| + |insertRoot!| |subresultantSequence| |leftOne| |d01apf| GF2FG + |semiDiscriminantEuclidean| |mulmod| |squareFreePrim| |doubleComplex?| + |point?| |lfinfieldint| |normalizedAssociate| |label| + |setTopPredicate| |terms| |getCurve| |monomials| |findCycle| |s19aaf| + |direction| |pdf2ef| |limit| |inHallBasis?| |dimensions| |entry| + |selectIntegrationRoutines| |squareTop| |messagePrint| |denominators| + |UnVectorise| |screenResolution3D| |clipWithRanges| |key?| |tanQ| + |mainPrimitivePart| |polarCoordinates| |zeroDimensional?| |isOp| + |polygon?| |genericLeftTrace| |linSolve| + |semiDegreeSubResultantEuclidean| |front| |norm| |UP2ifCan| + |optional?| |fullPartialFraction| |move| |fortranDoubleComplex| + |branchPoint?| |physicalLength!| |airyAi| |external?| + |semicolonSeparate| |d02kef| |shellSort| + |zeroSetSplitIntoTriangularSystems| |topFortranOutputStack| + |lastSubResultantEuclidean| |comparison| |exprex| |laguerre| + |printTypes| |concat| |pmComplexintegrate| |s19abf| |finiteBasis| + |mainMonomials| |tryFunctionalDecomposition| |antisymmetric?| + |startStats!| |title| |tableForDiscreteLogarithm| |internalAugment| + |distdfact| |listBranches| |ipow| |test| |ode2| |cycleEntry| |hcrf| + |univariatePolynomialsGcds| |bottom!| |factorAndSplit| |or| + |normalizedDivide| |rules| |semiIndiceSubResultantEuclidean| |f2st| + |fortranLiteral| |OMencodingSGML| |localReal?| |iExquo| + |zeroDimPrimary?| |bandedHessian| |f02bjf| |invertibleSet| |and| + |OMconnInDevice| |triangular?| |clipParametric| |row| |shallowExpand| + |coercePreimagesImages| |complexIntegrate| |halfExtendedResultant2| + |padecf| |rootProduct| |iiacoth| |prefix| |cyclicCopy| + |multiEuclideanTree| |cup| |d01amf| |pointSizeDefault| |cyclic?| + |copies| |iiexp| |redmat| |genericRightNorm| |normalElement| + |complexExpand| |normalDeriv| |nextPrimitiveNormalPoly| |appendPoint| + |morphism| |commonDenominator| |stack| |bsolve| + |unrankImproperPartitions0| |printStats!| |cyclePartition| |tableau| + |useSingleFactorBound| |operators| |f04mcf| |deepCopy| |leadingTerm| + |rightNorm| |option| |totalDegree| |mainVariable?| |randnum| + |sumOfSquares| |asecIfCan| |startTableGcd!| |pop!| |edf2efi| + |maxPoints| |linGenPos| |palgintegrate| |printStatement| |unary?| + |maxrow| |convergents| |conjugates| |precision| |subscriptedVariables| + |selectOrPolynomials| |escape| |BumInSepFFE| |nsqfree| |cCot| + |semiResultantEuclidean2| |makeprod| |setOfMinN| |isList| |upperCase| + |OMread| |shiftRight| |bezoutMatrix| |overlap| |stFunc2| |localAbs| + |dn| |quasiRegular| |retractIfCan| |addPoint2| |basisOfMiddleNucleus| + |expPot| |pmintegrate| |extractPoint| |rightOne| |fractionFreeGauss!| + |testModulus| |resultantnaif| |mainDefiningPolynomial| |indices| + |distFact| |primlimitedint| |normInvertible?| |reverseLex| + |modifyPoint| |dflist| |patternVariable| |cubic| |s17aef| + |trailingCoefficient| |setelt!| |e01bhf| |basis| |c05nbf| |c06ekf| + |replace| |LowTriBddDenomInv| |roughSubIdeal?| |cyclicParents| + |radicalEigenvector| |mathieu24| |hyperelliptic| |makeEq| |elem?| + |primes| |lazyResidueClass| |radicalSolve| + |generalizedContinuumHypothesisAssumed?| |root| |back| + |compactFraction| |e02ddf| |gcdprim| |consnewpol| |showScalarValues| + |varselect| |mainSquareFreePart| |argument| |setOrder| |listexp| + |multiplyCoefficients| |tRange| |rename!| |identitySquareMatrix| + |bits| |power!| |totalfract| |UpTriBddDenomInv| |iidprod| |iiGamma| + |exponential| |toseInvertible?| |preprocess| |setColumn!| + |genericRightDiscriminant| |iomode| |rightPower| |reflect| |fi2df| + |algebraicVariables| |s17adf| |mr| |zeroVector| |difference| + |equality| |leftRankPolynomial| |debug| + |stoseInternalLastSubResultant| |gethi| |splitSquarefree| |space| + |distance| |reducedQPowers| |semiSubResultantGcdEuclidean2| |simpsono| + |besselY| |neglist| |kmax| |setImagSteps| |curryRight| |aromberg| + |LyndonWordsList1| |startTable!| |or?| |linearPolynomials| |heapSort| + |product| |s14baf| |f07aef| |subtractIfCan| |enterPointData| + |unitNormal| |qelt| |romberg| |purelyAlgebraic?| |e02dcf| |wreath| + |low| |returnType!| |qinterval| |clipBoolean| |lifting| |dec| + |algebraicOf| |modulus| |map| |orOperands| |toseSquareFreePart| + |internal?| |nthFactor| |nthFractionalTerm| |rewriteSetWithReduction| + |monomialIntPoly| |e02dff| |pushdterm| |s13aaf| |color| |xRange| + |Vectorise| LODO2FUN |any| |twoFactor| |plotPolar| |rightZero| |Gamma| + |brillhartTrials| |properties| |e01baf| |outputAsTex| |getMatch| + |yRange| |matrixDimensions| |medialSet| |toseLastSubResultant| + |nullary?| |iFTable| |maxdeg| |puiseux| |lllp| |translate| |rightMult| + |argumentList!| |mainCharacterization| |zRange| |complementaryBasis| + |create| |members| |equivOperands| |reduceByQuasiMonic| + |multiplyExponents| |poisson| |createZechTable| + |subResultantGcdEuclidean| |map!| |region| |basisOfLeftNucleus| + |shufflein| |changeNameToObjf| |processTemplate| |symmetricSquare| + |compiledFunction| |inv| |complexElementary| |qsetelt!| |prindINFO| + |writeLine!| |completeSmith| |convert| |matrix| |polyred| |cot2trig| + |rootKerSimp| |fracPart| |s13acf| |ground?| |e02bdf| |unexpand| + |euclideanSize| |maxint| |univcase| |youngGroup| |powerAssociative?| + |diagonalProduct| |subPolSet?| |newSubProgram| |ground| + |var2StepsDefault| |putColorInfo| |OMopenString| |OMreceive| + |minPoints3D| |removeCoshSq| |linearAssociatedLog| |stronglyReduced?| + |po| |currentScope| |fortranComplex| |leadingMonomial| + |isAbsolutelyIrreducible?| |iCompose| |whatInfinity| |float?| + |fixedPointExquo| |removeZeroes| |setRealSteps| |style| |reset| + |split!| |e04jaf| |leadingCoefficient| |intcompBasis| + |prepareSubResAlgo| |exteriorDifferential| |merge| |rur| |graeffe| + |pushuconst| |primitiveMonomials| |slex| |pattern| |getOrder| + |removeRoughlyRedundantFactorsInContents| |btwFact| |parts| |tan2trig| + |acsch| |numberOfOperations| |complexNumericIfCan| |clikeUniv| |rk4f| + |conical| |prepareDecompose| |reductum| |remainder| |integerIfCan| + |edf2fi| |lazyPrem| |mainContent| |bumptab1| |e04naf| |exists?| + |mkcomm| |swapRows!| |quasiAlgebraicSet| |irreducible?| |OMputObject| + |axes| |divergence| |setMaxPoints3D| |prinb| |permanent| + |quasiComponent| |iiperm| |empty?| |void| |c06gcf| |f02awf| |kovacic| + |rquo| |viewPhiDefault| |mapSolve| |checkPrecision| |nextNormalPoly| + |addMatch| |divisors| |bat1| |OMUnknownCD?| |showClipRegion| |ratPoly| + |partialDenominators| |selectOptimizationRoutines| |e02baf| |f04maf| + |rightQuotient| |entries| |s17dhf| |showTypeInOutput| + |prolateSpheroidal| |insertBottom!| |mainValue| |hitherPlane| + |coth2tanh| |sqfrFactor| |calcRanges| |push| |point| |mdeg| + |atanIfCan| |besselJ| |inverseColeman| |OMsetEncoding| + |rationalPoints| |limitPlus| |toroidal| |outputForm| + |integralBasisAtInfinity| |normFactors| + |semiLastSubResultantEuclidean| |polynomialZeros| |implies?| + |shiftRoots| |twist| |problemPoints| |subspace| |explicitlyFinite?| + |dioSolve| |lastSubResultant| |untab| |lowerCase?| |linear| |makeCrit| + |coHeight| |alternatingGroup| |series| |stoseInvertibleSet| + |getDatabase| |unit?| |parametric?| |deepestTail| |length| |print| + |normalise| |write| |cothIfCan| |s13adf| |viewWriteAvailable| + |OMmakeConn| |makeViewport3D| |failed?| |scripts| |removeSinhSq| + |polynomial| |quasiMonicPolynomials| |create3Space| |save| NOT + |primaryDecomp| |modularGcd| |rightGcd| |c06gqf| |dihedralGroup| + |logpart| |colorDef| |normalDenom| |removeSuperfluousCases| OR + |linearlyDependentOverZ?| |signAround| |acscIfCan| |d01gbf| ~= + |torsion?| |exponent| |extendedEuclidean| |continuedFraction| + |stoseInvertible?sqfreg| AND |linearDependence| |min| |pow| + |symmetricGroup| |simplifyLog| |arg1| |d02gbf| |computeInt| + |leftFactor| |ocf2ocdf| |mkPrim| |areEquivalent?| |basisOfLeftNucloid| + |backOldPos| |c06ebf| |equation| |arg2| |polyRDE| |s17dcf| |factors| + |replaceKthElement| |numberOfMonomials| |lfunc| |leftScalarTimes!| + |monicModulo| |extendedIntegrate| |exactQuotient| |realRoots| + |recoverAfterFail| |setLabelValue| |selectAndPolynomials| + |validExponential| |generateIrredPoly| |explicitlyEmpty?| + |perfectNthPower?| |conditions| |mapmult| |birth| |complexForm| + |ODESolve| |clipPointsDefault| |multiple?| |drawStyle| |mainForm| + |e02gaf| |match| |e01bff| |subNode?| |s17ajf| |reducedDiscriminant| + |f07adf| |iiasin| |sPol| |selectsecond| |lazyPquo| |represents| + |getPickedPoints| |stopTable!| |merge!| |declare| |karatsubaOnce| + |maxColIndex| |localIntegralBasis| |OMgetError| |multiEuclidean| + |mapExpon| |symmetricRemainder| |insert| |cPower| |setProperties!| + |output| |polyRicDE| |node?| |separate| |groebner?| |OMwrite| + |tablePow| |s01eaf| |setAttributeButtonStep| |top| |numberOfVariables| + |addmod| |finite?| |removeSuperfluousQuasiComponents| |s18adf| + |endOfFile?| |continue| |mapBivariate| |cAcsc| |sylvesterSequence| + |critMTonD1| * |measure| |number?| |trapezoidal| |op| |compose| |Beta| + |setvalue!| |cot2tan| |inconsistent?| |complexNormalize| |e02daf| + |splitConstant| |acotIfCan| |isPower| |cschIfCan| |hMonic| |leftRank| + |PollardSmallFactor| |associator| |setMinPoints3D| |debug3D| + |setMinPoints| |ef2edf| ~ |extendedint| |fractRadix| + |stoseIntegralLastSubResultant| |idealSimplify| |gderiv| + |bezoutDiscriminant| |positiveRemainder| |lSpaceBasis| |leaf?| + |nullSpace| |hexDigit?| |surface| |roman| |lintgcd| |singularitiesOf| + |coth2trigh| |definingPolynomial| |sort| |iicsc| |rotatex| |initials| + |duplicates?| |supersub| |cAsech| |outputGeneral| |vspace| + |drawCurves| |numeric| |substring?| |viewDeltaXDefault| + |axesColorDefault| |delta| |bumptab| |iiasinh| |binaryTree| + |mindegTerm| |csc2sin| |exprToGenUPS| |rotatey| |property| |hexDigit| + |safeFloor| |gcdPrimitive| |explimitedint| |constructorName| + |factorsOfCyclicGroupSize| |quotient| |s20adf| |OMParseError?| + |internalIntegrate| |antiAssociative?| + |selectMultiDimensionalRoutines| |coshIfCan| |suffix?| + |stopTableInvSet!| |lazyEvaluate| |open| |upperCase!| |cycle| + |autoReduced?| |cfirst| |collectQuasiMonic| |subQuasiComponent?| + |rootPoly| |asinhIfCan| |dom| |elliptic?| + |rewriteIdealWithHeadRemainder| |e02ajf| |minimumExponent| |pquo| + |combineFeatureCompatibility| |branchPointAtInfinity?| + |HermiteIntegrate| |lazy?| |prefix?| |units| |quasiRegular?| |random| + |principal?| |f04axf| |argumentListOf| |lazyPseudoQuotient| + |OMgetEndBind| |lazyVariations| |OMputEndAtp| |SFunction| + |deleteProperty!| |resetNew| |zeroOf| |implies| |wholeRadix| + |rangePascalTriangle| |complexEigenvalues| |setref| |OMencodingBinary| + UTS2UP |elRow2!| |corrPoly| |one?| |expr| |singleFactorBound| |xor| + |qroot| |range| |OMreadStr| |showAll?| |pr2dmp| |revert| |polar| + |OMgetBind| |mathieu11| |complexSolve| |lambda| |sech2cosh| |powern| + |numericalIntegration| |integer?| |OMbindTCP| |radicalOfLeftTraceForm| + |log2| |complexNumeric| |bit?| |airyBi| |possiblyNewVariety?| + |setchildren!| |badNum| |permutationGroup| |numFunEvals| |graphStates| + |someBasis| |code| |pToHdmp| |showArrayValues| |rootDirectory| + |iiacsch| |iicot| |setPrologue!| |f02axf| |listOfLists| + |groebnerIdeal| |iicos| |rightExtendedGcd| |kernels| |squareMatrix| + |infix?| |quotedOperators| |e| |hdmpToP| |changeName| |prem| + |objectOf| |cCos| |solveInField| |generalizedEigenvector| + |splitDenominator| |nextNormalPrimitivePoly| |univariate| |mask| + |positiveSolve| |viewDefaults| |highCommonTerms| |arity| |setrest!| + |pseudoQuotient| |tail| |viewWriteDefault| |stoseInvertibleSetsqfreg| + |s17akf| |in?| |algebraicCoefficients?| |radPoly| |prinshINFO| + |bezoutResultant| |midpoints| |besselK| |socf2socdf| |makeMulti| + |simplifyPower| |noncommutativeJordanAlgebra?| |graphs| |imaginary| + |shift| |showTheSymbolTable| |tab1| |exponents| |viewZoomDefault| + |insertionSort!| |nlde| |irreducibleFactor| |factor| |nor| |leftUnit| + |opeval| |ldf2lst| |hue| |OMputError| |quoted?| |df2fi| |quartic| + |queue| |sqrt| |monicLeftDivide| |setMaxPoints| |closedCurve?| |node| + |cyclotomicDecomposition| |flatten| |cSech| |cycleRagits| + |buildSyntax| |vertConcat| |critBonD| |lfintegrate| |real| |yellow| + |changeThreshhold| |countable?| |say| |tensorProduct| |Lazard2| + |sec2cos| |reduced?| |chebyshevT| |formula| |physicalLength| + |numberOfComputedEntries| |imag| |moebius| |head| |ParCond| + |basisOfRightNucleus| |generalizedContinuumHypothesisAssumed| + |optAttributes| |invmultisect| |completeEchelonBasis| + |basisOfLeftAnnihilator| |identity| |directProduct| |d02gaf| |f01rdf| + |decreasePrecision| |Ci| |readLine!| |select!| |superHeight| |rotate!| + |f07fdf| |f2df| |acot| |OMReadError?| |SturmHabichtCoefficients| + |diophantineSystem| |closeComponent| |extractTop!| |compile| + |exponential1| |rationalPower| |zoom| |makeTerm| |badValues| + |destruct| |asec| |nativeModuleExtension| |cycleLength| |ScanArabic| + |generators| |c06gsf| |leftZero| |modularFactor| |OMputEndAttr| + |option?| |setPoly| |nrows| |acsc| |balancedBinaryTree| |llprop| |cap| + |numberOfImproperPartitions| |createLowComplexityTable| + |goodnessOfFit| |fmecg| |constantLeft| |computeCycleLength| + |OMsupportsSymbol?| |ncols| |sinh| |pushucoef| |extractIfCan| + |palgLODE| |accuracyIF| |deepExpand| |bright| |OMsend| |outerProduct| + |mainMonomial| |loadNativeModule| |radicalEigenvectors| |enumerate| + |laplace| |cosh| |sizeLess?| |roughEqualIdeals?| |f04mbf| |PDESolve| + |superscript| |blue| |s18aef| |toScale| |f01bsf| |mathieu23| + |monomial| |tanh| |iifact| |computeCycleEntry| |OMgetObject| |ratpart| + |makeFloatFunction| |notOperand| |positive?| |rootBound| + |setsubMatrix!| |fractRagits| |multivariate| |coth| |mergeDifference| + |lazyPseudoDivide| |round| |regime| |subResultantGcd| + |degreeSubResultantEuclidean| |inverse| |ksec| |variables| |sech| + |extensionDegree| |isExpt| |decompose| |groebner| |genericPosition| + |divisorCascade| |dequeue| |delete| |lastSubResultantElseSplit| + |ramified?| |expandTrigProducts| |solveRetract| |csch| |pointColor| + |symmetricTensors| |lfextlimint| |tanintegrate| |predicate| + |indicialEquationAtInfinity| |stirling2| |subresultantVector| + |irreducibleRepresentation| |halfExtendedSubResultantGcd2| + |musserTrials| |interval| |asinh| |double| |list| |aQuartic| + |extendedSubResultantGcd| |alphanumeric| |complete| |e02zaf| + |chebyshevU| |cyclotomicFactorization| |sub| |skewSFunction| |car| + |acosh| |showIntensityFunctions| |denominator| |integral?| + |zeroDimPrime?| |initiallyReduced?| |separateFactors| |squareFreePart| + |pol| |dim| |iiatan| |e01sef| |atanh| |infieldint| |cdr| |seed| + |phiCoord| |palginfieldint| |setProperty| |even?| |constantOperator| + |partition| |getProperty| |setDifference| |acoth| |taylor| + |extendedResultant| |hostPlatform| |selectPDERoutines| |palglimint| + |OMgetSymbol| |cylindrical| |changeWeightLevel| + |setLegalFortranSourceExtensions| |leftRecip| |freeOf?| + |createMultiplicationMatrix| |asech| |laurent| |setIntersection| + |adaptive?| |recolor| |startTableInvSet!| |nary?| |goto| + |numberOfNormalPoly| |pushup| |frst| |comp| |setUnion| |errorInfo| + |variable?| |swapColumns!| |karatsubaDivide| |rootNormalize| + |exprHasWeightCosWXorSinWX| |pade| |e02adf| |quote| |overset?| + |f01qdf| |apply| |isTimes| |cAcos| |att2Result| + |genericLeftMinimalPolynomial| BY |nilFactor| |cycles| |rootPower| + |and?| |getRef| |multiple| |declare!| |constantOpIfCan| |nthExpon| + |putGraph| |charpol| |subst| |integralBasis| |completeEval| + |graphCurves| |dAndcExp| |d01bbf| |applyQuote| |latex| |associates?| + |size| |enqueue!| |getButtonValue| |legendre| |log10| + |coerceListOfPairs| |modifyPointData| |heap| |OMputEndBVar| |open?| + |nand| |symbol| |univariate?| |monicDecomposeIfCan| |f04jgf| + |andOperands| |moreAlgebraic?| SEGMENT |getCode| |insert!| |iisqrt2| + |integralMatrix| |postfix| |divideIfCan!| |transcendent?| + |lieAdmissible?| |rightUnit| |cyclicGroup| |SturmHabichtSequence| + |factorials| |e02bcf| |infinityNorm| |movedPoints| |usingTable?| + |lieAlgebra?| |integer| |first| |removeZero| |f01qcf| |center| + |sequences| |totalLex| |tanh2coth| |figureUnits| + |firstUncouplingMatrix| |d02bbf| |listYoungTableaus| + |lazyIrreducibleFactors| |rest| |curry| |LazardQuotient2| F + |quadraticNorm| |bernoulli| |nextPrimitivePoly| |critB| |objects| + |qqq| |laurentRep| |frobenius| |sum| |leftExactQuotient| |substitute| + |firstNumer| |bitCoef| |solveLinearPolynomialEquation| + |semiResultantEuclidean1| |resultantEuclideannaif| |solve| |base| + |setright!| |s18acf| |partialQuotients| |bitLength| |removeDuplicates| + |useEisensteinCriterion?| |fortranLinkerArgs| |basisOfNucleus| |ode| + |close| |leadingCoefficientRicDE| |permutations| + |exprHasAlgebraicWeight| |getGoodPrime| |mapExponents| |nextColeman| + |lepol| |f04arf| |antiCommutative?| |setAdaptive| |inR?| + |fractionPart| |oddlambert| |increase| |redpps| |relativeApprox| + |splitLinear| |viewPosDefault| |totalGroebner| |display| + |unprotectedRemoveRedundantFactors| |trunc| |s17dgf| |reseed| + |constantIfCan| |lowerPolynomial| |binaryTournament| |unitCanonical| + |fintegrate| |iicosh| |rightAlternative?| |dfRange| |e04ucf| + |intensity| |standardBasisOfCyclicSubmodule| |exponentialOrder| + |digamma| |LagrangeInterpolation| |sn| |second| |scripted?| + |wholePart| |localUnquote| |moebiusMu| |epilogue| |generalSqFr| + |ParCondList| |d03faf| |typeLists| |third| |realZeros| |has?| + |segment| |coerce| |definingEquations| |ffactor| |taylorQuoByVar| + |nextPrime| |rowEch| |rdHack1| |subCase?| |abs| |construct| + |leftDivide| |systemSizeIF| |term| |input| |fixedPoints| |hspace| + |clearDenominator| |OMgetEndApp| |uniform| |iipow| |sturmVariationsOf| + |ref| |library| |RittWuCompare| |pastel| |alternative?| |OMputApp| + |fixedDivisor| |child?| |makeViewport2D| |lex| |genericLeftNorm| + |createLowComplexityNormalBasis| |errorKind| |bumprow| + |generalizedInverse| |dimension| |coerceP| |vector| |previous| + |minPoly| |lowerCase| |makeResult| |cons| |RemainderList| + |prinpolINFO| |cyclotomic| |innerSolve| |differentiate| |setPosition| + |OMgetEndAtp| |B1solve| Y |f01maf| |algintegrate| |rationalIfCan| + |approxSqrt| |set| |factorPolynomial| |paren| |reduceLODE| = |weights| + |seriesToOutputForm| |univariateSolve| |unaryFunction| |less?| + |topPredicate| |s14aaf| |modTree| |solve1| + |removeRoughlyRedundantFactorsInPols| |initTable!| |setleaves!| + |negative?| |startPolynomial| < |discriminant| |changeBase| |empty| + |outputList| |allRootsOf| |clipSurface| |subSet| |monomial?| > + |impliesOperands| |shade| |check| |iitan| |LiePoly| |rightTraceMatrix| + |mantissa| |repeating?| <= |closedCurve| |setprevious!| |anfactor| + |invertIfCan| |aCubic| |lookup| |normal?| >= |algebraic?| + |permutation| |e04ycf| |reverse| |trigs| |fortranCarriageReturn| + |primextintfrac| |pointColorDefault| |integralRepresents| |diagonal| + |int| |zerosOf| |reverse!| |tan2cot| |genericLeftTraceForm| + |bringDown| |genus| |linears| |thetaCoord| |summation| + |incrementKthElement| |mainVariables| |setelt| |generator| + + |wrregime| |init| |doubleDisc| + |rewriteSetByReducingWithParticularGenerators| |sinhcosh| |show| + |repSq| |leftUnits| |ptree| |cscIfCan| |box| - |digit| + |rightFactorCandidate| |showTheRoutinesTable| |mapGen| |depth| |zag| + |c06fqf| |OMgetEndAttr| |copy| / |basisOfRightAnnihilator| |parabolic| + |typeList| |tree| |tanhIfCan| |trace| |resize| |radical| |mesh?| + |collectUpper| |pdf2df| |colorFunction| |factorByRecursion| + |expenseOfEvaluationIF| |ideal| |setVariableOrder| |LazardQuotient| + |autoCoerce| |reciprocalPolynomial| |shallowCopy| |taylorIfCan| + |cAtanh| |mapMatrixIfCan| |internalIntegrate0| |functionIsOscillatory| + |homogeneous?| |absolutelyIrreducible?| |OMputInteger| + |transcendenceDegree| |sumSquares| |radicalSimplify| |pleskenSplit| + |symbolIfCan| |sorted?| |rotate| |df2st| |showSummary| |selectfirst| + |redPo| |stronglyReduce| |modularGcdPrimitive| |s21baf| + |numberOfComposites| |kroneckerDelta| |iisech| + |purelyAlgebraicLeadingMonomial?| |conjug| |lo| + |stosePrepareSubResAlgo| |shuffle| |lineColorDefault| + |euclideanGroebner| |showAttributes| |removeConstantTerm| + |rewriteIdealWithQuasiMonicGenerators| |transcendentalDecompose| + |initial| |incr| |zCoord| |randomLC| |f01rcf| |OMgetType| |status| + |OMreadFile| |OMclose| |infiniteProduct| |leviCivitaSymbol| |hi| + |generalizedEigenvectors| |outputAsScript| |rischDE| |viewport2D| + |cycleSplit!| |red| |useEisensteinCriterion| |rootSimp| + |setErrorBound| |inGroundField?| |copy!| |writable?| |normalize| + |wronskianMatrix| |drawComplex| |makingStats?| |intermediateResultsIF| + |recip| |maxPoints3D| |sumOfKthPowerDivisors| + |getMultiplicationMatrix| |setPredicates| |inverseLaplace| |level| + |iicoth| |sumOfDivisors| |bfEntry| |OMgetEndObject| |clip| |An| + |argscript| |triangSolve| |invertible?| |getlo| |numberOfCycles| |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) ((-840) -12 (|has| |#1| (-284)) (|has| |#1| (-840))) ((-851) -3172 (|has| |#1| (-325)) (|has| |#1| (-339)) (|has| |#1| (-284))) ((-930) -12 (|has| |#1| (-930)) (|has| |#1| (-1109))) ((-964 (-383 (-523))) |has| |#1| (-964 (-383 (-523)))) ((-964 (-523)) |has| |#1| (-964 (-523))) ((-964 |#1|) . T) ((-979 #0#) -3172 (|has| |#1| (-325)) (|has| |#1| (-339))) ((-979 |#1|) . T) ((-979 $) . T) ((-973) . T) ((-980) . T) ((-1028) . T) ((-1016) . T) ((-1063) |has| |#1| (-325)) ((-1109) |has| |#1| (-1109)) ((-1112) |has| |#1| (-1109)) ((-1123) . 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T) ((-23) . T) ((-25) . T) ((-37 #0=(-383 (-523))) -3255 (|has| |#1| (-325)) (|has| |#1| (-339))) ((-37 |#1|) . T) ((-37 $) -3255 (|has| |#1| (-515)) (|has| |#1| (-325)) (|has| |#1| (-339)) (|has| |#1| (-284))) ((-34) |has| |#1| (-1109)) ((-91) |has| |#1| (-1109)) ((-97) . T) ((-107 #0# #0#) -3255 (|has| |#1| (-325)) (|has| |#1| (-339))) ((-107 |#1| |#1|) . T) ((-107 $ $) . T) ((-124) . T) ((-134) -3255 (|has| |#1| (-325)) (|has| |#1| (-134))) ((-136) |has| |#1| (-136)) ((-563 (-794)) . T) ((-158) . T) ((-564 (-155 (-203))) |has| |#1| (-949)) ((-564 (-155 (-355))) |has| |#1| (-949)) ((-564 (-499)) |has| |#1| (-564 (-499))) ((-564 (-823 (-355))) |has| |#1| (-564 (-823 (-355)))) ((-564 (-823 (-523))) |has| |#1| (-564 (-823 (-523)))) ((-564 #1=(-1083 |#1|)) . T) ((-209 |#1|) . 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T) ((-37 |#2|) |has| |#2| (-158)) ((-97) -3172 (|has| |#2| (-1016)) (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-732)) (|has| |#2| (-344)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-107 |#2| |#2|) -3172 (|has| |#2| (-973)) (|has| |#2| (-339)) (|has| |#2| (-158))) ((-107 $ $) |has| |#2| (-158)) ((-124) -3172 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-732)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-124))) ((-563 (-794)) -3172 (|has| |#2| (-1016)) (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-732)) (|has| |#2| (-344)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-563 (-794))) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-563 (-1169 |#2|)) . T) ((-158) |has| |#2| (-158)) ((-209 |#2|) |has| |#2| (-973)) ((-211) -12 (|has| |#2| (-211)) (|has| |#2| (-973))) ((-263 #0=(-523) |#2|) . T) ((-265 #0# |#2|) . T) ((-286 |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((-344) |has| |#2| (-344)) ((-353 |#2|) |has| |#2| (-973)) ((-387 |#2|) |has| |#2| (-1016)) ((-462 |#2|) . T) ((-556 #0# |#2|) . T) ((-484 |#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((-591 |#2|) -3172 (|has| |#2| (-973)) (|has| |#2| (-339)) (|has| |#2| (-158))) ((-591 $) -3172 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-158))) ((-585 (-523)) -12 (|has| |#2| (-585 (-523))) (|has| |#2| (-973))) ((-585 |#2|) |has| |#2| (-973)) ((-657 |#2|) -3172 (|has| |#2| (-339)) (|has| |#2| (-158))) ((-666) -3172 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-158))) ((-730) |has| |#2| (-784)) ((-731) -3172 (|has| |#2| (-784)) (|has| |#2| (-732))) ((-732) |has| |#2| (-732)) ((-733) -3172 (|has| |#2| (-784)) (|has| |#2| (-732))) ((-734) -3172 (|has| |#2| (-784)) (|has| |#2| (-732))) ((-784) |has| |#2| (-784)) ((-786) -3172 (|has| |#2| (-784)) (|has| |#2| (-732))) ((-831 (-1087)) -12 (|has| |#2| (-831 (-1087))) (|has| |#2| (-973))) ((-964 (-383 (-523))) -12 (|has| |#2| (-964 (-383 (-523)))) (|has| |#2| (-1016))) ((-964 (-523)) -12 (|has| |#2| (-964 (-523))) (|has| |#2| (-1016))) ((-964 |#2|) |has| |#2| (-1016)) ((-979 |#2|) -3172 (|has| |#2| (-973)) (|has| |#2| (-339)) (|has| |#2| (-158))) ((-979 $) |has| |#2| (-158)) ((-973) -3172 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-158))) ((-980) -3172 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-158))) ((-1028) -3172 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-158))) ((-1016) -3172 (|has| |#2| (-1016)) (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-732)) (|has| |#2| (-344)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-1123) . T) ((-1176 |#2|) |has| |#2| (-339))) -((-4184 (((-218 |#1| |#3|) (-1 |#3| |#2| |#3|) (-218 |#1| |#2|) |#3|) 21)) (-2116 ((|#3| (-1 |#3| |#2| |#3|) (-218 |#1| |#2|) |#3|) 23)) (-1345 (((-218 |#1| |#3|) (-1 |#3| |#2|) (-218 |#1| |#2|)) 18))) -(((-217 |#1| |#2| |#3|) (-10 -7 (-15 -4184 ((-218 |#1| |#3|) (-1 |#3| |#2| |#3|) (-218 |#1| |#2|) |#3|)) (-15 -2116 (|#3| (-1 |#3| |#2| |#3|) (-218 |#1| |#2|) |#3|)) (-15 -1345 ((-218 |#1| |#3|) (-1 |#3| |#2|) (-218 |#1| |#2|)))) (-710) (-1123) (-1123)) (T -217)) -((-1345 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-218 *5 *6)) (-14 *5 (-710)) (-4 *6 (-1123)) (-4 *7 (-1123)) (-5 *2 (-218 *5 *7)) (-5 *1 (-217 *5 *6 *7)))) (-2116 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-218 *5 *6)) (-14 *5 (-710)) (-4 *6 (-1123)) (-4 *2 (-1123)) (-5 *1 (-217 *5 *6 *2)))) (-4184 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-218 *6 *7)) (-14 *6 (-710)) (-4 *7 (-1123)) (-4 *5 (-1123)) (-5 *2 (-218 *6 *5)) (-5 *1 (-217 *6 *7 *5))))) -(-10 -7 (-15 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T) ((-37 |#2|) |has| |#2| (-158)) ((-97) -3255 (|has| |#2| (-1016)) (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-732)) (|has| |#2| (-344)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-107 |#2| |#2|) -3255 (|has| |#2| (-973)) (|has| |#2| (-339)) (|has| |#2| (-158))) ((-107 $ $) |has| |#2| (-158)) ((-124) -3255 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-732)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-124))) ((-563 (-794)) -3255 (|has| |#2| (-1016)) (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-732)) (|has| |#2| (-344)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-563 (-794))) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-563 (-1169 |#2|)) . T) ((-158) |has| |#2| (-158)) ((-209 |#2|) |has| |#2| (-973)) ((-211) -12 (|has| |#2| (-211)) (|has| |#2| (-973))) ((-263 #0=(-523) |#2|) . T) ((-265 #0# |#2|) . T) ((-286 |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((-344) |has| |#2| (-344)) ((-353 |#2|) |has| |#2| (-973)) ((-387 |#2|) |has| |#2| (-1016)) ((-462 |#2|) . T) ((-556 #0# |#2|) . T) ((-484 |#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((-591 |#2|) -3255 (|has| |#2| (-973)) (|has| |#2| (-339)) (|has| |#2| (-158))) ((-591 $) -3255 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-158))) ((-585 (-523)) -12 (|has| |#2| (-585 (-523))) (|has| |#2| (-973))) ((-585 |#2|) |has| |#2| (-973)) ((-657 |#2|) -3255 (|has| |#2| (-339)) (|has| |#2| (-158))) ((-666) -3255 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-158))) ((-730) |has| |#2| (-784)) ((-731) -3255 (|has| |#2| (-784)) (|has| |#2| (-732))) ((-732) |has| |#2| (-732)) ((-733) -3255 (|has| |#2| (-784)) (|has| |#2| (-732))) ((-734) -3255 (|has| |#2| (-784)) (|has| |#2| (-732))) ((-784) |has| |#2| (-784)) ((-786) -3255 (|has| |#2| (-784)) (|has| |#2| (-732))) ((-831 (-1087)) -12 (|has| |#2| (-831 (-1087))) (|has| |#2| (-973))) ((-964 (-383 (-523))) -12 (|has| |#2| (-964 (-383 (-523)))) (|has| |#2| (-1016))) ((-964 (-523)) -12 (|has| |#2| (-964 (-523))) (|has| |#2| (-1016))) ((-964 |#2|) |has| |#2| (-1016)) ((-979 |#2|) -3255 (|has| |#2| (-973)) (|has| |#2| (-339)) (|has| |#2| (-158))) ((-979 $) |has| |#2| (-158)) ((-973) -3255 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-158))) ((-980) -3255 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-158))) ((-1028) -3255 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-158))) ((-1016) -3255 (|has| |#2| (-1016)) (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-732)) (|has| |#2| (-344)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-1123) . 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T) ((-23) . T) ((-46 |#1| |#4|) . T) ((-25) . T) ((-37 #0=(-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((-37 |#1|) |has| |#1| (-158)) ((-37 $) -3172 (|has| |#1| (-840)) (|has| |#1| (-515)) (|has| |#1| (-427))) ((-97) . T) ((-107 #0# #0#) |has| |#1| (-37 (-383 (-523)))) ((-107 |#1| |#1|) . T) ((-107 $ $) -3172 (|has| |#1| (-840)) (|has| |#1| (-515)) (|has| |#1| (-427)) (|has| |#1| (-158))) ((-124) . T) ((-134) |has| |#1| (-134)) ((-136) |has| |#1| (-136)) ((-563 (-794)) . T) ((-158) -3172 (|has| |#1| (-840)) (|has| |#1| (-515)) (|has| |#1| (-427)) (|has| |#1| (-158))) ((-564 (-499)) -12 (|has| |#1| (-564 (-499))) (|has| |#3| (-564 (-499)))) ((-564 (-823 (-355))) -12 (|has| |#1| (-564 (-823 (-355)))) (|has| |#3| (-564 (-823 (-355))))) ((-564 (-823 (-523))) -12 (|has| |#1| (-564 (-823 (-523)))) (|has| |#3| (-564 (-823 (-523))))) ((-209 |#1|) . T) ((-211) |has| |#1| (-211)) ((-267) -3172 (|has| |#1| (-840)) (|has| |#1| (-515)) (|has| |#1| (-427))) ((-286 $) . T) ((-302 |#1| |#4|) . T) ((-353 |#1|) . T) ((-387 |#1|) . T) ((-427) -3172 (|has| |#1| (-840)) (|has| |#1| (-427))) ((-484 |#2| |#1|) |has| |#1| (-211)) ((-484 |#2| $) |has| |#1| (-211)) ((-484 |#3| |#1|) . T) ((-484 |#3| $) . T) ((-484 $ $) . T) ((-515) -3172 (|has| |#1| (-840)) (|has| |#1| (-515)) (|has| |#1| (-427))) ((-591 #0#) |has| |#1| (-37 (-383 (-523)))) ((-591 |#1|) . T) ((-591 $) . T) ((-585 (-523)) |has| |#1| (-585 (-523))) ((-585 |#1|) . T) ((-657 #0#) |has| |#1| (-37 (-383 (-523)))) ((-657 |#1|) |has| |#1| (-158)) ((-657 $) -3172 (|has| |#1| (-840)) (|has| |#1| (-515)) (|has| |#1| (-427))) ((-666) . T) ((-786) |has| |#1| (-786)) ((-831 (-1087)) |has| |#1| (-831 (-1087))) ((-831 |#3|) . T) ((-817 (-355)) -12 (|has| |#1| (-817 (-355))) (|has| |#3| (-817 (-355)))) ((-817 (-523)) -12 (|has| |#1| (-817 (-523))) (|has| |#3| (-817 (-523)))) ((-880 |#1| |#4| |#3|) . 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T) ((-23) . T) ((-46 |#1| |#4|) . T) ((-25) . T) ((-37 #0=(-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((-37 |#1|) |has| |#1| (-158)) ((-37 $) -3255 (|has| |#1| (-840)) (|has| |#1| (-515)) (|has| |#1| (-427))) ((-97) . T) ((-107 #0# #0#) |has| |#1| (-37 (-383 (-523)))) ((-107 |#1| |#1|) . T) ((-107 $ $) -3255 (|has| |#1| (-840)) (|has| |#1| (-515)) (|has| |#1| (-427)) (|has| |#1| (-158))) ((-124) . T) ((-134) |has| |#1| (-134)) ((-136) |has| |#1| (-136)) ((-563 (-794)) . T) ((-158) -3255 (|has| |#1| (-840)) (|has| |#1| (-515)) (|has| |#1| (-427)) (|has| |#1| (-158))) ((-564 (-499)) -12 (|has| |#1| (-564 (-499))) (|has| |#3| (-564 (-499)))) ((-564 (-823 (-355))) -12 (|has| |#1| (-564 (-823 (-355)))) (|has| |#3| (-564 (-823 (-355))))) ((-564 (-823 (-523))) -12 (|has| |#1| (-564 (-823 (-523)))) (|has| |#3| (-564 (-823 (-523))))) ((-209 |#1|) . T) ((-211) |has| |#1| (-211)) ((-267) -3255 (|has| |#1| (-840)) (|has| |#1| (-515)) (|has| |#1| (-427))) ((-286 $) . T) ((-302 |#1| |#4|) . 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T) ((-102 #0=(-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T) ((-97) -3172 (|has| |#2| (-1016)) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-1016))) ((-563 (-794)) -3172 (|has| |#2| (-1016)) (|has| |#2| (-563 (-794))) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-1016)) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-563 (-794)))) ((-140 #0#) . T) ((-564 (-499)) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-564 (-499))) ((-207 #0#) . T) ((-213 #0#) . T) ((-263 |#1| |#2|) . T) ((-265 |#1| |#2|) . T) ((-286 #0#) -12 (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)))) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-1016))) ((-286 |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((-462 #0#) . T) ((-462 |#2|) . T) ((-556 |#1| |#2|) . T) ((-484 #0# #0#) -12 (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)))) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-1016))) ((-484 |#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((-560 |#1| |#2|) . T) ((-1016) -3172 (|has| |#2| (-1016)) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-1016))) ((-1123) . 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T) ((-23) . T) ((-46 |#1| #0=(-710)) . T) ((-25) . T) ((-37 #1=(-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((-37 |#1|) |has| |#1| (-158)) ((-37 $) -3255 (|has| |#1| (-840)) (|has| |#1| (-515)) (|has| |#1| (-427)) (|has| |#1| (-339))) ((-97) . T) ((-107 #1# #1#) |has| |#1| (-37 (-383 (-523)))) ((-107 |#1| |#1|) . T) ((-107 $ $) -3255 (|has| |#1| (-840)) (|has| |#1| (-515)) (|has| |#1| (-427)) (|has| |#1| (-339)) (|has| |#1| (-158))) ((-124) . T) ((-134) |has| |#1| (-134)) ((-136) |has| |#1| (-136)) ((-563 (-794)) . T) ((-158) -3255 (|has| |#1| (-840)) (|has| |#1| (-515)) (|has| |#1| (-427)) (|has| |#1| (-339)) (|has| |#1| (-158))) ((-564 (-499)) -12 (|has| (-1001) (-564 (-499))) (|has| |#1| (-564 (-499)))) ((-564 (-823 (-355))) -12 (|has| (-1001) (-564 (-823 (-355)))) (|has| |#1| (-564 (-823 (-355))))) ((-564 (-823 (-523))) -12 (|has| (-1001) (-564 (-823 (-523)))) (|has| |#1| (-564 (-823 (-523))))) ((-209 |#1|) . T) ((-211) . T) ((-263 (-383 $) (-383 $)) |has| |#1| (-515)) ((-263 |#1| |#1|) . T) ((-263 $ $) . T) ((-267) -3255 (|has| |#1| (-840)) (|has| |#1| (-515)) (|has| |#1| (-427)) (|has| |#1| (-339))) ((-284) |has| |#1| (-339)) ((-286 $) . T) ((-302 |#1| #0#) . T) ((-353 |#1|) . T) ((-387 |#1|) . T) ((-427) -3255 (|has| |#1| (-840)) (|has| |#1| (-427)) (|has| |#1| (-339))) ((-484 #2=(-1001) |#1|) . T) ((-484 #2# $) . T) ((-484 $ $) . T) ((-515) -3255 (|has| |#1| (-840)) (|has| |#1| (-515)) (|has| |#1| (-427)) (|has| |#1| (-339))) ((-591 #1#) |has| |#1| (-37 (-383 (-523)))) ((-591 |#1|) . T) ((-591 $) . T) ((-585 (-523)) |has| |#1| (-585 (-523))) ((-585 |#1|) . T) ((-657 #1#) |has| |#1| (-37 (-383 (-523)))) ((-657 |#1|) |has| |#1| (-158)) ((-657 $) -3255 (|has| |#1| (-840)) (|has| |#1| (-515)) (|has| |#1| (-427)) (|has| |#1| (-339))) ((-666) . T) ((-786) |has| |#1| (-786)) ((-831 #2#) . 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3122870 "XPR" 3123961 NIL XPR (NIL T T) -8 NIL NIL) (-1189 3118673 3120294 3120497 "XPOLY" 3120790 NIL XPOLY (NIL T) -8 NIL NIL) (-1188 3116487 3117865 3117919 "XPOLYC" 3118204 NIL XPOLYC (NIL T T) -9 NIL 3118317) (-1187 3112859 3115004 3115392 "XPBWPOLY" 3116145 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1186 3108787 3111100 3111142 "XF" 3111763 NIL XF (NIL T) -9 NIL 3112162) (-1185 3108408 3108496 3108665 "XF-" 3108670 NIL XF- (NIL T T) -8 NIL NIL) (-1184 3103788 3105087 3105141 "XFALG" 3107289 NIL XFALG (NIL T T) -9 NIL 3108076) (-1183 3102925 3103029 3103233 "XEXPPKG" 3103680 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1182 3101024 3102776 3102871 "XDPOLY" 3102876 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1181 3099903 3100513 3100555 "XALG" 3100617 NIL XALG (NIL T) -9 NIL 3100736) (-1180 3093379 3097887 3098380 "WUTSET" 3099495 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1179 3091191 3091998 3092349 "WP" 3093161 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1178 3090077 3090275 3090570 "WFFINTBS" 3090988 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1177 3087981 3088408 3088870 "WEIER" 3089649 NIL WEIER (NIL T) -7 NIL NIL) (-1176 3087130 3087554 3087596 "VSPACE" 3087732 NIL VSPACE (NIL T) -9 NIL 3087806) (-1175 3086968 3086995 3087086 "VSPACE-" 3087091 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1174 3086714 3086757 3086828 "VOID" 3086919 T VOID (NIL) -8 NIL NIL) (-1173 3084850 3085209 3085615 "VIEW" 3086330 T VIEW (NIL) -7 NIL NIL) (-1172 3081275 3081913 3082650 "VIEWDEF" 3084135 T VIEWDEF (NIL) -7 NIL NIL) (-1171 3070614 3072823 3074996 "VIEW3D" 3079124 T VIEW3D (NIL) -8 NIL NIL) (-1170 3062896 3064525 3066104 "VIEW2D" 3069057 T VIEW2D (NIL) -8 NIL NIL) (-1169 3058305 3062666 3062758 "VECTOR" 3062839 NIL VECTOR (NIL T) -8 NIL NIL) (-1168 3056882 3057141 3057459 "VECTOR2" 3058035 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1167 3050422 3054674 3054717 "VECTCAT" 3055705 NIL VECTCAT (NIL T) -9 NIL 3056289) (-1166 3049436 3049690 3050080 "VECTCAT-" 3050085 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1165 3048917 3049087 3049207 "VARIABLE" 3049351 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1164 3048850 3048855 3048885 "UTYPE" 3048890 T UTYPE (NIL) -9 NIL NIL) (-1163 3047685 3047839 3048100 "UTSODETL" 3048676 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1162 3045125 3045585 3046109 "UTSODE" 3047226 NIL UTSODE (NIL T T) -7 NIL NIL) (-1161 3036969 3042765 3043253 "UTS" 3044694 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1160 3028314 3033679 3033721 "UTSCAT" 3034822 NIL UTSCAT (NIL T) -9 NIL 3035579) (-1159 3025669 3026385 3027373 "UTSCAT-" 3027378 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1158 3025300 3025343 3025474 "UTS2" 3025620 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1157 3019576 3022141 3022184 "URAGG" 3024254 NIL URAGG (NIL T) -9 NIL 3024976) (-1156 3016515 3017378 3018501 "URAGG-" 3018506 NIL URAGG- (NIL T T) -8 NIL NIL) (-1155 3012201 3015132 3015603 "UPXSSING" 3016179 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1154 3004092 3011322 3011602 "UPXS" 3011978 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1153 2997121 3003997 3004068 "UPXSCONS" 3004073 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1152 2987410 2994240 2994301 "UPXSCCA" 2994950 NIL UPXSCCA (NIL T T) -9 NIL 2995191) (-1151 2987049 2987134 2987307 "UPXSCCA-" 2987312 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1150 2977260 2983863 2983905 "UPXSCAT" 2984548 NIL UPXSCAT (NIL T) -9 NIL 2985156) (-1149 2976694 2976773 2976950 "UPXS2" 2977175 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1148 2975348 2975601 2975952 "UPSQFREE" 2976437 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1147 2969239 2972294 2972348 "UPSCAT" 2973497 NIL UPSCAT (NIL T T) -9 NIL 2974271) (-1146 2968444 2968651 2968977 "UPSCAT-" 2968982 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1145 2954530 2962567 2962609 "UPOLYC" 2964687 NIL UPOLYC (NIL T) -9 NIL 2965908) (-1144 2945860 2948285 2951431 "UPOLYC-" 2951436 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1143 2945491 2945534 2945665 "UPOLYC2" 2945811 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1142 2936910 2945060 2945197 "UP" 2945401 NIL UP (NIL NIL T) -8 NIL NIL) (-1141 2936253 2936360 2936523 "UPMP" 2936799 NIL UPMP (NIL T T) -7 NIL NIL) (-1140 2935806 2935887 2936026 "UPDIVP" 2936166 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1139 2934374 2934623 2934939 "UPDECOMP" 2935555 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1138 2933609 2933721 2933906 "UPCDEN" 2934258 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1137 2933132 2933201 2933348 "UP2" 2933534 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1136 2931649 2932336 2932613 "UNISEG" 2932890 NIL UNISEG (NIL T) -8 NIL NIL) (-1135 2930864 2930991 2931196 "UNISEG2" 2931492 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1134 2929924 2930104 2930330 "UNIFACT" 2930680 NIL UNIFACT (NIL T) -7 NIL NIL) (-1133 2913820 2929105 2929355 "ULS" 2929731 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1132 2901785 2913725 2913796 "ULSCONS" 2913801 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1131 2884535 2896548 2896609 "ULSCCAT" 2897321 NIL ULSCCAT (NIL T T) -9 NIL 2897617) (-1130 2883586 2883831 2884218 "ULSCCAT-" 2884223 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1129 2873576 2880093 2880135 "ULSCAT" 2880991 NIL ULSCAT (NIL T) -9 NIL 2881721) (-1128 2873010 2873089 2873266 "ULS2" 2873491 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1127 2871408 2872375 2872405 "UFD" 2872617 T UFD (NIL) -9 NIL 2872731) (-1126 2871202 2871248 2871343 "UFD-" 2871348 NIL UFD- (NIL T) -8 NIL NIL) (-1125 2870284 2870467 2870683 "UDVO" 2871008 T UDVO (NIL) -7 NIL NIL) (-1124 2868100 2868509 2868980 "UDPO" 2869848 NIL UDPO (NIL T) -7 NIL NIL) (-1123 2868033 2868038 2868068 "TYPE" 2868073 T TYPE (NIL) -9 NIL NIL) (-1122 2867004 2867206 2867446 "TWOFACT" 2867827 NIL TWOFACT (NIL T) -7 NIL NIL) (-1121 2865942 2866279 2866542 "TUPLE" 2866776 NIL TUPLE (NIL T) -8 NIL NIL) (-1120 2863633 2864152 2864691 "TUBETOOL" 2865425 T TUBETOOL (NIL) -7 NIL NIL) (-1119 2862482 2862687 2862928 "TUBE" 2863426 NIL TUBE (NIL T) -8 NIL NIL) (-1118 2857206 2861460 2861742 "TS" 2862234 NIL TS (NIL T) -8 NIL NIL) (-1117 2845910 2850002 2850098 "TSETCAT" 2855332 NIL TSETCAT (NIL T T T T) -9 NIL 2856863) (-1116 2840645 2842243 2844133 "TSETCAT-" 2844138 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1115 2834908 2835754 2836696 "TRMANIP" 2839781 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1114 2834349 2834412 2834575 "TRIMAT" 2834840 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1113 2832155 2832392 2832755 "TRIGMNIP" 2834098 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1112 2831675 2831788 2831818 "TRIGCAT" 2832031 T TRIGCAT (NIL) -9 NIL NIL) (-1111 2831344 2831423 2831564 "TRIGCAT-" 2831569 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1110 2828243 2830204 2830484 "TREE" 2831099 NIL TREE (NIL T) -8 NIL NIL) (-1109 2827517 2828045 2828075 "TRANFUN" 2828110 T TRANFUN (NIL) -9 NIL 2828176) (-1108 2826796 2826987 2827267 "TRANFUN-" 2827272 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1107 2826600 2826632 2826693 "TOPSP" 2826757 T TOPSP (NIL) -7 NIL NIL) (-1106 2825952 2826067 2826220 "TOOLSIGN" 2826481 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1105 2824613 2825129 2825368 "TEXTFILE" 2825735 T TEXTFILE (NIL) -8 NIL NIL) (-1104 2822478 2822992 2823430 "TEX" 2824197 T TEX (NIL) -8 NIL NIL) (-1103 2822259 2822290 2822362 "TEX1" 2822441 NIL TEX1 (NIL T) -7 NIL NIL) (-1102 2821907 2821970 2822060 "TEMUTL" 2822191 T TEMUTL (NIL) -7 NIL NIL) (-1101 2820061 2820341 2820666 "TBCMPPK" 2821630 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1100 2811950 2818222 2818278 "TBAGG" 2818678 NIL TBAGG (NIL T T) -9 NIL 2818889) (-1099 2807020 2808508 2810262 "TBAGG-" 2810267 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1098 2806404 2806511 2806656 "TANEXP" 2806909 NIL TANEXP (NIL T) -7 NIL NIL) (-1097 2799905 2806261 2806354 "TABLE" 2806359 NIL TABLE (NIL T T) -8 NIL NIL) (-1096 2799318 2799416 2799554 "TABLEAU" 2799802 NIL TABLEAU (NIL T) -8 NIL NIL) (-1095 2793926 2795146 2796394 "TABLBUMP" 2798104 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1094 2793354 2793454 2793582 "SYSTEM" 2793820 T SYSTEM (NIL) -7 NIL NIL) (-1093 2789817 2790512 2791295 "SYSSOLP" 2792605 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1092 2786108 2786816 2787550 "SYNTAX" 2789105 T SYNTAX (NIL) -8 NIL NIL) (-1091 2783242 2783850 2784488 "SYMTAB" 2785492 T SYMTAB (NIL) -8 NIL NIL) (-1090 2778491 2779393 2780376 "SYMS" 2782281 T SYMS (NIL) -8 NIL NIL) (-1089 2775724 2777951 2778180 "SYMPOLY" 2778296 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1088 2775244 2775319 2775441 "SYMFUNC" 2775636 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1087 2771221 2772481 2773303 "SYMBOL" 2774444 T SYMBOL (NIL) -8 NIL NIL) (-1086 2764760 2766449 2768169 "SWITCH" 2769523 T SWITCH (NIL) -8 NIL NIL) (-1085 2757990 2763587 2763889 "SUTS" 2764515 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1084 2749880 2757111 2757391 "SUPXS" 2757767 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1083 2741372 2749501 2749626 "SUP" 2749789 NIL SUP (NIL T) -8 NIL NIL) (-1082 2740531 2740658 2740875 "SUPFRACF" 2741240 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1081 2740156 2740215 2740326 "SUP2" 2740466 NIL SUP2 (NIL T T) -7 NIL NIL) (-1080 2738574 2738848 2739210 "SUMRF" 2739855 NIL SUMRF (NIL T) -7 NIL NIL) (-1079 2737891 2737957 2738155 "SUMFS" 2738495 NIL SUMFS (NIL T T) -7 NIL NIL) (-1078 2721827 2737072 2737322 "SULS" 2737698 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1077 2721149 2721352 2721492 "SUCH" 2721735 NIL SUCH (NIL T T) -8 NIL NIL) (-1076 2715076 2716088 2717046 "SUBSPACE" 2720237 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1075 2714506 2714596 2714760 "SUBRESP" 2714964 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1074 2707875 2709171 2710482 "STTF" 2713242 NIL STTF (NIL T) -7 NIL NIL) (-1073 2702048 2703168 2704315 "STTFNC" 2706775 NIL STTFNC (NIL T) -7 NIL NIL) (-1072 2693399 2695266 2697059 "STTAYLOR" 2700289 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1071 2686643 2693263 2693346 "STRTBL" 2693351 NIL STRTBL (NIL T) -8 NIL NIL) (-1070 2682034 2686598 2686629 "STRING" 2686634 T STRING (NIL) -8 NIL NIL) (-1069 2676923 2681408 2681438 "STRICAT" 2681497 T STRICAT (NIL) -9 NIL 2681559) (-1068 2669639 2674446 2675066 "STREAM" 2676338 NIL STREAM (NIL T) -8 NIL NIL) (-1067 2669149 2669226 2669370 "STREAM3" 2669556 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1066 2668131 2668314 2668549 "STREAM2" 2668962 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1065 2667819 2667871 2667964 "STREAM1" 2668073 NIL STREAM1 (NIL T) -7 NIL NIL) (-1064 2666835 2667016 2667247 "STINPROD" 2667635 NIL STINPROD (NIL T) -7 NIL NIL) (-1063 2666414 2666598 2666628 "STEP" 2666708 T STEP (NIL) -9 NIL 2666786) (-1062 2659957 2666313 2666390 "STBL" 2666395 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1061 2655133 2659180 2659223 "STAGG" 2659376 NIL STAGG (NIL T) -9 NIL 2659465) (-1060 2652835 2653437 2654309 "STAGG-" 2654314 NIL STAGG- (NIL T T) -8 NIL NIL) (-1059 2651030 2652605 2652697 "STACK" 2652778 NIL STACK (NIL T) -8 NIL NIL) (-1058 2643761 2649177 2649632 "SREGSET" 2650660 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1057 2636201 2637569 2639081 "SRDCMPK" 2642367 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1056 2629169 2633642 2633672 "SRAGG" 2634975 T SRAGG (NIL) -9 NIL 2635583) (-1055 2628186 2628441 2628820 "SRAGG-" 2628825 NIL SRAGG- (NIL T) -8 NIL NIL) (-1054 2622635 2627105 2627532 "SQMATRIX" 2627805 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1053 2616387 2619355 2620081 "SPLTREE" 2621981 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1052 2612377 2613043 2613689 "SPLNODE" 2615813 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1051 2611424 2611657 2611687 "SPFCAT" 2612131 T SPFCAT (NIL) -9 NIL NIL) (-1050 2610161 2610371 2610635 "SPECOUT" 2611182 T SPECOUT (NIL) -7 NIL NIL) (-1049 2609922 2609962 2610031 "SPADPRSR" 2610114 T SPADPRSR (NIL) -7 NIL NIL) (-1048 2601945 2603692 2603734 "SPACEC" 2608057 NIL SPACEC (NIL T) -9 NIL 2609873) (-1047 2600117 2601878 2601926 "SPACE3" 2601931 NIL SPACE3 (NIL T) -8 NIL NIL) (-1046 2598869 2599040 2599331 "SORTPAK" 2599922 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1045 2596925 2597228 2597646 "SOLVETRA" 2598533 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1044 2595936 2596158 2596432 "SOLVESER" 2596698 NIL SOLVESER (NIL T) -7 NIL NIL) (-1043 2591156 2592037 2593039 "SOLVERAD" 2594988 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1042 2586971 2587580 2588309 "SOLVEFOR" 2590523 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1041 2581271 2586323 2586419 "SNTSCAT" 2586424 NIL SNTSCAT (NIL T T T T) -9 NIL 2586494) (-1040 2575375 2579602 2579992 "SMTS" 2580961 NIL SMTS (NIL T T T) -8 NIL NIL) (-1039 2569785 2575264 2575340 "SMP" 2575345 NIL SMP (NIL T T) -8 NIL NIL) (-1038 2567944 2568245 2568643 "SMITH" 2569482 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1037 2560909 2565105 2565207 "SMATCAT" 2566547 NIL SMATCAT (NIL NIL T T T) -9 NIL 2567096) (-1036 2557850 2558673 2559850 "SMATCAT-" 2559855 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1035 2555564 2557087 2557130 "SKAGG" 2557391 NIL SKAGG (NIL T) -9 NIL 2557526) (-1034 2551622 2554668 2554946 "SINT" 2555308 T SINT (NIL) -8 NIL NIL) (-1033 2551394 2551432 2551498 "SIMPAN" 2551578 T SIMPAN (NIL) -7 NIL NIL) (-1032 2550232 2550453 2550728 "SIGNRF" 2551153 NIL SIGNRF (NIL T) -7 NIL NIL) (-1031 2549041 2549192 2549482 "SIGNEF" 2550061 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1030 2546731 2547185 2547691 "SHP" 2548582 NIL SHP (NIL T NIL) -7 NIL NIL) (-1029 2540584 2546632 2546708 "SHDP" 2546713 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1028 2540074 2540266 2540296 "SGROUP" 2540448 T SGROUP (NIL) -9 NIL 2540535) (-1027 2539844 2539896 2540000 "SGROUP-" 2540005 NIL SGROUP- (NIL T) -8 NIL NIL) (-1026 2536680 2537377 2538100 "SGCF" 2539143 T SGCF (NIL) -7 NIL NIL) (-1025 2531079 2536131 2536227 "SFRTCAT" 2536232 NIL SFRTCAT (NIL T T T T) -9 NIL 2536270) (-1024 2524539 2525554 2526688 "SFRGCD" 2530062 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1023 2517705 2518776 2519960 "SFQCMPK" 2523472 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1022 2517327 2517416 2517526 "SFORT" 2517646 NIL SFORT (NIL T T) -8 NIL NIL) (-1021 2516472 2517167 2517288 "SEXOF" 2517293 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1020 2515606 2516353 2516421 "SEX" 2516426 T SEX (NIL) -8 NIL NIL) (-1019 2510383 2511072 2511167 "SEXCAT" 2514938 NIL SEXCAT (NIL T T T T T) -9 NIL 2515557) (-1018 2507563 2510317 2510365 "SET" 2510370 NIL SET (NIL T) -8 NIL NIL) (-1017 2505814 2506276 2506581 "SETMN" 2507304 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1016 2505422 2505548 2505578 "SETCAT" 2505695 T SETCAT (NIL) -9 NIL 2505779) (-1015 2505202 2505254 2505353 "SETCAT-" 2505358 NIL SETCAT- (NIL T) -8 NIL NIL) (-1014 2501590 2503664 2503707 "SETAGG" 2504577 NIL SETAGG (NIL T) -9 NIL 2504917) (-1013 2501048 2501164 2501401 "SETAGG-" 2501406 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1012 2500252 2500545 2500606 "SEGXCAT" 2500892 NIL SEGXCAT (NIL T T) -9 NIL 2501012) (-1011 2499308 2499918 2500100 "SEG" 2500105 NIL SEG (NIL T) -8 NIL NIL) (-1010 2498215 2498428 2498471 "SEGCAT" 2499053 NIL SEGCAT (NIL T) -9 NIL 2499291) (-1009 2497264 2497594 2497794 "SEGBIND" 2498050 NIL SEGBIND (NIL T) -8 NIL NIL) (-1008 2496885 2496944 2497057 "SEGBIND2" 2497199 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1007 2496104 2496230 2496434 "SEG2" 2496729 NIL SEG2 (NIL T T) -7 NIL NIL) (-1006 2495541 2496039 2496086 "SDVAR" 2496091 NIL SDVAR (NIL T) -8 NIL NIL) (-1005 2487793 2495314 2495442 "SDPOL" 2495447 NIL SDPOL (NIL T) -8 NIL NIL) (-1004 2486386 2486652 2486971 "SCPKG" 2487508 NIL SCPKG (NIL T) -7 NIL NIL) (-1003 2485523 2485702 2485902 "SCOPE" 2486208 T SCOPE (NIL) -8 NIL NIL) (-1002 2484744 2484877 2485056 "SCACHE" 2485378 NIL SCACHE (NIL T) -7 NIL NIL) (-1001 2484183 2484504 2484589 "SAOS" 2484681 T SAOS (NIL) -8 NIL NIL) (-1000 2483748 2483783 2483956 "SAERFFC" 2484142 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-999 2477644 2483647 2483725 "SAE" 2483730 NIL SAE (NIL T T NIL) -8 NIL NIL) (-998 2477240 2477275 2477432 "SAEFACT" 2477603 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-997 2475566 2475880 2476279 "RURPK" 2476906 NIL RURPK (NIL T NIL) -7 NIL NIL) (-996 2474219 2474496 2474803 "RULESET" 2475402 NIL RULESET (NIL T T T) -8 NIL NIL) (-995 2471427 2471930 2472391 "RULE" 2473901 NIL RULE (NIL T T T) -8 NIL NIL) (-994 2471069 2471224 2471305 "RULECOLD" 2471379 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-993 2465961 2466755 2467671 "RSETGCD" 2470268 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-992 2455276 2460328 2460422 "RSETCAT" 2464487 NIL RSETCAT (NIL T T T T) -9 NIL 2465584) (-991 2453207 2453746 2454566 "RSETCAT-" 2454571 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-990 2445637 2447012 2448528 "RSDCMPK" 2451806 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-989 2443655 2444096 2444168 "RRCC" 2445244 NIL RRCC (NIL T T) -9 NIL 2445588) (-988 2443009 2443183 2443459 "RRCC-" 2443464 NIL RRCC- (NIL T T T) -8 NIL NIL) (-987 2417376 2427001 2427065 "RPOLCAT" 2437567 NIL RPOLCAT (NIL T T T) -9 NIL 2440725) (-986 2408880 2411218 2414336 "RPOLCAT-" 2414341 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-985 2399946 2407110 2407590 "ROUTINE" 2408420 T ROUTINE (NIL) -8 NIL NIL) (-984 2396651 2399502 2399649 "ROMAN" 2399819 T ROMAN (NIL) -8 NIL NIL) (-983 2394937 2395522 2395779 "ROIRC" 2396457 NIL ROIRC (NIL T T) -8 NIL NIL) (-982 2391342 2393646 2393674 "RNS" 2393970 T RNS (NIL) -9 NIL 2394240) (-981 2389856 2390239 2390770 "RNS-" 2390843 NIL RNS- (NIL T) -8 NIL NIL) (-980 2389282 2389690 2389718 "RNG" 2389723 T RNG (NIL) -9 NIL 2389744) (-979 2388680 2389042 2389082 "RMODULE" 2389142 NIL RMODULE (NIL T) -9 NIL 2389184) (-978 2387532 2387626 2387956 "RMCAT2" 2388581 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-977 2384246 2386715 2387036 "RMATRIX" 2387267 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-976 2377243 2379477 2379589 "RMATCAT" 2382898 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2383880) (-975 2376622 2376769 2377072 "RMATCAT-" 2377077 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-974 2376192 2376267 2376393 "RINTERP" 2376541 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-973 2375243 2375807 2375835 "RING" 2375945 T RING (NIL) -9 NIL 2376039) (-972 2375038 2375082 2375176 "RING-" 2375181 NIL RING- (NIL T) -8 NIL NIL) (-971 2373886 2374123 2374379 "RIDIST" 2374802 T RIDIST (NIL) -7 NIL NIL) (-970 2365208 2373360 2373563 "RGCHAIN" 2373735 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-969 2362213 2362827 2363495 "RF" 2364572 NIL RF (NIL T) -7 NIL NIL) (-968 2361862 2361925 2362026 "RFFACTOR" 2362144 NIL RFFACTOR (NIL T) -7 NIL NIL) (-967 2361590 2361625 2361720 "RFFACT" 2361821 NIL RFFACT (NIL T) -7 NIL NIL) (-966 2359720 2360084 2360464 "RFDIST" 2361230 T RFDIST (NIL) -7 NIL NIL) (-965 2359178 2359270 2359430 "RETSOL" 2359622 NIL RETSOL (NIL T T) -7 NIL NIL) (-964 2358771 2358851 2358892 "RETRACT" 2359082 NIL RETRACT (NIL T) -9 NIL NIL) (-963 2358623 2358648 2358732 "RETRACT-" 2358737 NIL RETRACT- (NIL T T) -8 NIL NIL) (-962 2351481 2358280 2358405 "RESULT" 2358518 T RESULT (NIL) -8 NIL NIL) (-961 2350066 2350755 2350952 "RESRING" 2351384 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-960 2349706 2349755 2349851 "RESLATC" 2350003 NIL RESLATC (NIL T) -7 NIL NIL) (-959 2349415 2349449 2349554 "REPSQ" 2349665 NIL REPSQ (NIL T) -7 NIL NIL) (-958 2346846 2347426 2348026 "REP" 2348835 T REP (NIL) -7 NIL NIL) (-957 2346547 2346581 2346690 "REPDB" 2346805 NIL REPDB (NIL T) -7 NIL NIL) (-956 2340492 2341871 2343091 "REP2" 2345359 NIL REP2 (NIL T) -7 NIL NIL) (-955 2336898 2337579 2338384 "REP1" 2339719 NIL REP1 (NIL T) -7 NIL NIL) (-954 2329644 2335059 2335511 "REGSET" 2336529 NIL REGSET (NIL T T T T) -8 NIL NIL) (-953 2328465 2328800 2329048 "REF" 2329429 NIL REF (NIL T) -8 NIL NIL) (-952 2327846 2327949 2328114 "REDORDER" 2328349 NIL REDORDER (NIL T T) -7 NIL NIL) (-951 2323815 2327080 2327301 "RECLOS" 2327677 NIL RECLOS (NIL T) -8 NIL NIL) (-950 2322872 2323053 2323266 "REALSOLV" 2323622 T REALSOLV (NIL) -7 NIL NIL) (-949 2322720 2322761 2322789 "REAL" 2322794 T REAL (NIL) -9 NIL 2322829) (-948 2319211 2320013 2320895 "REAL0Q" 2321885 NIL REAL0Q (NIL T) -7 NIL NIL) (-947 2314822 2315810 2316869 "REAL0" 2318192 NIL REAL0 (NIL T) -7 NIL NIL) (-946 2314230 2314302 2314507 "RDIV" 2314744 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-945 2313303 2313477 2313688 "RDIST" 2314052 NIL RDIST (NIL T) -7 NIL NIL) (-944 2311907 2312194 2312563 "RDETRS" 2313011 NIL RDETRS (NIL T T) -7 NIL NIL) (-943 2309728 2310182 2310717 "RDETR" 2311449 NIL RDETR (NIL T T) -7 NIL NIL) (-942 2308344 2308622 2309023 "RDEEFS" 2309444 NIL RDEEFS (NIL T T) -7 NIL NIL) (-941 2306844 2307150 2307579 "RDEEF" 2308032 NIL RDEEF (NIL T T) -7 NIL NIL) (-940 2301129 2304061 2304089 "RCFIELD" 2305366 T RCFIELD (NIL) -9 NIL 2306096) (-939 2299198 2299702 2300395 "RCFIELD-" 2300468 NIL RCFIELD- (NIL T) -8 NIL NIL) (-938 2295530 2297315 2297356 "RCAGG" 2298427 NIL RCAGG (NIL T) -9 NIL 2298892) (-937 2295161 2295255 2295415 "RCAGG-" 2295420 NIL RCAGG- (NIL T T) -8 NIL NIL) (-936 2294506 2294617 2294779 "RATRET" 2295045 NIL RATRET (NIL T) -7 NIL NIL) (-935 2294063 2294130 2294249 "RATFACT" 2294434 NIL RATFACT (NIL T) -7 NIL NIL) (-934 2293378 2293498 2293648 "RANDSRC" 2293933 T RANDSRC (NIL) -7 NIL NIL) (-933 2293115 2293159 2293230 "RADUTIL" 2293327 T RADUTIL (NIL) -7 NIL NIL) (-932 2286122 2291858 2292175 "RADIX" 2292830 NIL RADIX (NIL NIL) -8 NIL NIL) (-931 2277692 2285966 2286094 "RADFF" 2286099 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-930 2277344 2277419 2277447 "RADCAT" 2277604 T RADCAT (NIL) -9 NIL NIL) (-929 2277129 2277177 2277274 "RADCAT-" 2277279 NIL RADCAT- (NIL T) -8 NIL NIL) (-928 2275280 2276904 2276993 "QUEUE" 2277073 NIL QUEUE (NIL T) -8 NIL NIL) (-927 2271777 2275217 2275262 "QUAT" 2275267 NIL QUAT (NIL T) -8 NIL NIL) (-926 2271415 2271458 2271585 "QUATCT2" 2271728 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-925 2265209 2268589 2268629 "QUATCAT" 2269408 NIL QUATCAT (NIL T) -9 NIL 2270173) (-924 2261353 2262390 2263777 "QUATCAT-" 2263871 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-923 2258874 2260438 2260479 "QUAGG" 2260854 NIL QUAGG (NIL T) -9 NIL 2261029) (-922 2257799 2258272 2258444 "QFORM" 2258746 NIL QFORM (NIL NIL T) -8 NIL NIL) (-921 2249096 2254354 2254394 "QFCAT" 2255052 NIL QFCAT (NIL T) -9 NIL 2256045) (-920 2244668 2245869 2247460 "QFCAT-" 2247554 NIL QFCAT- (NIL T T) -8 NIL NIL) (-919 2244306 2244349 2244476 "QFCAT2" 2244619 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-918 2243766 2243876 2244006 "QEQUAT" 2244196 T QEQUAT (NIL) -8 NIL NIL) (-917 2236952 2238023 2239205 "QCMPACK" 2242699 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-916 2234528 2234949 2235377 "QALGSET" 2236607 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-915 2233773 2233947 2234179 "QALGSET2" 2234348 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-914 2232464 2232687 2233004 "PWFFINTB" 2233546 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-913 2230652 2230820 2231173 "PUSHVAR" 2232278 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-912 2226570 2227624 2227665 "PTRANFN" 2229549 NIL PTRANFN (NIL T) -9 NIL NIL) (-911 2224982 2225273 2225594 "PTPACK" 2226281 NIL PTPACK (NIL T) -7 NIL NIL) (-910 2224618 2224675 2224782 "PTFUNC2" 2224919 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-909 2219095 2223436 2223476 "PTCAT" 2223844 NIL PTCAT (NIL T) -9 NIL 2224006) (-908 2218753 2218788 2218912 "PSQFR" 2219054 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-907 2217348 2217646 2217980 "PSEUDLIN" 2218451 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-906 2204156 2206520 2208843 "PSETPK" 2215108 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-905 2197243 2199957 2200051 "PSETCAT" 2203032 NIL PSETCAT (NIL T T T T) -9 NIL 2203846) (-904 2195081 2195715 2196534 "PSETCAT-" 2196539 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-903 2194430 2194595 2194623 "PSCURVE" 2194891 T PSCURVE (NIL) -9 NIL 2195058) (-902 2190882 2192408 2192472 "PSCAT" 2193308 NIL PSCAT (NIL T T T) -9 NIL 2193548) (-901 2189946 2190162 2190561 "PSCAT-" 2190566 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-900 2188599 2189231 2189445 "PRTITION" 2189752 T PRTITION (NIL) -8 NIL NIL) (-899 2177697 2179903 2182091 "PRS" 2186461 NIL PRS (NIL T T) -7 NIL NIL) (-898 2175556 2177048 2177088 "PRQAGG" 2177271 NIL PRQAGG (NIL T) -9 NIL 2177373) (-897 2175127 2175229 2175257 "PROPLOG" 2175442 T PROPLOG (NIL) -9 NIL NIL) (-896 2172250 2172815 2173342 "PROPFRML" 2174632 NIL PROPFRML (NIL T) -8 NIL NIL) (-895 2171710 2171820 2171950 "PROPERTY" 2172140 T PROPERTY (NIL) -8 NIL NIL) (-894 2165484 2169876 2170696 "PRODUCT" 2170936 NIL PRODUCT (NIL T T) -8 NIL NIL) (-893 2162760 2164944 2165177 "PR" 2165295 NIL PR (NIL T T) -8 NIL NIL) (-892 2162556 2162588 2162647 "PRINT" 2162721 T PRINT (NIL) -7 NIL NIL) (-891 2161896 2162013 2162165 "PRIMES" 2162436 NIL PRIMES (NIL T) -7 NIL NIL) (-890 2159961 2160362 2160828 "PRIMELT" 2161475 NIL PRIMELT (NIL T) -7 NIL NIL) (-889 2159690 2159739 2159767 "PRIMCAT" 2159891 T PRIMCAT (NIL) -9 NIL NIL) (-888 2155851 2159628 2159673 "PRIMARR" 2159678 NIL PRIMARR (NIL T) -8 NIL NIL) (-887 2154858 2155036 2155264 "PRIMARR2" 2155669 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-886 2154501 2154557 2154668 "PREASSOC" 2154796 NIL PREASSOC (NIL T T) -7 NIL NIL) (-885 2153976 2154109 2154137 "PPCURVE" 2154342 T PPCURVE (NIL) -9 NIL 2154478) (-884 2151335 2151734 2152326 "POLYROOT" 2153557 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-883 2145241 2150941 2151100 "POLY" 2151208 NIL POLY (NIL T) -8 NIL NIL) (-882 2144626 2144684 2144917 "POLYLIFT" 2145177 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-881 2140911 2141360 2141988 "POLYCATQ" 2144171 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-880 2127952 2133349 2133413 "POLYCAT" 2136898 NIL POLYCAT (NIL T T T) -9 NIL 2138825) (-879 2121403 2123264 2125647 "POLYCAT-" 2125652 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-878 2120992 2121060 2121179 "POLY2UP" 2121329 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-877 2120628 2120685 2120792 "POLY2" 2120929 NIL POLY2 (NIL T T) -7 NIL NIL) (-876 2119313 2119552 2119828 "POLUTIL" 2120402 NIL POLUTIL (NIL T T) -7 NIL NIL) (-875 2117675 2117952 2118282 "POLTOPOL" 2119035 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-874 2113198 2117612 2117657 "POINT" 2117662 NIL POINT (NIL T) -8 NIL NIL) (-873 2111385 2111742 2112117 "PNTHEORY" 2112843 T PNTHEORY (NIL) -7 NIL NIL) (-872 2109813 2110110 2110519 "PMTOOLS" 2111083 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-871 2109406 2109484 2109601 "PMSYM" 2109729 NIL PMSYM (NIL T) -7 NIL NIL) (-870 2108916 2108985 2109159 "PMQFCAT" 2109331 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-869 2108271 2108381 2108537 "PMPRED" 2108793 NIL PMPRED (NIL T) -7 NIL NIL) (-868 2107667 2107753 2107914 "PMPREDFS" 2108172 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-867 2106313 2106521 2106905 "PMPLCAT" 2107429 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-866 2105845 2105924 2106076 "PMLSAGG" 2106228 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-865 2105322 2105398 2105578 "PMKERNEL" 2105763 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-864 2104939 2105014 2105127 "PMINS" 2105241 NIL PMINS (NIL T) -7 NIL NIL) (-863 2104369 2104438 2104653 "PMFS" 2104864 NIL PMFS (NIL T T T) -7 NIL NIL) (-862 2103600 2103718 2103922 "PMDOWN" 2104246 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-861 2102763 2102922 2103104 "PMASS" 2103438 T PMASS (NIL) -7 NIL NIL) (-860 2102037 2102148 2102311 "PMASSFS" 2102649 NIL PMASSFS (NIL T T) -7 NIL NIL) (-859 2101692 2101760 2101854 "PLOTTOOL" 2101963 T PLOTTOOL (NIL) -7 NIL NIL) (-858 2096314 2097503 2098651 "PLOT" 2100564 T PLOT (NIL) -8 NIL NIL) (-857 2092128 2093162 2094083 "PLOT3D" 2095413 T PLOT3D (NIL) -8 NIL NIL) (-856 2091040 2091217 2091452 "PLOT1" 2091932 NIL PLOT1 (NIL T) -7 NIL NIL) (-855 2066435 2071106 2075957 "PLEQN" 2086306 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-854 2065753 2065875 2066055 "PINTERP" 2066300 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-853 2065446 2065493 2065596 "PINTERPA" 2065700 NIL PINTERPA (NIL T T) -7 NIL NIL) (-852 2064673 2065240 2065333 "PI" 2065373 T PI (NIL) -8 NIL NIL) (-851 2063065 2064050 2064078 "PID" 2064260 T PID (NIL) -9 NIL 2064394) (-850 2062790 2062827 2062915 "PICOERCE" 2063022 NIL PICOERCE (NIL T) -7 NIL NIL) (-849 2062111 2062249 2062425 "PGROEB" 2062646 NIL PGROEB (NIL T) -7 NIL NIL) (-848 2057698 2058512 2059417 "PGE" 2061226 T PGE (NIL) -7 NIL NIL) (-847 2055822 2056068 2056434 "PGCD" 2057415 NIL PGCD (NIL T T T T) -7 NIL NIL) (-846 2055160 2055263 2055424 "PFRPAC" 2055706 NIL PFRPAC (NIL T) -7 NIL NIL) (-845 2051775 2053708 2054061 "PFR" 2054839 NIL PFR (NIL T) -8 NIL NIL) (-844 2050164 2050408 2050733 "PFOTOOLS" 2051522 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-843 2048697 2048936 2049287 "PFOQ" 2049921 NIL PFOQ (NIL T T T) -7 NIL NIL) (-842 2047174 2047386 2047748 "PFO" 2048481 NIL PFO (NIL T T T T T) -7 NIL NIL) (-841 2043697 2047063 2047132 "PF" 2047137 NIL PF (NIL NIL) -8 NIL NIL) (-840 2041126 2042407 2042435 "PFECAT" 2043020 T PFECAT (NIL) -9 NIL 2043404) (-839 2040571 2040725 2040939 "PFECAT-" 2040944 NIL PFECAT- (NIL T) -8 NIL NIL) (-838 2039175 2039426 2039727 "PFBRU" 2040320 NIL PFBRU (NIL T T) -7 NIL NIL) (-837 2037042 2037393 2037825 "PFBR" 2038826 NIL PFBR (NIL T T T T) -7 NIL NIL) (-836 2032894 2034418 2035094 "PERM" 2036399 NIL PERM (NIL T) -8 NIL NIL) (-835 2028159 2029101 2029971 "PERMGRP" 2032057 NIL PERMGRP (NIL T) -8 NIL NIL) (-834 2026230 2027223 2027264 "PERMCAT" 2027710 NIL PERMCAT (NIL T) -9 NIL 2028015) (-833 2025885 2025926 2026049 "PERMAN" 2026183 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-832 2023325 2025454 2025585 "PENDTREE" 2025787 NIL PENDTREE (NIL T) -8 NIL NIL) (-831 2021398 2022176 2022217 "PDRING" 2022874 NIL PDRING (NIL T) -9 NIL 2023159) (-830 2020501 2020719 2021081 "PDRING-" 2021086 NIL PDRING- (NIL T T) -8 NIL NIL) (-829 2017643 2018393 2019084 "PDEPROB" 2019830 T PDEPROB (NIL) -8 NIL NIL) (-828 2015214 2015710 2016259 "PDEPACK" 2017114 T PDEPACK (NIL) -7 NIL NIL) (-827 2014126 2014316 2014567 "PDECOMP" 2015013 NIL PDECOMP (NIL T T) -7 NIL NIL) (-826 2011738 2012553 2012581 "PDECAT" 2013366 T PDECAT (NIL) -9 NIL 2014077) (-825 2011491 2011524 2011613 "PCOMP" 2011699 NIL PCOMP (NIL T T) -7 NIL NIL) (-824 2009698 2010294 2010590 "PBWLB" 2011221 NIL PBWLB (NIL T) -8 NIL NIL) (-823 2002206 2003775 2005111 "PATTERN" 2008383 NIL PATTERN (NIL T) -8 NIL NIL) (-822 2001838 2001895 2002004 "PATTERN2" 2002143 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-821 1999595 1999983 2000440 "PATTERN1" 2001427 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-820 1996990 1997544 1998025 "PATRES" 1999160 NIL PATRES (NIL T T) -8 NIL NIL) (-819 1996554 1996621 1996753 "PATRES2" 1996917 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-818 1994451 1994851 1995256 "PATMATCH" 1996223 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-817 1993988 1994171 1994212 "PATMAB" 1994319 NIL PATMAB (NIL T) -9 NIL 1994402) (-816 1992533 1992842 1993100 "PATLRES" 1993793 NIL PATLRES (NIL T T T) -8 NIL NIL) (-815 1992079 1992202 1992243 "PATAB" 1992248 NIL PATAB (NIL T) -9 NIL 1992420) (-814 1989560 1990092 1990665 "PARTPERM" 1991526 T PARTPERM (NIL) -7 NIL NIL) (-813 1989181 1989244 1989346 "PARSURF" 1989491 NIL PARSURF (NIL T) -8 NIL NIL) (-812 1988813 1988870 1988979 "PARSU2" 1989118 NIL PARSU2 (NIL T T) -7 NIL NIL) (-811 1988577 1988617 1988684 "PARSER" 1988766 T PARSER (NIL) -7 NIL NIL) (-810 1988198 1988261 1988363 "PARSCURV" 1988508 NIL PARSCURV (NIL T) -8 NIL NIL) (-809 1987830 1987887 1987996 "PARSC2" 1988135 NIL PARSC2 (NIL T T) -7 NIL NIL) (-808 1987469 1987527 1987624 "PARPCURV" 1987766 NIL PARPCURV (NIL T) -8 NIL NIL) (-807 1987101 1987158 1987267 "PARPC2" 1987406 NIL PARPC2 (NIL T T) -7 NIL NIL) (-806 1986621 1986707 1986826 "PAN2EXPR" 1987002 T PAN2EXPR (NIL) -7 NIL NIL) (-805 1985427 1985742 1985970 "PALETTE" 1986413 T PALETTE (NIL) -8 NIL NIL) (-804 1983895 1984432 1984792 "PAIR" 1985113 NIL PAIR (NIL T T) -8 NIL NIL) (-803 1977745 1983154 1983348 "PADICRC" 1983750 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-802 1970953 1977091 1977275 "PADICRAT" 1977593 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-801 1969257 1970890 1970935 "PADIC" 1970940 NIL PADIC (NIL NIL) -8 NIL NIL) (-800 1966462 1968036 1968076 "PADICCT" 1968657 NIL PADICCT (NIL NIL) -9 NIL 1968939) (-799 1965419 1965619 1965887 "PADEPAC" 1966249 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-798 1964631 1964764 1964970 "PADE" 1965281 NIL PADE (NIL T T T) -7 NIL NIL) (-797 1962642 1963474 1963789 "OWP" 1964399 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-796 1961751 1962247 1962419 "OVAR" 1962510 NIL OVAR (NIL NIL) -8 NIL NIL) (-795 1961015 1961136 1961297 "OUT" 1961610 T OUT (NIL) -7 NIL NIL) (-794 1950069 1952240 1954410 "OUTFORM" 1958865 T OUTFORM (NIL) -8 NIL NIL) (-793 1949477 1949798 1949887 "OSI" 1950000 T OSI (NIL) -8 NIL NIL) (-792 1948222 1948449 1948734 "ORTHPOL" 1949224 NIL ORTHPOL (NIL T) -7 NIL NIL) (-791 1945593 1947883 1948021 "OREUP" 1948165 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-790 1942989 1945286 1945412 "ORESUP" 1945535 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-789 1940524 1941024 1941584 "OREPCTO" 1942478 NIL OREPCTO (NIL T T) -7 NIL NIL) (-788 1934434 1936640 1936680 "OREPCAT" 1939001 NIL OREPCAT (NIL T) -9 NIL 1940104) (-787 1931582 1932364 1933421 "OREPCAT-" 1933426 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-786 1930760 1931032 1931060 "ORDSET" 1931369 T ORDSET (NIL) -9 NIL 1931533) (-785 1930279 1930401 1930594 "ORDSET-" 1930599 NIL ORDSET- (NIL T) -8 NIL NIL) (-784 1928893 1929694 1929722 "ORDRING" 1929924 T ORDRING (NIL) -9 NIL 1930048) (-783 1928538 1928632 1928776 "ORDRING-" 1928781 NIL ORDRING- (NIL T) -8 NIL NIL) (-782 1927914 1928395 1928423 "ORDMON" 1928428 T ORDMON (NIL) -9 NIL 1928449) (-781 1927076 1927223 1927418 "ORDFUNS" 1927763 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-780 1926588 1926947 1926975 "ORDFIN" 1926980 T ORDFIN (NIL) -9 NIL 1927001) (-779 1923100 1925174 1925583 "ORDCOMP" 1926212 NIL ORDCOMP (NIL T) -8 NIL NIL) (-778 1922366 1922493 1922679 "ORDCOMP2" 1922960 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-777 1918874 1919756 1920593 "OPTPROB" 1921549 T OPTPROB (NIL) -8 NIL NIL) (-776 1915716 1916345 1917039 "OPTPACK" 1918200 T OPTPACK (NIL) -7 NIL NIL) (-775 1913442 1914178 1914206 "OPTCAT" 1915021 T OPTCAT (NIL) -9 NIL 1915667) (-774 1913210 1913249 1913315 "OPQUERY" 1913396 T OPQUERY (NIL) -7 NIL NIL) (-773 1910346 1911537 1912037 "OP" 1912742 NIL OP (NIL T) -8 NIL NIL) (-772 1907111 1909143 1909512 "ONECOMP" 1910010 NIL ONECOMP (NIL T) -8 NIL NIL) (-771 1906416 1906531 1906705 "ONECOMP2" 1906983 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-770 1905835 1905941 1906071 "OMSERVER" 1906306 T OMSERVER (NIL) -7 NIL NIL) (-769 1902724 1905276 1905316 "OMSAGG" 1905377 NIL OMSAGG (NIL T) -9 NIL 1905441) (-768 1901347 1901610 1901892 "OMPKG" 1902462 T OMPKG (NIL) -7 NIL NIL) (-767 1900777 1900880 1900908 "OM" 1901207 T OM (NIL) -9 NIL NIL) (-766 1899316 1900329 1900497 "OMLO" 1900658 NIL OMLO (NIL T T) -8 NIL NIL) (-765 1898246 1898393 1898619 "OMEXPR" 1899142 NIL OMEXPR (NIL T) -7 NIL NIL) (-764 1897564 1897792 1897928 "OMERR" 1898130 T OMERR (NIL) -8 NIL NIL) (-763 1896742 1896985 1897145 "OMERRK" 1897424 T OMERRK (NIL) -8 NIL NIL) (-762 1896220 1896419 1896527 "OMENC" 1896654 T OMENC (NIL) -8 NIL NIL) (-761 1890115 1891300 1892471 "OMDEV" 1895069 T OMDEV (NIL) -8 NIL NIL) (-760 1889184 1889355 1889549 "OMCONN" 1889941 T OMCONN (NIL) -8 NIL NIL) (-759 1887800 1888786 1888814 "OINTDOM" 1888819 T OINTDOM (NIL) -9 NIL 1888840) (-758 1883562 1884792 1885507 "OFMONOID" 1887117 NIL OFMONOID (NIL T) -8 NIL NIL) (-757 1883000 1883499 1883544 "ODVAR" 1883549 NIL ODVAR (NIL T) -8 NIL NIL) (-756 1880125 1882497 1882682 "ODR" 1882875 NIL ODR (NIL T T NIL) -8 NIL NIL) (-755 1872431 1879904 1880028 "ODPOL" 1880033 NIL ODPOL (NIL T) -8 NIL NIL) (-754 1866254 1872303 1872408 "ODP" 1872413 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-753 1865020 1865235 1865510 "ODETOOLS" 1866028 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-752 1861989 1862645 1863361 "ODESYS" 1864353 NIL ODESYS (NIL T T) -7 NIL NIL) (-751 1856893 1857801 1858824 "ODERTRIC" 1861064 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-750 1856319 1856401 1856595 "ODERED" 1856805 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-749 1853221 1853769 1854444 "ODERAT" 1855742 NIL ODERAT (NIL T T) -7 NIL NIL) (-748 1850189 1850653 1851249 "ODEPRRIC" 1852750 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-747 1848060 1848627 1849136 "ODEPROB" 1849700 T ODEPROB (NIL) -8 NIL NIL) (-746 1844592 1845075 1845721 "ODEPRIM" 1847539 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-745 1843845 1843947 1844205 "ODEPAL" 1844484 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-744 1840047 1840828 1841682 "ODEPACK" 1843011 T ODEPACK (NIL) -7 NIL NIL) (-743 1839084 1839191 1839419 "ODEINT" 1839936 NIL ODEINT (NIL T T) -7 NIL NIL) (-742 1833185 1834610 1836057 "ODEIFTBL" 1837657 T ODEIFTBL (NIL) -8 NIL NIL) (-741 1828529 1829315 1830273 "ODEEF" 1832344 NIL ODEEF (NIL T T) -7 NIL NIL) (-740 1827866 1827955 1828184 "ODECONST" 1828434 NIL ODECONST (NIL T T T) -7 NIL NIL) (-739 1826024 1826657 1826685 "ODECAT" 1827288 T ODECAT (NIL) -9 NIL 1827817) (-738 1822896 1825736 1825855 "OCT" 1825937 NIL OCT (NIL T) -8 NIL NIL) (-737 1822534 1822577 1822704 "OCTCT2" 1822847 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-736 1817368 1819806 1819846 "OC" 1820942 NIL OC (NIL T) -9 NIL 1821799) (-735 1814595 1815343 1816333 "OC-" 1816427 NIL OC- (NIL T T) -8 NIL NIL) (-734 1813974 1814416 1814444 "OCAMON" 1814449 T OCAMON (NIL) -9 NIL 1814470) (-733 1813428 1813835 1813863 "OASGP" 1813868 T OASGP (NIL) -9 NIL 1813888) (-732 1812716 1813179 1813207 "OAMONS" 1813247 T OAMONS (NIL) -9 NIL 1813290) (-731 1812157 1812564 1812592 "OAMON" 1812597 T OAMON (NIL) -9 NIL 1812617) (-730 1811462 1811954 1811982 "OAGROUP" 1811987 T OAGROUP (NIL) -9 NIL 1812007) (-729 1811152 1811202 1811290 "NUMTUBE" 1811406 NIL NUMTUBE (NIL T) -7 NIL NIL) (-728 1804725 1806243 1807779 "NUMQUAD" 1809636 T NUMQUAD (NIL) -7 NIL NIL) (-727 1800481 1801469 1802494 "NUMODE" 1803720 T NUMODE (NIL) -7 NIL NIL) (-726 1797885 1798731 1798759 "NUMINT" 1799676 T NUMINT (NIL) -9 NIL 1800432) (-725 1796833 1797030 1797248 "NUMFMT" 1797687 T NUMFMT (NIL) -7 NIL NIL) (-724 1783215 1786149 1788679 "NUMERIC" 1794342 NIL NUMERIC (NIL T) -7 NIL NIL) (-723 1777616 1782668 1782762 "NTSCAT" 1782767 NIL NTSCAT (NIL T T T T) -9 NIL 1782805) (-722 1776810 1776975 1777168 "NTPOLFN" 1777455 NIL NTPOLFN (NIL T) -7 NIL NIL) (-721 1764626 1773652 1774462 "NSUP" 1776032 NIL NSUP (NIL T) -8 NIL NIL) (-720 1764262 1764319 1764426 "NSUP2" 1764563 NIL NSUP2 (NIL T T) -7 NIL NIL) (-719 1754224 1764041 1764171 "NSMP" 1764176 NIL NSMP (NIL T T) -8 NIL NIL) (-718 1752656 1752957 1753314 "NREP" 1753912 NIL NREP (NIL T) -7 NIL NIL) (-717 1751247 1751499 1751857 "NPCOEF" 1752399 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-716 1750313 1750428 1750644 "NORMRETR" 1751128 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-715 1748366 1748656 1749063 "NORMPK" 1750021 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-714 1748051 1748079 1748203 "NORMMA" 1748332 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-713 1747878 1748008 1748037 "NONE" 1748042 T NONE (NIL) -8 NIL NIL) (-712 1747667 1747696 1747765 "NONE1" 1747842 NIL NONE1 (NIL T) -7 NIL NIL) (-711 1747152 1747214 1747399 "NODE1" 1747599 NIL NODE1 (NIL T T) -7 NIL NIL) (-710 1745445 1746315 1746570 "NNI" 1746917 T NNI (NIL) -8 NIL NIL) (-709 1743865 1744178 1744542 "NLINSOL" 1745113 NIL NLINSOL (NIL T) -7 NIL NIL) (-708 1740033 1741000 1741922 "NIPROB" 1742963 T NIPROB (NIL) -8 NIL NIL) (-707 1738790 1739024 1739326 "NFINTBAS" 1739795 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-706 1737498 1737729 1738010 "NCODIV" 1738558 NIL NCODIV (NIL T T) -7 NIL NIL) (-705 1737260 1737297 1737372 "NCNTFRAC" 1737455 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-704 1735440 1735804 1736224 "NCEP" 1736885 NIL NCEP (NIL T) -7 NIL NIL) (-703 1734352 1735091 1735119 "NASRING" 1735229 T NASRING (NIL) -9 NIL 1735303) (-702 1734147 1734191 1734285 "NASRING-" 1734290 NIL NASRING- (NIL T) -8 NIL NIL) (-701 1733301 1733800 1733828 "NARNG" 1733945 T NARNG (NIL) -9 NIL 1734036) (-700 1732993 1733060 1733194 "NARNG-" 1733199 NIL NARNG- (NIL T) -8 NIL NIL) (-699 1731872 1732079 1732314 "NAGSP" 1732778 T NAGSP (NIL) -7 NIL NIL) (-698 1723296 1724942 1726577 "NAGS" 1730257 T NAGS (NIL) -7 NIL NIL) (-697 1721860 1722164 1722491 "NAGF07" 1722989 T NAGF07 (NIL) -7 NIL NIL) (-696 1716442 1717722 1719018 "NAGF04" 1720584 T NAGF04 (NIL) -7 NIL NIL) (-695 1709474 1711072 1712689 "NAGF02" 1714845 T NAGF02 (NIL) -7 NIL NIL) (-694 1704738 1705828 1706935 "NAGF01" 1708387 T NAGF01 (NIL) -7 NIL NIL) (-693 1698398 1699956 1701533 "NAGE04" 1703181 T NAGE04 (NIL) -7 NIL NIL) (-692 1689639 1691742 1693854 "NAGE02" 1696306 T NAGE02 (NIL) -7 NIL NIL) (-691 1685632 1686569 1687523 "NAGE01" 1688705 T NAGE01 (NIL) -7 NIL NIL) (-690 1683439 1683970 1684525 "NAGD03" 1685097 T NAGD03 (NIL) -7 NIL NIL) (-689 1675225 1677144 1679089 "NAGD02" 1681514 T NAGD02 (NIL) -7 NIL NIL) (-688 1669084 1670497 1671925 "NAGD01" 1673817 T NAGD01 (NIL) -7 NIL NIL) (-687 1665341 1666151 1666976 "NAGC06" 1668279 T NAGC06 (NIL) -7 NIL NIL) (-686 1663818 1664147 1664500 "NAGC05" 1665008 T NAGC05 (NIL) -7 NIL NIL) (-685 1663202 1663319 1663461 "NAGC02" 1663696 T NAGC02 (NIL) -7 NIL NIL) (-684 1662264 1662821 1662861 "NAALG" 1662940 NIL NAALG (NIL T) -9 NIL 1663001) (-683 1662099 1662128 1662218 "NAALG-" 1662223 NIL NAALG- (NIL T T) -8 NIL NIL) (-682 1656049 1657157 1658344 "MULTSQFR" 1660995 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-681 1655368 1655443 1655627 "MULTFACT" 1655961 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-680 1648562 1652473 1652525 "MTSCAT" 1653585 NIL MTSCAT (NIL T T) -9 NIL 1654099) (-679 1648274 1648328 1648420 "MTHING" 1648502 NIL MTHING (NIL T) -7 NIL NIL) (-678 1648066 1648099 1648159 "MSYSCMD" 1648234 T MSYSCMD (NIL) -7 NIL NIL) (-677 1644178 1646821 1647141 "MSET" 1647779 NIL MSET (NIL T) -8 NIL NIL) (-676 1641274 1643740 1643781 "MSETAGG" 1643786 NIL MSETAGG (NIL T) -9 NIL 1643820) (-675 1637130 1638672 1639413 "MRING" 1640577 NIL MRING (NIL T T) -8 NIL NIL) (-674 1636700 1636767 1636896 "MRF2" 1637057 NIL MRF2 (NIL T T T) -7 NIL NIL) (-673 1636318 1636353 1636497 "MRATFAC" 1636659 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-672 1633930 1634225 1634656 "MPRFF" 1636023 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-671 1627950 1633785 1633881 "MPOLY" 1633886 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-670 1627440 1627475 1627683 "MPCPF" 1627909 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-669 1626956 1626999 1627182 "MPC3" 1627391 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-668 1626157 1626238 1626457 "MPC2" 1626871 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-667 1624458 1624795 1625185 "MONOTOOL" 1625817 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-666 1623583 1623918 1623946 "MONOID" 1624223 T MONOID (NIL) -9 NIL 1624395) (-665 1622961 1623124 1623367 "MONOID-" 1623372 NIL MONOID- (NIL T) -8 NIL NIL) (-664 1613942 1619928 1619987 "MONOGEN" 1620661 NIL MONOGEN (NIL T T) -9 NIL 1621117) (-663 1611160 1611895 1612895 "MONOGEN-" 1613014 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-662 1610020 1610440 1610468 "MONADWU" 1610860 T MONADWU (NIL) -9 NIL 1611098) (-661 1609392 1609551 1609799 "MONADWU-" 1609804 NIL MONADWU- (NIL T) -8 NIL NIL) (-660 1608778 1608996 1609024 "MONAD" 1609231 T MONAD (NIL) -9 NIL 1609343) (-659 1608463 1608541 1608673 "MONAD-" 1608678 NIL MONAD- (NIL T) -8 NIL NIL) (-658 1606714 1607376 1607655 "MOEBIUS" 1608216 NIL MOEBIUS (NIL T) -8 NIL NIL) (-657 1606108 1606486 1606526 "MODULE" 1606531 NIL MODULE (NIL T) -9 NIL 1606557) (-656 1605676 1605772 1605962 "MODULE-" 1605967 NIL MODULE- (NIL T T) -8 NIL NIL) (-655 1603347 1604042 1604368 "MODRING" 1605501 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-654 1600303 1601468 1601985 "MODOP" 1602879 NIL MODOP (NIL T T) -8 NIL NIL) (-653 1598490 1598942 1599283 "MODMONOM" 1600102 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-652 1588169 1596694 1597116 "MODMON" 1598118 NIL MODMON (NIL T T) -8 NIL NIL) (-651 1585295 1587013 1587289 "MODFIELD" 1588044 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-650 1584299 1584576 1584766 "MMLFORM" 1585125 T MMLFORM (NIL) -8 NIL NIL) (-649 1583825 1583868 1584047 "MMAP" 1584250 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-648 1582062 1582839 1582879 "MLO" 1583296 NIL MLO (NIL T) -9 NIL 1583537) (-647 1579429 1579944 1580546 "MLIFT" 1581543 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-646 1578820 1578904 1579058 "MKUCFUNC" 1579340 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-645 1578419 1578489 1578612 "MKRECORD" 1578743 NIL MKRECORD (NIL T T) -7 NIL NIL) (-644 1577467 1577628 1577856 "MKFUNC" 1578230 NIL MKFUNC (NIL T) -7 NIL NIL) (-643 1576855 1576959 1577115 "MKFLCFN" 1577350 NIL MKFLCFN (NIL T) -7 NIL NIL) (-642 1576281 1576648 1576737 "MKCHSET" 1576799 NIL MKCHSET (NIL T) -8 NIL NIL) (-641 1575558 1575660 1575845 "MKBCFUNC" 1576174 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-640 1572242 1575112 1575248 "MINT" 1575442 T MINT (NIL) -8 NIL NIL) (-639 1571054 1571297 1571574 "MHROWRED" 1571997 NIL MHROWRED (NIL T) -7 NIL NIL) (-638 1566325 1569499 1569923 "MFLOAT" 1570650 T MFLOAT (NIL) -8 NIL NIL) (-637 1565682 1565758 1565929 "MFINFACT" 1566237 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-636 1561997 1562845 1563729 "MESH" 1564818 T MESH (NIL) -7 NIL NIL) (-635 1560387 1560699 1561052 "MDDFACT" 1561684 NIL MDDFACT (NIL T) -7 NIL NIL) (-634 1557230 1559547 1559588 "MDAGG" 1559843 NIL MDAGG (NIL T) -9 NIL 1559986) (-633 1546928 1556523 1556730 "MCMPLX" 1557043 T MCMPLX (NIL) -8 NIL NIL) (-632 1546069 1546215 1546415 "MCDEN" 1546777 NIL MCDEN (NIL T T) -7 NIL NIL) (-631 1543959 1544229 1544609 "MCALCFN" 1545799 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-630 1541581 1542104 1542665 "MATSTOR" 1543430 NIL MATSTOR (NIL T) -7 NIL NIL) (-629 1537590 1540956 1541203 "MATRIX" 1541366 NIL MATRIX (NIL T) -8 NIL NIL) (-628 1533360 1534063 1534799 "MATLIN" 1536947 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-627 1523558 1526696 1526772 "MATCAT" 1531610 NIL MATCAT (NIL T T T) -9 NIL 1533027) (-626 1519923 1520936 1522291 "MATCAT-" 1522296 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-625 1518525 1518678 1519009 "MATCAT2" 1519758 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-624 1516637 1516961 1517345 "MAPPKG3" 1518200 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-623 1515618 1515791 1516013 "MAPPKG2" 1516461 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-622 1514117 1514401 1514728 "MAPPKG1" 1515324 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-621 1513728 1513786 1513909 "MAPHACK3" 1514053 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-620 1513320 1513381 1513495 "MAPHACK2" 1513660 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-619 1512758 1512861 1513003 "MAPHACK1" 1513211 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-618 1510866 1511460 1511763 "MAGMA" 1512487 NIL MAGMA (NIL T) -8 NIL NIL) (-617 1507340 1509110 1509570 "M3D" 1510439 NIL M3D (NIL T) -8 NIL NIL) (-616 1501496 1505711 1505752 "LZSTAGG" 1506534 NIL LZSTAGG (NIL T) -9 NIL 1506829) (-615 1497469 1498627 1500084 "LZSTAGG-" 1500089 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-614 1494585 1495362 1495848 "LWORD" 1497015 NIL LWORD (NIL T) -8 NIL NIL) (-613 1487745 1494356 1494490 "LSQM" 1494495 NIL LSQM (NIL NIL T) -8 NIL NIL) (-612 1486969 1487108 1487336 "LSPP" 1487600 NIL LSPP (NIL T T T T) -7 NIL NIL) (-611 1484781 1485082 1485538 "LSMP" 1486658 NIL LSMP (NIL T T T T) -7 NIL NIL) (-610 1481560 1482234 1482964 "LSMP1" 1484083 NIL LSMP1 (NIL T) -7 NIL NIL) (-609 1475487 1480729 1480770 "LSAGG" 1480832 NIL LSAGG (NIL T) -9 NIL 1480910) (-608 1472182 1473106 1474319 "LSAGG-" 1474324 NIL LSAGG- (NIL T T) -8 NIL NIL) (-607 1469808 1471326 1471575 "LPOLY" 1471977 NIL LPOLY (NIL T T) -8 NIL NIL) (-606 1469390 1469475 1469598 "LPEFRAC" 1469717 NIL LPEFRAC (NIL T) -7 NIL NIL) (-605 1467737 1468484 1468737 "LO" 1469222 NIL LO (NIL T T T) -8 NIL NIL) (-604 1467391 1467503 1467531 "LOGIC" 1467642 T LOGIC (NIL) -9 NIL 1467722) (-603 1467253 1467276 1467347 "LOGIC-" 1467352 NIL LOGIC- (NIL T) -8 NIL NIL) (-602 1466446 1466586 1466779 "LODOOPS" 1467109 NIL LODOOPS (NIL T T) -7 NIL NIL) (-601 1463864 1466363 1466428 "LODO" 1466433 NIL LODO (NIL T NIL) -8 NIL NIL) (-600 1462410 1462645 1462996 "LODOF" 1463611 NIL LODOF (NIL T T) -7 NIL NIL) (-599 1458830 1461266 1461306 "LODOCAT" 1461738 NIL LODOCAT (NIL T) -9 NIL 1461949) (-598 1458564 1458622 1458748 "LODOCAT-" 1458753 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-597 1455878 1458405 1458523 "LODO2" 1458528 NIL LODO2 (NIL T T) -8 NIL NIL) (-596 1453307 1455815 1455860 "LODO1" 1455865 NIL LODO1 (NIL T) -8 NIL NIL) (-595 1452170 1452335 1452646 "LODEEF" 1453130 NIL LODEEF (NIL T T T) -7 NIL NIL) (-594 1447457 1450301 1450342 "LNAGG" 1451289 NIL LNAGG (NIL T) -9 NIL 1451733) (-593 1446604 1446818 1447160 "LNAGG-" 1447165 NIL LNAGG- (NIL T T) -8 NIL NIL) (-592 1442769 1443531 1444169 "LMOPS" 1446020 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-591 1442167 1442529 1442569 "LMODULE" 1442629 NIL LMODULE (NIL T) -9 NIL 1442671) (-590 1439413 1441812 1441935 "LMDICT" 1442077 NIL LMDICT (NIL T) -8 NIL NIL) (-589 1432640 1438359 1438657 "LIST" 1439148 NIL LIST (NIL T) -8 NIL NIL) (-588 1432165 1432239 1432378 "LIST3" 1432560 NIL LIST3 (NIL T T T) -7 NIL NIL) (-587 1431172 1431350 1431578 "LIST2" 1431983 NIL LIST2 (NIL T T) -7 NIL NIL) (-586 1429306 1429618 1430017 "LIST2MAP" 1430819 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-585 1428019 1428699 1428739 "LINEXP" 1428992 NIL LINEXP (NIL T) -9 NIL 1429140) (-584 1426666 1426926 1427223 "LINDEP" 1427771 NIL LINDEP (NIL T T) -7 NIL NIL) (-583 1423433 1424152 1424929 "LIMITRF" 1425921 NIL LIMITRF (NIL T) -7 NIL NIL) (-582 1421713 1422008 1422423 "LIMITPS" 1423128 NIL LIMITPS (NIL T T) -7 NIL NIL) (-581 1416168 1421224 1421452 "LIE" 1421534 NIL LIE (NIL T T) -8 NIL NIL) (-580 1415219 1415662 1415702 "LIECAT" 1415842 NIL LIECAT (NIL T) -9 NIL 1415993) (-579 1415060 1415087 1415175 "LIECAT-" 1415180 NIL LIECAT- (NIL T T) -8 NIL NIL) (-578 1407672 1414509 1414674 "LIB" 1414915 T LIB (NIL) -8 NIL NIL) (-577 1403309 1404190 1405125 "LGROBP" 1406789 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-576 1401175 1401449 1401811 "LF" 1403030 NIL LF (NIL T T) -7 NIL NIL) (-575 1400015 1400707 1400735 "LFCAT" 1400942 T LFCAT (NIL) -9 NIL 1401081) (-574 1396927 1397553 1398239 "LEXTRIPK" 1399381 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-573 1393633 1394497 1395000 "LEXP" 1396507 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-572 1392031 1392344 1392745 "LEADCDET" 1393315 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-571 1391227 1391301 1391528 "LAZM3PK" 1391952 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-570 1386144 1389306 1389843 "LAUPOL" 1390740 NIL LAUPOL (NIL T T) -8 NIL NIL) (-569 1385711 1385755 1385922 "LAPLACE" 1386094 NIL LAPLACE (NIL T T) -7 NIL NIL) (-568 1383639 1384812 1385063 "LA" 1385544 NIL LA (NIL T T T) -8 NIL NIL) (-567 1382702 1383296 1383336 "LALG" 1383397 NIL LALG (NIL T) -9 NIL 1383455) (-566 1382417 1382476 1382611 "LALG-" 1382616 NIL LALG- (NIL T T) -8 NIL NIL) (-565 1381327 1381514 1381811 "KOVACIC" 1382217 NIL KOVACIC (NIL T T) -7 NIL NIL) (-564 1381162 1381186 1381227 "KONVERT" 1381289 NIL KONVERT (NIL T) -9 NIL NIL) (-563 1380997 1381021 1381062 "KOERCE" 1381124 NIL KOERCE (NIL T) -9 NIL NIL) (-562 1378731 1379491 1379884 "KERNEL" 1380636 NIL KERNEL (NIL T) -8 NIL NIL) (-561 1378233 1378314 1378444 "KERNEL2" 1378645 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-560 1372085 1376773 1376827 "KDAGG" 1377204 NIL KDAGG (NIL T T) -9 NIL 1377410) (-559 1371614 1371738 1371943 "KDAGG-" 1371948 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-558 1364789 1371275 1371430 "KAFILE" 1371492 NIL KAFILE (NIL T) -8 NIL NIL) (-557 1359244 1364300 1364528 "JORDAN" 1364610 NIL JORDAN (NIL T T) -8 NIL NIL) (-556 1355544 1357450 1357504 "IXAGG" 1358433 NIL IXAGG (NIL T T) -9 NIL 1358892) (-555 1354463 1354769 1355188 "IXAGG-" 1355193 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-554 1350048 1354385 1354444 "IVECTOR" 1354449 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-553 1348814 1349051 1349317 "ITUPLE" 1349815 NIL ITUPLE (NIL T) -8 NIL NIL) (-552 1347250 1347427 1347733 "ITRIGMNP" 1348636 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-551 1345995 1346199 1346482 "ITFUN3" 1347026 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-550 1345627 1345684 1345793 "ITFUN2" 1345932 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-549 1343429 1344500 1344797 "ITAYLOR" 1345362 NIL ITAYLOR (NIL T) -8 NIL NIL) (-548 1332417 1337615 1338774 "ISUPS" 1342302 NIL ISUPS (NIL T) -8 NIL NIL) (-547 1331521 1331661 1331897 "ISUMP" 1332264 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-546 1326785 1331322 1331401 "ISTRING" 1331474 NIL ISTRING (NIL NIL) -8 NIL NIL) (-545 1325998 1326079 1326294 "IRURPK" 1326699 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-544 1324934 1325135 1325375 "IRSN" 1325778 T IRSN (NIL) -7 NIL NIL) (-543 1322969 1323324 1323759 "IRRF2F" 1324572 NIL IRRF2F (NIL T) -7 NIL NIL) (-542 1322716 1322754 1322830 "IRREDFFX" 1322925 NIL IRREDFFX (NIL T) -7 NIL NIL) (-541 1321331 1321590 1321889 "IROOT" 1322449 NIL IROOT (NIL T) -7 NIL NIL) (-540 1317969 1319020 1319710 "IR" 1320673 NIL IR (NIL T) -8 NIL NIL) (-539 1315582 1316077 1316643 "IR2" 1317447 NIL IR2 (NIL T T) -7 NIL NIL) (-538 1314658 1314771 1314991 "IR2F" 1315465 NIL IR2F (NIL T T) -7 NIL NIL) (-537 1314449 1314483 1314543 "IPRNTPK" 1314618 T IPRNTPK (NIL) -7 NIL NIL) (-536 1311003 1314338 1314407 "IPF" 1314412 NIL IPF (NIL NIL) -8 NIL NIL) (-535 1309320 1310928 1310985 "IPADIC" 1310990 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-534 1308819 1308877 1309066 "INVLAPLA" 1309256 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-533 1298468 1300821 1303207 "INTTR" 1306483 NIL INTTR (NIL T T) -7 NIL NIL) (-532 1294816 1295557 1296420 "INTTOOLS" 1297654 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-531 1294402 1294493 1294610 "INTSLPE" 1294719 T INTSLPE (NIL) -7 NIL NIL) (-530 1292352 1294325 1294384 "INTRVL" 1294389 NIL INTRVL (NIL T) -8 NIL NIL) (-529 1289959 1290471 1291045 "INTRF" 1291837 NIL INTRF (NIL T) -7 NIL NIL) (-528 1289374 1289471 1289612 "INTRET" 1289857 NIL INTRET (NIL T) -7 NIL NIL) (-527 1287376 1287765 1288234 "INTRAT" 1288982 NIL INTRAT (NIL T T) -7 NIL NIL) (-526 1284609 1285192 1285817 "INTPM" 1286861 NIL INTPM (NIL T T) -7 NIL NIL) (-525 1281318 1281917 1282661 "INTPAF" 1283995 NIL INTPAF (NIL T T T) -7 NIL NIL) (-524 1276561 1277507 1278542 "INTPACK" 1280303 T INTPACK (NIL) -7 NIL NIL) (-523 1273415 1276290 1276417 "INT" 1276454 T INT (NIL) -8 NIL NIL) (-522 1272667 1272819 1273027 "INTHERTR" 1273257 NIL INTHERTR (NIL T T) -7 NIL NIL) (-521 1272106 1272186 1272374 "INTHERAL" 1272581 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-520 1269952 1270395 1270852 "INTHEORY" 1271669 T INTHEORY (NIL) -7 NIL NIL) (-519 1261275 1262895 1264673 "INTG0" 1268304 NIL INTG0 (NIL T T T) -7 NIL NIL) (-518 1241848 1246638 1251448 "INTFTBL" 1256485 T INTFTBL (NIL) -8 NIL NIL) (-517 1241097 1241235 1241408 "INTFACT" 1241707 NIL INTFACT (NIL T) -7 NIL NIL) (-516 1238488 1238934 1239497 "INTEF" 1240651 NIL INTEF (NIL T T) -7 NIL NIL) (-515 1236950 1237699 1237727 "INTDOM" 1238028 T INTDOM (NIL) -9 NIL 1238235) (-514 1236319 1236493 1236735 "INTDOM-" 1236740 NIL INTDOM- (NIL T) -8 NIL NIL) (-513 1232812 1234744 1234798 "INTCAT" 1235597 NIL INTCAT (NIL T) -9 NIL 1235916) (-512 1232285 1232387 1232515 "INTBIT" 1232704 T INTBIT (NIL) -7 NIL NIL) (-511 1230960 1231114 1231427 "INTALG" 1232130 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-510 1230417 1230507 1230677 "INTAF" 1230864 NIL INTAF (NIL T T) -7 NIL NIL) (-509 1223871 1230227 1230367 "INTABL" 1230372 NIL INTABL (NIL T T T) -8 NIL NIL) (-508 1218822 1221551 1221579 "INS" 1222547 T INS (NIL) -9 NIL 1223228) (-507 1216062 1216833 1217807 "INS-" 1217880 NIL INS- (NIL T) -8 NIL NIL) (-506 1214841 1215068 1215365 "INPSIGN" 1215815 NIL INPSIGN (NIL T T) -7 NIL NIL) (-505 1213959 1214076 1214273 "INPRODPF" 1214721 NIL INPRODPF (NIL T T) -7 NIL NIL) (-504 1212853 1212970 1213207 "INPRODFF" 1213839 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-503 1211853 1212005 1212265 "INNMFACT" 1212689 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-502 1211050 1211147 1211335 "INMODGCD" 1211752 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-501 1209559 1209803 1210127 "INFSP" 1210795 NIL INFSP (NIL T T T) -7 NIL NIL) (-500 1208743 1208860 1209043 "INFPROD0" 1209439 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-499 1205753 1206912 1207403 "INFORM" 1208260 T INFORM (NIL) -8 NIL NIL) (-498 1205363 1205423 1205521 "INFORM1" 1205688 NIL INFORM1 (NIL T) -7 NIL NIL) (-497 1204886 1204975 1205089 "INFINITY" 1205269 T INFINITY (NIL) -7 NIL NIL) (-496 1203504 1203752 1204073 "INEP" 1204634 NIL INEP (NIL T T T) -7 NIL NIL) (-495 1202780 1203401 1203466 "INDE" 1203471 NIL INDE (NIL T) -8 NIL NIL) (-494 1202344 1202412 1202529 "INCRMAPS" 1202707 NIL INCRMAPS (NIL T) -7 NIL NIL) (-493 1197655 1198580 1199524 "INBFF" 1201432 NIL INBFF (NIL T) -7 NIL NIL) (-492 1194150 1197500 1197603 "IMATRIX" 1197608 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-491 1192862 1192985 1193300 "IMATQF" 1194006 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-490 1191082 1191309 1191646 "IMATLIN" 1192618 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-489 1185708 1191006 1191064 "ILIST" 1191069 NIL ILIST (NIL T NIL) -8 NIL NIL) (-488 1183661 1185568 1185681 "IIARRAY2" 1185686 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-487 1179029 1183572 1183636 "IFF" 1183641 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-486 1174072 1178321 1178509 "IFARRAY" 1178886 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-485 1173279 1173976 1174049 "IFAMON" 1174054 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-484 1172863 1172928 1172982 "IEVALAB" 1173189 NIL IEVALAB (NIL T T) -9 NIL NIL) (-483 1172538 1172606 1172766 "IEVALAB-" 1172771 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-482 1172196 1172452 1172515 "IDPO" 1172520 NIL IDPO (NIL T T) -8 NIL NIL) (-481 1171473 1172085 1172160 "IDPOAMS" 1172165 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-480 1170807 1171362 1171437 "IDPOAM" 1171442 NIL IDPOAM (NIL T T) -8 NIL NIL) (-479 1169893 1170143 1170196 "IDPC" 1170609 NIL IDPC (NIL T T) -9 NIL 1170758) (-478 1169389 1169785 1169858 "IDPAM" 1169863 NIL IDPAM (NIL T T) -8 NIL NIL) (-477 1168792 1169281 1169354 "IDPAG" 1169359 NIL IDPAG (NIL T T) -8 NIL NIL) (-476 1165047 1165895 1166790 "IDECOMP" 1167949 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-475 1157920 1158970 1160017 "IDEAL" 1164083 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-474 1157084 1157196 1157395 "ICDEN" 1157804 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-473 1156183 1156564 1156711 "ICARD" 1156957 T ICARD (NIL) -8 NIL NIL) (-472 1154255 1154568 1154971 "IBPTOOLS" 1155860 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-471 1149869 1153875 1153988 "IBITS" 1154174 NIL IBITS (NIL NIL) -8 NIL NIL) (-470 1146592 1147168 1147863 "IBATOOL" 1149286 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-469 1144372 1144833 1145366 "IBACHIN" 1146127 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-468 1142249 1144218 1144321 "IARRAY2" 1144326 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-467 1138402 1142175 1142232 "IARRAY1" 1142237 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-466 1132341 1136820 1137298 "IAN" 1137944 T IAN (NIL) -8 NIL NIL) (-465 1131852 1131909 1132082 "IALGFACT" 1132278 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-464 1131380 1131493 1131521 "HYPCAT" 1131728 T HYPCAT (NIL) -9 NIL NIL) (-463 1130918 1131035 1131221 "HYPCAT-" 1131226 NIL HYPCAT- (NIL T) -8 NIL NIL) (-462 1127598 1128929 1128970 "HOAGG" 1129951 NIL HOAGG (NIL T) -9 NIL 1130630) (-461 1126192 1126591 1127117 "HOAGG-" 1127122 NIL HOAGG- (NIL T T) -8 NIL NIL) (-460 1120023 1125633 1125799 "HEXADEC" 1126046 T HEXADEC (NIL) -8 NIL NIL) (-459 1118771 1118993 1119256 "HEUGCD" 1119800 NIL HEUGCD (NIL T) -7 NIL NIL) (-458 1117874 1118608 1118738 "HELLFDIV" 1118743 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-457 1116102 1117651 1117739 "HEAP" 1117818 NIL HEAP (NIL T) -8 NIL NIL) (-456 1109969 1116017 1116079 "HDP" 1116084 NIL HDP (NIL NIL T) -8 NIL NIL) (-455 1103681 1109606 1109757 "HDMP" 1109870 NIL HDMP (NIL NIL T) -8 NIL NIL) (-454 1103006 1103145 1103309 "HB" 1103537 T HB (NIL) -7 NIL NIL) (-453 1096503 1102852 1102956 "HASHTBL" 1102961 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-452 1094256 1096131 1096310 "HACKPI" 1096344 T HACKPI (NIL) -8 NIL NIL) (-451 1089952 1094110 1094222 "GTSET" 1094227 NIL GTSET (NIL T T T T) -8 NIL NIL) (-450 1083478 1089830 1089928 "GSTBL" 1089933 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-449 1075711 1082514 1082778 "GSERIES" 1083269 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-448 1074734 1075187 1075215 "GROUP" 1075476 T GROUP (NIL) -9 NIL 1075635) (-447 1073850 1074073 1074417 "GROUP-" 1074422 NIL GROUP- (NIL T) -8 NIL NIL) (-446 1072219 1072538 1072925 "GROEBSOL" 1073527 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-445 1071160 1071422 1071473 "GRMOD" 1072002 NIL GRMOD (NIL T T) -9 NIL 1072170) (-444 1070928 1070964 1071092 "GRMOD-" 1071097 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-443 1066254 1067282 1068282 "GRIMAGE" 1069948 T GRIMAGE (NIL) -8 NIL NIL) (-442 1064721 1064981 1065305 "GRDEF" 1065950 T GRDEF (NIL) -7 NIL NIL) (-441 1064165 1064281 1064422 "GRAY" 1064600 T GRAY (NIL) -7 NIL NIL) (-440 1063399 1063779 1063830 "GRALG" 1063983 NIL GRALG (NIL T T) -9 NIL 1064075) (-439 1063060 1063133 1063296 "GRALG-" 1063301 NIL GRALG- (NIL T T T) -8 NIL NIL) (-438 1059868 1062649 1062825 "GPOLSET" 1062967 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-437 1059224 1059281 1059538 "GOSPER" 1059805 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-436 1054983 1055662 1056188 "GMODPOL" 1058923 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-435 1053988 1054172 1054410 "GHENSEL" 1054795 NIL GHENSEL (NIL T T) -7 NIL NIL) (-434 1048054 1048897 1049923 "GENUPS" 1053072 NIL GENUPS (NIL T T) -7 NIL NIL) (-433 1047751 1047802 1047891 "GENUFACT" 1047997 NIL GENUFACT (NIL T) -7 NIL NIL) (-432 1047163 1047240 1047405 "GENPGCD" 1047669 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-431 1046637 1046672 1046885 "GENMFACT" 1047122 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-430 1045205 1045460 1045767 "GENEEZ" 1046380 NIL GENEEZ (NIL T T) -7 NIL NIL) (-429 1039079 1044818 1044979 "GDMP" 1045128 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-428 1028461 1032850 1033956 "GCNAALG" 1038062 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-427 1026883 1027755 1027783 "GCDDOM" 1028038 T GCDDOM (NIL) -9 NIL 1028195) (-426 1026353 1026480 1026695 "GCDDOM-" 1026700 NIL GCDDOM- (NIL T) -8 NIL NIL) (-425 1025025 1025210 1025514 "GB" 1026132 NIL GB (NIL T T T T) -7 NIL NIL) (-424 1013645 1015971 1018363 "GBINTERN" 1022716 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-423 1011482 1011774 1012195 "GBF" 1013320 NIL GBF (NIL T T T T) -7 NIL NIL) (-422 1010263 1010428 1010695 "GBEUCLID" 1011298 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-421 1009612 1009737 1009886 "GAUSSFAC" 1010134 T GAUSSFAC (NIL) -7 NIL NIL) (-420 1007989 1008291 1008604 "GALUTIL" 1009331 NIL GALUTIL (NIL T) -7 NIL NIL) (-419 1006306 1006580 1006903 "GALPOLYU" 1007716 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-418 1003695 1003985 1004390 "GALFACTU" 1006003 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-417 995501 997000 998608 "GALFACT" 1002127 NIL GALFACT (NIL T) -7 NIL NIL) (-416 992889 993547 993575 "FVFUN" 994731 T FVFUN (NIL) -9 NIL 995451) (-415 992155 992337 992365 "FVC" 992656 T FVC (NIL) -9 NIL 992839) (-414 991797 991952 992033 "FUNCTION" 992107 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-413 989467 990018 990507 "FT" 991328 T FT (NIL) -8 NIL NIL) (-412 988285 988768 988971 "FTEM" 989284 T FTEM (NIL) -8 NIL NIL) (-411 986550 986838 987240 "FSUPFACT" 987977 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-410 984947 985236 985568 "FST" 986238 T FST (NIL) -8 NIL NIL) (-409 984122 984228 984422 "FSRED" 984829 NIL FSRED (NIL T T) -7 NIL NIL) (-408 982801 983056 983410 "FSPRMELT" 983837 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-407 979886 980324 980823 "FSPECF" 982364 NIL FSPECF (NIL T T) -7 NIL NIL) (-406 962260 970817 970857 "FS" 974695 NIL FS (NIL T) -9 NIL 976977) (-405 950910 953900 957956 "FS-" 958253 NIL FS- (NIL T T) -8 NIL NIL) (-404 950426 950480 950656 "FSINT" 950851 NIL FSINT (NIL T T) -7 NIL NIL) (-403 948707 949419 949722 "FSERIES" 950205 NIL FSERIES (NIL T T) -8 NIL NIL) (-402 947725 947841 948071 "FSCINT" 948587 NIL FSCINT (NIL T T) -7 NIL NIL) (-401 943960 946670 946711 "FSAGG" 947081 NIL FSAGG (NIL T) -9 NIL 947340) (-400 941722 942323 943119 "FSAGG-" 943214 NIL FSAGG- (NIL T T) -8 NIL NIL) (-399 940764 940907 941134 "FSAGG2" 941575 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-398 938423 938702 939255 "FS2UPS" 940482 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-397 938009 938052 938205 "FS2" 938374 NIL FS2 (NIL T T T T) -7 NIL NIL) (-396 936869 937040 937348 "FS2EXPXP" 937834 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-395 936295 936410 936562 "FRUTIL" 936749 NIL FRUTIL (NIL T) -7 NIL NIL) (-394 927715 931794 933150 "FR" 934971 NIL FR (NIL T) -8 NIL NIL) (-393 922792 925435 925475 "FRNAALG" 926871 NIL FRNAALG (NIL T) -9 NIL 927478) (-392 918471 919541 920816 "FRNAALG-" 921566 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-391 918109 918152 918279 "FRNAAF2" 918422 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-390 916474 916966 917260 "FRMOD" 917922 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-389 914197 914865 915181 "FRIDEAL" 916265 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-388 913396 913483 913770 "FRIDEAL2" 914104 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-387 912654 913062 913103 "FRETRCT" 913108 NIL FRETRCT (NIL T) -9 NIL 913279) (-386 911766 911997 912348 "FRETRCT-" 912353 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-385 908976 910196 910255 "FRAMALG" 911137 NIL FRAMALG (NIL T T) -9 NIL 911429) (-384 907109 907565 908195 "FRAMALG-" 908418 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-383 901011 906584 906860 "FRAC" 906865 NIL FRAC (NIL T) -8 NIL NIL) (-382 900647 900704 900811 "FRAC2" 900948 NIL FRAC2 (NIL T T) -7 NIL NIL) (-381 900283 900340 900447 "FR2" 900584 NIL FR2 (NIL T T) -7 NIL NIL) (-380 894957 897870 897898 "FPS" 899017 T FPS (NIL) -9 NIL 899573) (-379 894406 894515 894679 "FPS-" 894825 NIL FPS- (NIL T) -8 NIL NIL) (-378 891855 893552 893580 "FPC" 893805 T FPC (NIL) -9 NIL 893947) (-377 891648 891688 891785 "FPC-" 891790 NIL FPC- (NIL T) -8 NIL NIL) (-376 890527 891137 891178 "FPATMAB" 891183 NIL FPATMAB (NIL T) -9 NIL 891335) (-375 888227 888703 889129 "FPARFRAC" 890164 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-374 883622 884119 884801 "FORTRAN" 887659 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-373 881338 881838 882377 "FORT" 883103 T FORT (NIL) -7 NIL NIL) (-372 879014 879576 879604 "FORTFN" 880664 T FORTFN (NIL) -9 NIL 881288) (-371 878778 878828 878856 "FORTCAT" 878915 T FORTCAT (NIL) -9 NIL 878977) (-370 876838 877321 877720 "FORMULA" 878399 T FORMULA (NIL) -8 NIL NIL) (-369 876626 876656 876725 "FORMULA1" 876802 NIL FORMULA1 (NIL T) -7 NIL NIL) (-368 876149 876201 876374 "FORDER" 876568 NIL FORDER (NIL T T T T) -7 NIL NIL) (-367 875245 875409 875602 "FOP" 875976 T FOP (NIL) -7 NIL NIL) (-366 873853 874525 874699 "FNLA" 875127 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-365 872522 872911 872939 "FNCAT" 873511 T FNCAT (NIL) -9 NIL 873804) (-364 872088 872481 872509 "FNAME" 872514 T FNAME (NIL) -8 NIL NIL) (-363 870748 871721 871749 "FMTC" 871754 T FMTC (NIL) -9 NIL 871789) (-362 867066 868273 868901 "FMONOID" 870153 NIL FMONOID (NIL T) -8 NIL NIL) (-361 866286 866809 866957 "FM" 866962 NIL FM (NIL T T) -8 NIL NIL) (-360 863710 864356 864384 "FMFUN" 865528 T FMFUN (NIL) -9 NIL 866236) (-359 862979 863160 863188 "FMC" 863478 T FMC (NIL) -9 NIL 863660) (-358 860209 861043 861096 "FMCAT" 862278 NIL FMCAT (NIL T T) -9 NIL 862772) (-357 859104 859977 860076 "FM1" 860154 NIL FM1 (NIL T T) -8 NIL NIL) (-356 856878 857294 857788 "FLOATRP" 858655 NIL FLOATRP (NIL T) -7 NIL NIL) (-355 850364 854534 855164 "FLOAT" 856268 T FLOAT (NIL) -8 NIL NIL) (-354 847802 848302 848880 "FLOATCP" 849831 NIL FLOATCP (NIL T) -7 NIL NIL) (-353 846591 847439 847479 "FLINEXP" 847484 NIL FLINEXP (NIL T) -9 NIL 847577) (-352 845746 845981 846308 "FLINEXP-" 846313 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-351 844822 844966 845190 "FLASORT" 845598 NIL FLASORT (NIL T T) -7 NIL NIL) (-350 842041 842883 842935 "FLALG" 844162 NIL FLALG (NIL T T) -9 NIL 844629) (-349 835826 839528 839569 "FLAGG" 840831 NIL FLAGG (NIL T) -9 NIL 841483) (-348 834552 834891 835381 "FLAGG-" 835386 NIL FLAGG- (NIL T T) -8 NIL NIL) (-347 833594 833737 833964 "FLAGG2" 834405 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-346 830567 831585 831644 "FINRALG" 832772 NIL FINRALG (NIL T T) -9 NIL 833280) (-345 829727 829956 830295 "FINRALG-" 830300 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-344 829134 829347 829375 "FINITE" 829571 T FINITE (NIL) -9 NIL 829678) (-343 821594 823755 823795 "FINAALG" 827462 NIL FINAALG (NIL T) -9 NIL 828915) (-342 816935 817976 819120 "FINAALG-" 820499 NIL FINAALG- (NIL T T) -8 NIL NIL) (-341 816330 816690 816793 "FILE" 816865 NIL FILE (NIL T) -8 NIL NIL) (-340 815015 815327 815381 "FILECAT" 816065 NIL FILECAT (NIL T T) -9 NIL 816281) (-339 812878 814434 814462 "FIELD" 814502 T FIELD (NIL) -9 NIL 814582) (-338 811498 811883 812394 "FIELD-" 812399 NIL FIELD- (NIL T) -8 NIL NIL) (-337 809313 810135 810481 "FGROUP" 811185 NIL FGROUP (NIL T) -8 NIL NIL) (-336 808403 808567 808787 "FGLMICPK" 809145 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-335 804205 808328 808385 "FFX" 808390 NIL FFX (NIL T NIL) -8 NIL NIL) (-334 803806 803867 804002 "FFSLPE" 804138 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-333 799799 800578 801374 "FFPOLY" 803042 NIL FFPOLY (NIL T) -7 NIL NIL) (-332 799303 799339 799548 "FFPOLY2" 799757 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-331 795125 799222 799285 "FFP" 799290 NIL FFP (NIL T NIL) -8 NIL NIL) (-330 790493 795036 795100 "FF" 795105 NIL FF (NIL NIL NIL) -8 NIL NIL) (-329 785589 789836 790026 "FFNBX" 790347 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-328 780499 784724 784982 "FFNBP" 785443 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-327 775102 779783 779994 "FFNB" 780332 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-326 773934 774132 774447 "FFINTBAS" 774899 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-325 770158 772398 772426 "FFIELDC" 773046 T FFIELDC (NIL) -9 NIL 773422) (-324 768821 769191 769688 "FFIELDC-" 769693 NIL FFIELDC- (NIL T) -8 NIL NIL) (-323 768391 768436 768560 "FFHOM" 768763 NIL FFHOM (NIL T T T) -7 NIL NIL) (-322 766089 766573 767090 "FFF" 767906 NIL FFF (NIL T) -7 NIL NIL) (-321 761677 765831 765932 "FFCGX" 766032 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-320 757279 761409 761516 "FFCGP" 761620 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-319 752432 757006 757114 "FFCG" 757215 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-318 734378 743501 743587 "FFCAT" 748752 NIL FFCAT (NIL T T T) -9 NIL 750239) (-317 729576 730623 731937 "FFCAT-" 733167 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-316 728987 729030 729265 "FFCAT2" 729527 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-315 718187 721977 723194 "FEXPR" 727842 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-314 717187 717622 717663 "FEVALAB" 717747 NIL FEVALAB (NIL T) -9 NIL 718008) (-313 716346 716556 716894 "FEVALAB-" 716899 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-312 714939 715729 715932 "FDIV" 716245 NIL FDIV (NIL T T T T) -8 NIL NIL) (-311 712006 712721 712836 "FDIVCAT" 714404 NIL FDIVCAT (NIL T T T T) -9 NIL 714841) (-310 711768 711795 711965 "FDIVCAT-" 711970 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-309 710988 711075 711352 "FDIV2" 711675 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-308 709674 709933 710222 "FCPAK1" 710719 T FCPAK1 (NIL) -7 NIL NIL) (-307 708802 709174 709315 "FCOMP" 709565 NIL FCOMP (NIL T) -8 NIL NIL) (-306 692438 695851 699412 "FC" 705261 T FC (NIL) -8 NIL NIL) (-305 685034 689080 689120 "FAXF" 690922 NIL FAXF (NIL T) -9 NIL 691613) (-304 682313 682968 683793 "FAXF-" 684258 NIL FAXF- (NIL T T) -8 NIL NIL) (-303 677413 681689 681865 "FARRAY" 682170 NIL FARRAY (NIL T) -8 NIL NIL) (-302 672804 674875 674927 "FAMR" 675939 NIL FAMR (NIL T T) -9 NIL 676399) (-301 671695 671997 672431 "FAMR-" 672436 NIL FAMR- (NIL T T T) -8 NIL NIL) (-300 670891 671617 671670 "FAMONOID" 671675 NIL FAMONOID (NIL T) -8 NIL NIL) (-299 668724 669408 669461 "FAMONC" 670402 NIL FAMONC (NIL T T) -9 NIL 670787) (-298 667416 668478 668615 "FAGROUP" 668620 NIL FAGROUP (NIL T) -8 NIL NIL) (-297 665219 665538 665940 "FACUTIL" 667097 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-296 664318 664503 664725 "FACTFUNC" 665029 NIL FACTFUNC (NIL T) -7 NIL NIL) (-295 656638 663569 663781 "EXPUPXS" 664174 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-294 654121 654661 655247 "EXPRTUBE" 656072 T EXPRTUBE (NIL) -7 NIL NIL) (-293 650315 650907 651644 "EXPRODE" 653460 NIL EXPRODE (NIL T T) -7 NIL NIL) (-292 635474 648974 649400 "EXPR" 649921 NIL EXPR (NIL T) -8 NIL NIL) (-291 629902 630489 631301 "EXPR2UPS" 634772 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-290 629538 629595 629702 "EXPR2" 629839 NIL EXPR2 (NIL T T) -7 NIL NIL) (-289 620892 628675 628970 "EXPEXPAN" 629376 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-288 620719 620849 620878 "EXIT" 620883 T EXIT (NIL) -8 NIL NIL) (-287 620346 620408 620521 "EVALCYC" 620651 NIL EVALCYC (NIL T) -7 NIL NIL) (-286 619887 620005 620046 "EVALAB" 620216 NIL EVALAB (NIL T) -9 NIL 620320) (-285 619368 619490 619711 "EVALAB-" 619716 NIL EVALAB- (NIL T T) -8 NIL NIL) (-284 616831 618143 618171 "EUCDOM" 618726 T EUCDOM (NIL) -9 NIL 619076) (-283 615236 615678 616268 "EUCDOM-" 616273 NIL EUCDOM- (NIL T) -8 NIL NIL) (-282 602814 605562 608302 "ESTOOLS" 612516 T ESTOOLS (NIL) -7 NIL NIL) (-281 602450 602507 602614 "ESTOOLS2" 602751 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-280 602201 602243 602323 "ESTOOLS1" 602402 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-279 596139 597863 597891 "ES" 600655 T ES (NIL) -9 NIL 602061) (-278 591087 592373 594190 "ES-" 594354 NIL ES- (NIL T) -8 NIL NIL) (-277 587462 588222 589002 "ESCONT" 590327 T ESCONT (NIL) -7 NIL NIL) (-276 587207 587239 587321 "ESCONT1" 587424 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-275 586882 586932 587032 "ES2" 587151 NIL ES2 (NIL T T) -7 NIL NIL) (-274 586512 586570 586679 "ES1" 586818 NIL ES1 (NIL T T) -7 NIL NIL) (-273 585728 585857 586033 "ERROR" 586356 T ERROR (NIL) -7 NIL NIL) (-272 579231 585587 585678 "EQTBL" 585683 NIL EQTBL (NIL T T) -8 NIL NIL) (-271 571668 574549 575996 "EQ" 577817 NIL -2531 (NIL T) -8 NIL NIL) (-270 571300 571357 571466 "EQ2" 571605 NIL EQ2 (NIL T T) -7 NIL NIL) (-269 566592 567638 568731 "EP" 570239 NIL EP (NIL T) -7 NIL NIL) (-268 565175 565475 565792 "ENV" 566295 T ENV (NIL) -8 NIL NIL) (-267 564335 564899 564927 "ENTIRER" 564932 T ENTIRER (NIL) -9 NIL 564977) (-266 560791 562290 562660 "EMR" 564134 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-265 559935 560120 560174 "ELTAGG" 560554 NIL ELTAGG (NIL T T) -9 NIL 560765) (-264 559654 559716 559857 "ELTAGG-" 559862 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-263 559443 559472 559526 "ELTAB" 559610 NIL ELTAB (NIL T T) -9 NIL NIL) (-262 558569 558715 558914 "ELFUTS" 559294 NIL ELFUTS (NIL T T) -7 NIL NIL) (-261 558311 558367 558395 "ELEMFUN" 558500 T ELEMFUN (NIL) -9 NIL NIL) (-260 558181 558202 558270 "ELEMFUN-" 558275 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-259 553073 556282 556323 "ELAGG" 557263 NIL ELAGG (NIL T) -9 NIL 557726) (-258 551358 551792 552455 "ELAGG-" 552460 NIL ELAGG- (NIL T T) -8 NIL NIL) (-257 550015 550295 550590 "ELABEXPR" 551083 T ELABEXPR (NIL) -8 NIL NIL) (-256 542883 544682 545509 "EFUPXS" 549291 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-255 536333 538134 538944 "EFULS" 542159 NIL EFULS (NIL T T T) -8 NIL NIL) (-254 533764 534122 534600 "EFSTRUC" 535965 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-253 522836 524401 525961 "EF" 532279 NIL EF (NIL T T) -7 NIL NIL) (-252 521937 522321 522470 "EAB" 522707 T EAB (NIL) -8 NIL NIL) (-251 521150 521896 521924 "E04UCFA" 521929 T E04UCFA (NIL) -8 NIL NIL) (-250 520363 521109 521137 "E04NAFA" 521142 T E04NAFA (NIL) -8 NIL NIL) (-249 519576 520322 520350 "E04MBFA" 520355 T E04MBFA (NIL) -8 NIL NIL) (-248 518789 519535 519563 "E04JAFA" 519568 T E04JAFA (NIL) -8 NIL NIL) (-247 518004 518748 518776 "E04GCFA" 518781 T E04GCFA (NIL) -8 NIL NIL) (-246 517219 517963 517991 "E04FDFA" 517996 T E04FDFA (NIL) -8 NIL NIL) (-245 516432 517178 517206 "E04DGFA" 517211 T E04DGFA (NIL) -8 NIL NIL) (-244 510617 511962 513324 "E04AGNT" 515090 T E04AGNT (NIL) -7 NIL NIL) (-243 509344 509824 509864 "DVARCAT" 510339 NIL DVARCAT (NIL T) -9 NIL 510537) (-242 508548 508760 509074 "DVARCAT-" 509079 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-241 501410 508350 508477 "DSMP" 508482 NIL DSMP (NIL T T T) -8 NIL NIL) (-240 496220 497355 498423 "DROPT" 500362 T DROPT (NIL) -8 NIL NIL) (-239 495885 495944 496042 "DROPT1" 496155 NIL DROPT1 (NIL T) -7 NIL NIL) (-238 491000 492126 493263 "DROPT0" 494768 T DROPT0 (NIL) -7 NIL NIL) (-237 489345 489670 490056 "DRAWPT" 490634 T DRAWPT (NIL) -7 NIL NIL) (-236 483932 484855 485934 "DRAW" 488319 NIL DRAW (NIL T) -7 NIL NIL) (-235 483565 483618 483736 "DRAWHACK" 483873 NIL DRAWHACK (NIL T) -7 NIL NIL) (-234 482296 482565 482856 "DRAWCX" 483294 T DRAWCX (NIL) -7 NIL NIL) (-233 481814 481882 482032 "DRAWCURV" 482222 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-232 472286 474244 476359 "DRAWCFUN" 479719 T DRAWCFUN (NIL) -7 NIL NIL) (-231 469100 470982 471023 "DQAGG" 471652 NIL DQAGG (NIL T) -9 NIL 471925) (-230 457607 464345 464427 "DPOLCAT" 466265 NIL DPOLCAT (NIL T T T T) -9 NIL 466809) (-229 452447 453793 455750 "DPOLCAT-" 455755 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-228 446531 452309 452406 "DPMO" 452411 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-227 440518 446312 446478 "DPMM" 446483 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-226 440031 440129 440249 "DOMAIN" 440418 T DOMAIN (NIL) -8 NIL NIL) (-225 433743 439668 439819 "DMP" 439932 NIL DMP (NIL NIL T) -8 NIL NIL) (-224 433343 433399 433543 "DLP" 433681 NIL DLP (NIL T) -7 NIL NIL) (-223 426987 432444 432671 "DLIST" 433148 NIL DLIST (NIL T) -8 NIL NIL) (-222 423834 425843 425884 "DLAGG" 426434 NIL DLAGG (NIL T) -9 NIL 426663) (-221 422544 423236 423264 "DIVRING" 423414 T DIVRING (NIL) -9 NIL 423522) (-220 421532 421785 422178 "DIVRING-" 422183 NIL DIVRING- (NIL T) -8 NIL NIL) (-219 419634 419991 420397 "DISPLAY" 421146 T DISPLAY (NIL) -7 NIL NIL) (-218 413523 419548 419611 "DIRPROD" 419616 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-217 412371 412574 412839 "DIRPROD2" 413316 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-216 402002 408007 408060 "DIRPCAT" 408468 NIL DIRPCAT (NIL NIL T) -9 NIL 409295) (-215 399328 399970 400851 "DIRPCAT-" 401188 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-214 398615 398775 398961 "DIOSP" 399162 T DIOSP (NIL) -7 NIL NIL) (-213 395318 397528 397569 "DIOPS" 398003 NIL DIOPS (NIL T) -9 NIL 398232) (-212 394867 394981 395172 "DIOPS-" 395177 NIL DIOPS- (NIL T T) -8 NIL NIL) (-211 393739 394377 394405 "DIFRING" 394592 T DIFRING (NIL) -9 NIL 394701) (-210 393385 393462 393614 "DIFRING-" 393619 NIL DIFRING- (NIL T) -8 NIL NIL) (-209 391175 392457 392497 "DIFEXT" 392856 NIL DIFEXT (NIL T) -9 NIL 393149) (-208 389461 389889 390554 "DIFEXT-" 390559 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-207 386784 388994 389035 "DIAGG" 389040 NIL DIAGG (NIL T) -9 NIL 389060) (-206 386168 386325 386577 "DIAGG-" 386582 NIL DIAGG- (NIL T T) -8 NIL NIL) (-205 381633 385127 385404 "DHMATRIX" 385937 NIL DHMATRIX (NIL T) -8 NIL NIL) (-204 377245 378154 379164 "DFSFUN" 380643 T DFSFUN (NIL) -7 NIL NIL) (-203 372031 375959 376324 "DFLOAT" 376900 T DFLOAT (NIL) -8 NIL NIL) (-202 370264 370545 370940 "DFINTTLS" 371739 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-201 367297 368299 368697 "DERHAM" 369931 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-200 365146 367072 367161 "DEQUEUE" 367241 NIL DEQUEUE (NIL T) -8 NIL NIL) (-199 364364 364497 364692 "DEGRED" 365008 NIL DEGRED (NIL T T) -7 NIL NIL) (-198 360764 361509 362361 "DEFINTRF" 363592 NIL DEFINTRF (NIL T) -7 NIL NIL) (-197 358295 358764 359362 "DEFINTEF" 360283 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-196 352126 357736 357902 "DECIMAL" 358149 T DECIMAL (NIL) -8 NIL NIL) (-195 349638 350096 350602 "DDFACT" 351670 NIL DDFACT (NIL T T) -7 NIL NIL) (-194 349234 349277 349428 "DBLRESP" 349589 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-193 346944 347278 347647 "DBASE" 348992 NIL DBASE (NIL T) -8 NIL NIL) (-192 346079 346903 346931 "D03FAFA" 346936 T D03FAFA (NIL) -8 NIL NIL) (-191 345215 346038 346066 "D03EEFA" 346071 T D03EEFA (NIL) -8 NIL NIL) (-190 343165 343631 344120 "D03AGNT" 344746 T D03AGNT (NIL) -7 NIL NIL) (-189 342483 343124 343152 "D02EJFA" 343157 T D02EJFA (NIL) -8 NIL NIL) (-188 341801 342442 342470 "D02CJFA" 342475 T D02CJFA (NIL) -8 NIL NIL) (-187 341119 341760 341788 "D02BHFA" 341793 T D02BHFA (NIL) -8 NIL NIL) (-186 340437 341078 341106 "D02BBFA" 341111 T D02BBFA (NIL) -8 NIL NIL) (-185 333635 335223 336829 "D02AGNT" 338851 T D02AGNT (NIL) -7 NIL NIL) (-184 331404 331926 332472 "D01WGTS" 333109 T D01WGTS (NIL) -7 NIL NIL) (-183 330507 331363 331391 "D01TRNS" 331396 T D01TRNS (NIL) -8 NIL NIL) (-182 329610 330466 330494 "D01GBFA" 330499 T D01GBFA (NIL) -8 NIL NIL) (-181 328713 329569 329597 "D01FCFA" 329602 T D01FCFA (NIL) -8 NIL NIL) (-180 327816 328672 328700 "D01ASFA" 328705 T D01ASFA (NIL) -8 NIL NIL) (-179 326919 327775 327803 "D01AQFA" 327808 T D01AQFA (NIL) -8 NIL NIL) (-178 326022 326878 326906 "D01APFA" 326911 T D01APFA (NIL) -8 NIL NIL) (-177 325125 325981 326009 "D01ANFA" 326014 T D01ANFA (NIL) -8 NIL NIL) (-176 324228 325084 325112 "D01AMFA" 325117 T D01AMFA (NIL) -8 NIL NIL) (-175 323331 324187 324215 "D01ALFA" 324220 T D01ALFA (NIL) -8 NIL NIL) (-174 322434 323290 323318 "D01AKFA" 323323 T D01AKFA (NIL) -8 NIL NIL) (-173 321537 322393 322421 "D01AJFA" 322426 T D01AJFA (NIL) -8 NIL NIL) (-172 314841 316390 317949 "D01AGNT" 319998 T D01AGNT (NIL) -7 NIL NIL) (-171 314178 314306 314458 "CYCLOTOM" 314709 T CYCLOTOM (NIL) -7 NIL NIL) (-170 310913 311626 312353 "CYCLES" 313471 T CYCLES (NIL) -7 NIL NIL) (-169 310225 310359 310530 "CVMP" 310774 NIL CVMP (NIL T) -7 NIL NIL) (-168 308007 308264 308639 "CTRIGMNP" 309953 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-167 307612 307695 307800 "CTORCALL" 307922 T CTORCALL (NIL) -8 NIL NIL) (-166 306986 307085 307238 "CSTTOOLS" 307509 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-165 302785 303442 304200 "CRFP" 306298 NIL CRFP (NIL T T) -7 NIL NIL) (-164 301832 302017 302245 "CRAPACK" 302589 NIL CRAPACK (NIL T) -7 NIL NIL) (-163 301216 301317 301521 "CPMATCH" 301708 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-162 300941 300969 301075 "CPIMA" 301182 NIL CPIMA (NIL T T T) -7 NIL NIL) (-161 297305 297977 298695 "COORDSYS" 300276 NIL COORDSYS (NIL T) -7 NIL NIL) (-160 296689 296818 296968 "CONTOUR" 297175 T CONTOUR (NIL) -8 NIL NIL) (-159 292550 294692 295184 "CONTFRAC" 296229 NIL CONTFRAC (NIL T) -8 NIL NIL) (-158 291704 292268 292296 "COMRING" 292301 T COMRING (NIL) -9 NIL 292352) (-157 290785 291062 291246 "COMPPROP" 291540 T COMPPROP (NIL) -8 NIL NIL) (-156 290446 290481 290609 "COMPLPAT" 290744 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-155 280427 290255 290364 "COMPLEX" 290369 NIL COMPLEX (NIL T) -8 NIL NIL) (-154 280063 280120 280227 "COMPLEX2" 280364 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-153 279781 279816 279914 "COMPFACT" 280022 NIL COMPFACT (NIL T T) -7 NIL NIL) (-152 264116 274410 274450 "COMPCAT" 275452 NIL COMPCAT (NIL T) -9 NIL 276845) (-151 253631 256555 260182 "COMPCAT-" 260538 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-150 253362 253390 253492 "COMMUPC" 253597 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-149 253157 253190 253249 "COMMONOP" 253323 T COMMONOP (NIL) -7 NIL NIL) (-148 252740 252908 252995 "COMM" 253090 T COMM (NIL) -8 NIL NIL) (-147 251989 252183 252211 "COMBOPC" 252549 T COMBOPC (NIL) -9 NIL 252724) (-146 250885 251095 251337 "COMBINAT" 251779 NIL COMBINAT (NIL T) -7 NIL NIL) (-145 247083 247656 248296 "COMBF" 250307 NIL COMBF (NIL T T) -7 NIL NIL) (-144 245869 246199 246434 "COLOR" 246868 T COLOR (NIL) -8 NIL NIL) (-143 245509 245556 245681 "CMPLXRT" 245816 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-142 241011 242039 243119 "CLIP" 244449 T CLIP (NIL) -7 NIL NIL) (-141 239349 240119 240357 "CLIF" 240839 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-140 235572 237496 237537 "CLAGG" 238466 NIL CLAGG (NIL T) -9 NIL 239002) (-139 233994 234451 235034 "CLAGG-" 235039 NIL CLAGG- (NIL T T) -8 NIL NIL) (-138 233538 233623 233763 "CINTSLPE" 233903 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-137 231039 231510 232058 "CHVAR" 233066 NIL CHVAR (NIL T T T) -7 NIL NIL) (-136 230262 230826 230854 "CHARZ" 230859 T CHARZ (NIL) -9 NIL 230873) (-135 230016 230056 230134 "CHARPOL" 230216 NIL CHARPOL (NIL T) -7 NIL NIL) (-134 229123 229720 229748 "CHARNZ" 229795 T CHARNZ (NIL) -9 NIL 229850) (-133 227148 227813 228148 "CHAR" 228808 T CHAR (NIL) -8 NIL NIL) (-132 226874 226935 226963 "CFCAT" 227074 T CFCAT (NIL) -9 NIL NIL) (-131 226119 226230 226412 "CDEN" 226758 NIL CDEN (NIL T T T) -7 NIL NIL) (-130 222111 225272 225552 "CCLASS" 225859 T CCLASS (NIL) -8 NIL NIL) (-129 222030 222056 222091 "CATEGORY" 222096 T -10 (NIL) -8 NIL NIL) (-128 217082 218059 218812 "CARTEN" 221333 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-127 216190 216338 216559 "CARTEN2" 216929 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-126 214488 215342 215598 "CARD" 215954 T CARD (NIL) -8 NIL NIL) (-125 213861 214189 214217 "CACHSET" 214349 T CACHSET (NIL) -9 NIL 214426) (-124 213358 213654 213682 "CABMON" 213732 T CABMON (NIL) -9 NIL 213788) (-123 210915 213050 213157 "BTREE" 213284 NIL BTREE (NIL T) -8 NIL NIL) (-122 208413 210563 210685 "BTOURN" 210825 NIL BTOURN (NIL T) -8 NIL NIL) (-121 205832 207885 207926 "BTCAT" 207994 NIL BTCAT (NIL T) -9 NIL 208071) (-120 205499 205579 205728 "BTCAT-" 205733 NIL BTCAT- (NIL T T) -8 NIL NIL) (-119 200720 204591 204619 "BTAGG" 204875 T BTAGG (NIL) -9 NIL 205054) (-118 200143 200287 200517 "BTAGG-" 200522 NIL BTAGG- (NIL T) -8 NIL NIL) (-117 197187 199421 199636 "BSTREE" 199960 NIL BSTREE (NIL T) -8 NIL NIL) (-116 196325 196451 196635 "BRILL" 197043 NIL BRILL (NIL T) -7 NIL NIL) (-115 193027 195054 195095 "BRAGG" 195744 NIL BRAGG (NIL T) -9 NIL 196001) (-114 191556 191962 192517 "BRAGG-" 192522 NIL BRAGG- (NIL T T) -8 NIL NIL) (-113 184764 190902 191086 "BPADICRT" 191404 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-112 183068 184701 184746 "BPADIC" 184751 NIL BPADIC (NIL NIL) -8 NIL NIL) (-111 182768 182798 182911 "BOUNDZRO" 183032 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-110 178283 179374 180241 "BOP" 181921 T BOP (NIL) -8 NIL NIL) (-109 175904 176348 176868 "BOP1" 177796 NIL BOP1 (NIL T) -7 NIL NIL) (-108 174523 175234 175457 "BOOLEAN" 175701 T BOOLEAN (NIL) -8 NIL NIL) (-107 173890 174268 174320 "BMODULE" 174325 NIL BMODULE (NIL T T) -9 NIL 174389) (-106 169700 173688 173761 "BITS" 173837 T BITS (NIL) -8 NIL NIL) (-105 168797 169232 169384 "BINFILE" 169568 T BINFILE (NIL) -8 NIL NIL) (-104 168209 168331 168473 "BINDING" 168675 T BINDING (NIL) -8 NIL NIL) (-103 162044 167653 167818 "BINARY" 168064 T BINARY (NIL) -8 NIL NIL) (-102 159872 161300 161341 "BGAGG" 161601 NIL BGAGG (NIL T) -9 NIL 161738) (-101 159703 159735 159826 "BGAGG-" 159831 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 158801 159087 159292 "BFUNCT" 159518 T BFUNCT (NIL) -8 NIL NIL) (-99 157502 157680 157965 "BEZOUT" 158625 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 154027 156362 156690 "BBTREE" 157205 NIL BBTREE (NIL T) -8 NIL NIL) (-97 153765 153818 153844 "BASTYPE" 153961 T BASTYPE (NIL) -9 NIL NIL) (-96 153620 153649 153719 "BASTYPE-" 153724 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 153058 153134 153284 "BALFACT" 153531 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 151880 152477 152662 "AUTOMOR" 152903 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151606 151611 151637 "ATTREG" 151642 T ATTREG (NIL) -9 NIL NIL) (-92 149885 150303 150655 "ATTRBUT" 151272 T ATTRBUT (NIL) -8 NIL NIL) (-91 149421 149534 149560 "ATRIG" 149761 T ATRIG (NIL) -9 NIL NIL) (-90 149230 149271 149358 "ATRIG-" 149363 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147427 149006 149094 "ASTACK" 149173 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145932 146229 146594 "ASSOCEQ" 147109 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144964 145591 145715 "ASP9" 145839 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144728 144912 144951 "ASP8" 144956 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143598 144333 144475 "ASP80" 144617 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142497 143233 143365 "ASP7" 143497 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141453 142174 142292 "ASP78" 142410 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140424 141133 141250 "ASP77" 141367 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139338 140062 140193 "ASP74" 140324 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 138239 138973 139105 "ASP73" 139237 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 137194 137916 138034 "ASP6" 138152 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136143 136871 136989 "ASP55" 137107 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135093 135817 135936 "ASP50" 136055 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134181 134794 134904 "ASP4" 135014 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 133269 133882 133992 "ASP49" 134102 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 132054 132808 132976 "ASP42" 133158 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130832 131587 131757 "ASP41" 131941 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129784 130509 130627 "ASP35" 130745 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129549 129732 129771 "ASP34" 129776 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 129286 129353 129429 "ASP33" 129504 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 128182 128921 129053 "ASP31" 129185 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127947 128130 128169 "ASP30" 128174 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127682 127751 127827 "ASP29" 127902 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127447 127630 127669 "ASP28" 127674 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 127212 127395 127434 "ASP27" 127439 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 126296 126910 127021 "ASP24" 127132 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 125213 125937 126067 "ASP20" 126197 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124301 124914 125024 "ASP1" 125134 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 123245 123975 124094 "ASP19" 124213 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122982 123049 123125 "ASP12" 123200 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121835 122581 122725 "ASP10" 122869 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119734 121679 121770 "ARRAY2" 121775 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115550 119382 119496 "ARRAY1" 119651 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114582 114755 114976 "ARRAY12" 115373 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108942 110813 110888 "ARR2CAT" 113518 NIL ARR2CAT (NIL T T T) -9 NIL 114276) (-54 106376 107120 108074 "ARR2CAT-" 108079 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 105136 105286 105589 "APPRULE" 106214 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 104789 104837 104955 "APPLYORE" 105082 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 103763 104054 104249 "ANY" 104612 T ANY (NIL) -8 NIL NIL) (-50 103041 103164 103321 "ANY1" 103637 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100573 101491 101816 "ANTISYM" 102766 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100088 100277 100374 "ANON" 100494 T ANON (NIL) -8 NIL NIL) (-47 94165 98633 99084 "AN" 99655 T AN (NIL) -8 NIL NIL) (-46 90519 91917 91967 "AMR" 92706 NIL AMR (NIL T T) -9 NIL 93305) (-45 89632 89853 90215 "AMR-" 90220 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74182 89549 89610 "ALIST" 89615 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71019 73776 73945 "ALGSC" 74100 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 67575 68129 68736 "ALGPKG" 70459 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 66852 66953 67137 "ALGMFACT" 67461 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 62602 63282 63936 "ALGMANIP" 66376 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 53921 62228 62378 "ALGFF" 62535 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53117 53248 53427 "ALGFACT" 53779 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52108 52718 52756 "ALGEBRA" 52816 NIL ALGEBRA (NIL T) -9 NIL 52874) (-36 51826 51885 52017 "ALGEBRA-" 52022 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34087 49830 49882 "ALAGG" 50018 NIL ALAGG (NIL T T) -9 NIL 50179) (-34 33623 33736 33762 "AHYP" 33963 T AHYP (NIL) -9 NIL NIL) (-33 32554 32802 32828 "AGG" 33327 T AGG (NIL) -9 NIL 33606) (-32 31988 32150 32364 "AGG-" 32369 NIL AGG- (NIL T) -8 NIL NIL) (-31 29675 30093 30510 "AF" 31631 NIL AF (NIL T T) -7 NIL NIL) (-30 28944 29202 29358 "ACPLOT" 29537 T ACPLOT (NIL) -8 NIL NIL) (-29 18411 26357 26408 "ACFS" 27119 NIL ACFS (NIL T) -9 NIL 27358) (-28 16425 16915 17690 "ACFS-" 17695 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12693 14649 14675 "ACF" 15554 T ACF (NIL) -9 NIL 15966) (-26 11397 11731 12224 "ACF-" 12229 NIL ACF- (NIL T) -8 NIL NIL) (-25 10996 11165 11191 "ABELSG" 11283 T ABELSG (NIL) -9 NIL 11348) (-24 10863 10888 10954 "ABELSG-" 10959 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10233 10494 10520 "ABELMON" 10690 T ABELMON (NIL) -9 NIL 10802) (-22 9897 9981 10119 "ABELMON-" 10124 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9232 9578 9604 "ABELGRP" 9729 T ABELGRP (NIL) -9 NIL 9811) (-20 8695 8824 9040 "ABELGRP-" 9045 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
\ No newline at end of file +((-3 3139929 3139934 3139939 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-2 3139914 3139919 3139924 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1 3139899 3139904 3139909 NIL NIL NIL NIL (NIL) -8 NIL NIL) (0 3139884 3139889 3139894 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1195 3139014 3139759 3139836 "ZMOD" 3139841 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1194 3138124 3138288 3138497 "ZLINDEP" 3138846 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1193 3127528 3129273 3131225 "ZDSOLVE" 3136273 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1192 3126774 3126915 3127104 "YSTREAM" 3127374 NIL YSTREAM (NIL T) -7 NIL NIL) (-1191 3124543 3126079 3126282 "XRPOLY" 3126617 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1190 3121005 3122334 3122916 "XPR" 3124007 NIL XPR (NIL T T) -8 NIL NIL) (-1189 3118719 3120340 3120543 "XPOLY" 3120836 NIL XPOLY (NIL T) -8 NIL NIL) (-1188 3116533 3117911 3117965 "XPOLYC" 3118250 NIL XPOLYC (NIL T T) -9 NIL 3118363) (-1187 3112905 3115050 3115438 "XPBWPOLY" 3116191 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1186 3108833 3111146 3111188 "XF" 3111809 NIL XF (NIL T) -9 NIL 3112208) (-1185 3108454 3108542 3108711 "XF-" 3108716 NIL XF- (NIL T T) -8 NIL NIL) (-1184 3103834 3105133 3105187 "XFALG" 3107335 NIL XFALG (NIL T T) -9 NIL 3108122) (-1183 3102971 3103075 3103279 "XEXPPKG" 3103726 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1182 3101070 3102822 3102917 "XDPOLY" 3102922 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1181 3099949 3100559 3100601 "XALG" 3100663 NIL XALG (NIL T) -9 NIL 3100782) (-1180 3093425 3097933 3098426 "WUTSET" 3099541 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1179 3091237 3092044 3092395 "WP" 3093207 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1178 3090123 3090321 3090616 "WFFINTBS" 3091034 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1177 3088027 3088454 3088916 "WEIER" 3089695 NIL WEIER (NIL T) -7 NIL NIL) (-1176 3087176 3087600 3087642 "VSPACE" 3087778 NIL VSPACE (NIL T) -9 NIL 3087852) (-1175 3087014 3087041 3087132 "VSPACE-" 3087137 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1174 3086760 3086803 3086874 "VOID" 3086965 T VOID (NIL) -8 NIL NIL) (-1173 3084896 3085255 3085661 "VIEW" 3086376 T VIEW (NIL) -7 NIL NIL) (-1172 3081321 3081959 3082696 "VIEWDEF" 3084181 T VIEWDEF (NIL) -7 NIL NIL) (-1171 3070659 3072869 3075042 "VIEW3D" 3079170 T VIEW3D (NIL) -8 NIL NIL) (-1170 3062941 3064570 3066149 "VIEW2D" 3069102 T VIEW2D (NIL) -8 NIL NIL) (-1169 3058350 3062711 3062803 "VECTOR" 3062884 NIL VECTOR (NIL T) -8 NIL NIL) (-1168 3056927 3057186 3057504 "VECTOR2" 3058080 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1167 3050467 3054719 3054762 "VECTCAT" 3055750 NIL VECTCAT (NIL T) -9 NIL 3056334) (-1166 3049481 3049735 3050125 "VECTCAT-" 3050130 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1165 3048962 3049132 3049252 "VARIABLE" 3049396 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1164 3048895 3048900 3048930 "UTYPE" 3048935 T UTYPE (NIL) -9 NIL NIL) (-1163 3047730 3047884 3048145 "UTSODETL" 3048721 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1162 3045170 3045630 3046154 "UTSODE" 3047271 NIL UTSODE (NIL T T) -7 NIL NIL) (-1161 3037014 3042810 3043298 "UTS" 3044739 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1160 3028359 3033724 3033766 "UTSCAT" 3034867 NIL UTSCAT (NIL T) -9 NIL 3035624) (-1159 3025714 3026430 3027418 "UTSCAT-" 3027423 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1158 3025345 3025388 3025519 "UTS2" 3025665 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1157 3019621 3022186 3022229 "URAGG" 3024299 NIL URAGG (NIL T) -9 NIL 3025021) (-1156 3016560 3017423 3018546 "URAGG-" 3018551 NIL URAGG- (NIL T T) -8 NIL NIL) (-1155 3012246 3015177 3015648 "UPXSSING" 3016224 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1154 3004137 3011367 3011647 "UPXS" 3012023 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1153 2997166 3004042 3004113 "UPXSCONS" 3004118 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1152 2987455 2994285 2994346 "UPXSCCA" 2994995 NIL UPXSCCA (NIL T T) -9 NIL 2995236) (-1151 2987094 2987179 2987352 "UPXSCCA-" 2987357 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1150 2977305 2983908 2983950 "UPXSCAT" 2984593 NIL UPXSCAT (NIL T) -9 NIL 2985201) (-1149 2976739 2976818 2976995 "UPXS2" 2977220 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1148 2975393 2975646 2975997 "UPSQFREE" 2976482 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1147 2969284 2972339 2972393 "UPSCAT" 2973542 NIL UPSCAT (NIL T T) -9 NIL 2974316) (-1146 2968489 2968696 2969022 "UPSCAT-" 2969027 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1145 2954575 2962612 2962654 "UPOLYC" 2964732 NIL UPOLYC (NIL T) -9 NIL 2965953) (-1144 2945905 2948330 2951476 "UPOLYC-" 2951481 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1143 2945536 2945579 2945710 "UPOLYC2" 2945856 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1142 2936955 2945105 2945242 "UP" 2945446 NIL UP (NIL NIL T) -8 NIL NIL) (-1141 2936298 2936405 2936568 "UPMP" 2936844 NIL UPMP (NIL T T) -7 NIL NIL) (-1140 2935851 2935932 2936071 "UPDIVP" 2936211 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1139 2934419 2934668 2934984 "UPDECOMP" 2935600 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1138 2933654 2933766 2933951 "UPCDEN" 2934303 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1137 2933177 2933246 2933393 "UP2" 2933579 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1136 2931694 2932381 2932658 "UNISEG" 2932935 NIL UNISEG (NIL T) -8 NIL NIL) (-1135 2930909 2931036 2931241 "UNISEG2" 2931537 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1134 2929969 2930149 2930375 "UNIFACT" 2930725 NIL UNIFACT (NIL T) -7 NIL NIL) (-1133 2913865 2929150 2929400 "ULS" 2929776 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1132 2901830 2913770 2913841 "ULSCONS" 2913846 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1131 2884580 2896593 2896654 "ULSCCAT" 2897366 NIL ULSCCAT (NIL T T) -9 NIL 2897662) (-1130 2883631 2883876 2884263 "ULSCCAT-" 2884268 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1129 2873621 2880138 2880180 "ULSCAT" 2881036 NIL ULSCAT (NIL T) -9 NIL 2881766) (-1128 2873055 2873134 2873311 "ULS2" 2873536 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1127 2871453 2872420 2872450 "UFD" 2872662 T UFD (NIL) -9 NIL 2872776) (-1126 2871247 2871293 2871388 "UFD-" 2871393 NIL UFD- (NIL T) -8 NIL NIL) (-1125 2870329 2870512 2870728 "UDVO" 2871053 T UDVO (NIL) -7 NIL NIL) (-1124 2868145 2868554 2869025 "UDPO" 2869893 NIL UDPO (NIL T) -7 NIL NIL) (-1123 2868078 2868083 2868113 "TYPE" 2868118 T TYPE (NIL) -9 NIL NIL) (-1122 2867049 2867251 2867491 "TWOFACT" 2867872 NIL TWOFACT (NIL T) -7 NIL NIL) (-1121 2865987 2866324 2866587 "TUPLE" 2866821 NIL TUPLE (NIL T) -8 NIL NIL) (-1120 2863678 2864197 2864736 "TUBETOOL" 2865470 T TUBETOOL (NIL) -7 NIL NIL) (-1119 2862527 2862732 2862973 "TUBE" 2863471 NIL TUBE (NIL T) -8 NIL NIL) (-1118 2857251 2861505 2861787 "TS" 2862279 NIL TS (NIL T) -8 NIL NIL) (-1117 2845955 2850047 2850143 "TSETCAT" 2855377 NIL TSETCAT (NIL T T T T) -9 NIL 2856908) (-1116 2840690 2842288 2844178 "TSETCAT-" 2844183 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1115 2834953 2835799 2836741 "TRMANIP" 2839826 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1114 2834394 2834457 2834620 "TRIMAT" 2834885 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1113 2832200 2832437 2832800 "TRIGMNIP" 2834143 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1112 2831720 2831833 2831863 "TRIGCAT" 2832076 T TRIGCAT (NIL) -9 NIL NIL) (-1111 2831389 2831468 2831609 "TRIGCAT-" 2831614 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1110 2828288 2830249 2830529 "TREE" 2831144 NIL TREE (NIL T) -8 NIL NIL) (-1109 2827562 2828090 2828120 "TRANFUN" 2828155 T TRANFUN (NIL) -9 NIL 2828221) (-1108 2826841 2827032 2827312 "TRANFUN-" 2827317 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1107 2826645 2826677 2826738 "TOPSP" 2826802 T TOPSP (NIL) -7 NIL NIL) (-1106 2825997 2826112 2826265 "TOOLSIGN" 2826526 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1105 2824658 2825174 2825413 "TEXTFILE" 2825780 T TEXTFILE (NIL) -8 NIL NIL) (-1104 2822523 2823037 2823475 "TEX" 2824242 T TEX (NIL) -8 NIL NIL) (-1103 2822304 2822335 2822407 "TEX1" 2822486 NIL TEX1 (NIL T) -7 NIL NIL) (-1102 2821952 2822015 2822105 "TEMUTL" 2822236 T TEMUTL (NIL) -7 NIL NIL) (-1101 2820106 2820386 2820711 "TBCMPPK" 2821675 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1100 2811995 2818267 2818323 "TBAGG" 2818723 NIL TBAGG (NIL T T) -9 NIL 2818934) (-1099 2807065 2808553 2810307 "TBAGG-" 2810312 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1098 2806449 2806556 2806701 "TANEXP" 2806954 NIL TANEXP (NIL T) -7 NIL NIL) (-1097 2799950 2806306 2806399 "TABLE" 2806404 NIL TABLE (NIL T T) -8 NIL NIL) (-1096 2799362 2799461 2799599 "TABLEAU" 2799847 NIL TABLEAU (NIL T) -8 NIL NIL) (-1095 2793970 2795190 2796438 "TABLBUMP" 2798148 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1094 2793398 2793498 2793626 "SYSTEM" 2793864 T SYSTEM (NIL) -7 NIL NIL) (-1093 2789861 2790556 2791339 "SYSSOLP" 2792649 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1092 2786152 2786860 2787594 "SYNTAX" 2789149 T SYNTAX (NIL) -8 NIL NIL) (-1091 2783286 2783894 2784532 "SYMTAB" 2785536 T SYMTAB (NIL) -8 NIL NIL) (-1090 2778535 2779437 2780420 "SYMS" 2782325 T SYMS (NIL) -8 NIL NIL) (-1089 2775768 2777995 2778224 "SYMPOLY" 2778340 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1088 2775288 2775363 2775485 "SYMFUNC" 2775680 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1087 2771265 2772525 2773347 "SYMBOL" 2774488 T SYMBOL (NIL) -8 NIL NIL) (-1086 2764804 2766493 2768213 "SWITCH" 2769567 T SWITCH (NIL) -8 NIL NIL) (-1085 2758034 2763631 2763933 "SUTS" 2764559 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1084 2749924 2757155 2757435 "SUPXS" 2757811 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1083 2741416 2749545 2749670 "SUP" 2749833 NIL SUP (NIL T) -8 NIL NIL) (-1082 2740575 2740702 2740919 "SUPFRACF" 2741284 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1081 2740200 2740259 2740370 "SUP2" 2740510 NIL SUP2 (NIL T T) -7 NIL NIL) (-1080 2738618 2738892 2739254 "SUMRF" 2739899 NIL SUMRF (NIL T) -7 NIL NIL) (-1079 2737935 2738001 2738199 "SUMFS" 2738539 NIL SUMFS (NIL T T) -7 NIL NIL) (-1078 2721871 2737116 2737366 "SULS" 2737742 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1077 2721193 2721396 2721536 "SUCH" 2721779 NIL SUCH (NIL T T) -8 NIL NIL) (-1076 2715120 2716132 2717090 "SUBSPACE" 2720281 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1075 2714550 2714640 2714804 "SUBRESP" 2715008 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1074 2707919 2709215 2710526 "STTF" 2713286 NIL STTF (NIL T) -7 NIL NIL) (-1073 2702092 2703212 2704359 "STTFNC" 2706819 NIL STTFNC (NIL T) -7 NIL NIL) (-1072 2693443 2695310 2697103 "STTAYLOR" 2700333 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1071 2686687 2693307 2693390 "STRTBL" 2693395 NIL STRTBL (NIL T) -8 NIL NIL) (-1070 2682078 2686642 2686673 "STRING" 2686678 T STRING (NIL) -8 NIL NIL) (-1069 2676967 2681452 2681482 "STRICAT" 2681541 T STRICAT (NIL) -9 NIL 2681603) (-1068 2669683 2674490 2675110 "STREAM" 2676382 NIL STREAM (NIL T) -8 NIL NIL) (-1067 2669193 2669270 2669414 "STREAM3" 2669600 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1066 2668175 2668358 2668593 "STREAM2" 2669006 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1065 2667863 2667915 2668008 "STREAM1" 2668117 NIL STREAM1 (NIL T) -7 NIL NIL) (-1064 2666879 2667060 2667291 "STINPROD" 2667679 NIL STINPROD (NIL T) -7 NIL NIL) (-1063 2666458 2666642 2666672 "STEP" 2666752 T STEP (NIL) -9 NIL 2666830) (-1062 2660001 2666357 2666434 "STBL" 2666439 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1061 2655177 2659224 2659267 "STAGG" 2659420 NIL STAGG (NIL T) -9 NIL 2659509) (-1060 2652879 2653481 2654353 "STAGG-" 2654358 NIL STAGG- (NIL T T) -8 NIL NIL) (-1059 2651074 2652649 2652741 "STACK" 2652822 NIL STACK (NIL T) -8 NIL NIL) (-1058 2643805 2649221 2649676 "SREGSET" 2650704 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1057 2636245 2637613 2639125 "SRDCMPK" 2642411 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1056 2629213 2633686 2633716 "SRAGG" 2635019 T SRAGG (NIL) -9 NIL 2635627) (-1055 2628230 2628485 2628864 "SRAGG-" 2628869 NIL SRAGG- (NIL T) -8 NIL NIL) (-1054 2622679 2627149 2627576 "SQMATRIX" 2627849 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1053 2616431 2619399 2620125 "SPLTREE" 2622025 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1052 2612421 2613087 2613733 "SPLNODE" 2615857 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1051 2611468 2611701 2611731 "SPFCAT" 2612175 T SPFCAT (NIL) -9 NIL NIL) (-1050 2610205 2610415 2610679 "SPECOUT" 2611226 T SPECOUT (NIL) -7 NIL NIL) (-1049 2609966 2610006 2610075 "SPADPRSR" 2610158 T SPADPRSR (NIL) -7 NIL NIL) (-1048 2601989 2603736 2603778 "SPACEC" 2608101 NIL SPACEC (NIL T) -9 NIL 2609917) (-1047 2600160 2601922 2601970 "SPACE3" 2601975 NIL SPACE3 (NIL T) -8 NIL NIL) (-1046 2598912 2599083 2599374 "SORTPAK" 2599965 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1045 2596968 2597271 2597689 "SOLVETRA" 2598576 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1044 2595979 2596201 2596475 "SOLVESER" 2596741 NIL SOLVESER (NIL T) -7 NIL NIL) (-1043 2591199 2592080 2593082 "SOLVERAD" 2595031 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1042 2587014 2587623 2588352 "SOLVEFOR" 2590566 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1041 2581314 2586366 2586462 "SNTSCAT" 2586467 NIL SNTSCAT (NIL T T T T) -9 NIL 2586537) (-1040 2575418 2579645 2580035 "SMTS" 2581004 NIL SMTS (NIL T T T) -8 NIL NIL) (-1039 2569828 2575307 2575383 "SMP" 2575388 NIL SMP (NIL T T) -8 NIL NIL) (-1038 2567987 2568288 2568686 "SMITH" 2569525 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1037 2560952 2565148 2565250 "SMATCAT" 2566590 NIL SMATCAT (NIL NIL T T T) -9 NIL 2567139) (-1036 2557893 2558716 2559893 "SMATCAT-" 2559898 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1035 2555607 2557130 2557173 "SKAGG" 2557434 NIL SKAGG (NIL T) -9 NIL 2557569) (-1034 2551665 2554711 2554989 "SINT" 2555351 T SINT (NIL) -8 NIL NIL) (-1033 2551437 2551475 2551541 "SIMPAN" 2551621 T SIMPAN (NIL) -7 NIL NIL) (-1032 2550275 2550496 2550771 "SIGNRF" 2551196 NIL SIGNRF (NIL T) -7 NIL NIL) (-1031 2549084 2549235 2549525 "SIGNEF" 2550104 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1030 2546774 2547228 2547734 "SHP" 2548625 NIL SHP (NIL T NIL) -7 NIL NIL) (-1029 2540627 2546675 2546751 "SHDP" 2546756 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1028 2540117 2540309 2540339 "SGROUP" 2540491 T SGROUP (NIL) -9 NIL 2540578) (-1027 2539887 2539939 2540043 "SGROUP-" 2540048 NIL SGROUP- (NIL T) -8 NIL NIL) (-1026 2536723 2537420 2538143 "SGCF" 2539186 T SGCF (NIL) -7 NIL NIL) (-1025 2531122 2536174 2536270 "SFRTCAT" 2536275 NIL SFRTCAT (NIL T T T T) -9 NIL 2536313) (-1024 2524582 2525597 2526731 "SFRGCD" 2530105 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1023 2517748 2518819 2520003 "SFQCMPK" 2523515 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1022 2517370 2517459 2517569 "SFORT" 2517689 NIL SFORT (NIL T T) -8 NIL NIL) (-1021 2516515 2517210 2517331 "SEXOF" 2517336 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1020 2515649 2516396 2516464 "SEX" 2516469 T SEX (NIL) -8 NIL NIL) (-1019 2510426 2511115 2511210 "SEXCAT" 2514981 NIL SEXCAT (NIL T T T T T) -9 NIL 2515600) (-1018 2507606 2510360 2510408 "SET" 2510413 NIL SET (NIL T) -8 NIL NIL) (-1017 2505857 2506319 2506624 "SETMN" 2507347 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1016 2505465 2505591 2505621 "SETCAT" 2505738 T SETCAT (NIL) -9 NIL 2505822) (-1015 2505245 2505297 2505396 "SETCAT-" 2505401 NIL SETCAT- (NIL T) -8 NIL NIL) (-1014 2501633 2503707 2503750 "SETAGG" 2504620 NIL SETAGG (NIL T) -9 NIL 2504960) (-1013 2501091 2501207 2501444 "SETAGG-" 2501449 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1012 2500295 2500588 2500649 "SEGXCAT" 2500935 NIL SEGXCAT (NIL T T) -9 NIL 2501055) (-1011 2499351 2499961 2500143 "SEG" 2500148 NIL SEG (NIL T) -8 NIL NIL) (-1010 2498258 2498471 2498514 "SEGCAT" 2499096 NIL SEGCAT (NIL T) -9 NIL 2499334) (-1009 2497307 2497637 2497837 "SEGBIND" 2498093 NIL SEGBIND (NIL T) -8 NIL NIL) (-1008 2496928 2496987 2497100 "SEGBIND2" 2497242 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1007 2496147 2496273 2496477 "SEG2" 2496772 NIL SEG2 (NIL T T) -7 NIL NIL) (-1006 2495584 2496082 2496129 "SDVAR" 2496134 NIL SDVAR (NIL T) -8 NIL NIL) (-1005 2487836 2495357 2495485 "SDPOL" 2495490 NIL SDPOL (NIL T) -8 NIL NIL) (-1004 2486429 2486695 2487014 "SCPKG" 2487551 NIL SCPKG (NIL T) -7 NIL NIL) (-1003 2485566 2485745 2485945 "SCOPE" 2486251 T SCOPE (NIL) -8 NIL NIL) (-1002 2484787 2484920 2485099 "SCACHE" 2485421 NIL SCACHE (NIL T) -7 NIL NIL) (-1001 2484226 2484547 2484632 "SAOS" 2484724 T SAOS (NIL) -8 NIL NIL) (-1000 2483791 2483826 2483999 "SAERFFC" 2484185 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-999 2477687 2483690 2483768 "SAE" 2483773 NIL SAE (NIL T T NIL) -8 NIL NIL) (-998 2477283 2477318 2477475 "SAEFACT" 2477646 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-997 2475609 2475923 2476322 "RURPK" 2476949 NIL RURPK (NIL T NIL) -7 NIL NIL) (-996 2474262 2474539 2474846 "RULESET" 2475445 NIL RULESET (NIL T T T) -8 NIL NIL) (-995 2471470 2471973 2472434 "RULE" 2473944 NIL RULE (NIL T T T) -8 NIL NIL) (-994 2471112 2471267 2471348 "RULECOLD" 2471422 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-993 2466004 2466798 2467714 "RSETGCD" 2470311 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-992 2455319 2460371 2460465 "RSETCAT" 2464530 NIL RSETCAT (NIL T T T T) -9 NIL 2465627) (-991 2453250 2453789 2454609 "RSETCAT-" 2454614 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-990 2445680 2447055 2448571 "RSDCMPK" 2451849 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-989 2443698 2444139 2444211 "RRCC" 2445287 NIL RRCC (NIL T T) -9 NIL 2445631) (-988 2443052 2443226 2443502 "RRCC-" 2443507 NIL RRCC- (NIL T T T) -8 NIL NIL) (-987 2417419 2427044 2427108 "RPOLCAT" 2437610 NIL RPOLCAT (NIL T T T) -9 NIL 2440768) (-986 2408923 2411261 2414379 "RPOLCAT-" 2414384 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-985 2399989 2407153 2407633 "ROUTINE" 2408463 T ROUTINE (NIL) -8 NIL NIL) (-984 2396694 2399545 2399692 "ROMAN" 2399862 T ROMAN (NIL) -8 NIL NIL) (-983 2394980 2395565 2395822 "ROIRC" 2396500 NIL ROIRC (NIL T T) -8 NIL NIL) (-982 2391385 2393689 2393717 "RNS" 2394013 T RNS (NIL) -9 NIL 2394283) (-981 2389899 2390282 2390813 "RNS-" 2390886 NIL RNS- (NIL T) -8 NIL NIL) (-980 2389325 2389733 2389761 "RNG" 2389766 T RNG (NIL) -9 NIL 2389787) (-979 2388723 2389085 2389125 "RMODULE" 2389185 NIL RMODULE (NIL T) -9 NIL 2389227) (-978 2387575 2387669 2387999 "RMCAT2" 2388624 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-977 2384289 2386758 2387079 "RMATRIX" 2387310 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-976 2377286 2379520 2379632 "RMATCAT" 2382941 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2383923) (-975 2376665 2376812 2377115 "RMATCAT-" 2377120 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-974 2376235 2376310 2376436 "RINTERP" 2376584 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-973 2375286 2375850 2375878 "RING" 2375988 T RING (NIL) -9 NIL 2376082) (-972 2375081 2375125 2375219 "RING-" 2375224 NIL RING- (NIL T) -8 NIL NIL) (-971 2373929 2374166 2374422 "RIDIST" 2374845 T RIDIST (NIL) -7 NIL NIL) (-970 2365251 2373403 2373606 "RGCHAIN" 2373778 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-969 2362256 2362870 2363538 "RF" 2364615 NIL RF (NIL T) -7 NIL NIL) (-968 2361905 2361968 2362069 "RFFACTOR" 2362187 NIL RFFACTOR (NIL T) -7 NIL NIL) (-967 2361633 2361668 2361763 "RFFACT" 2361864 NIL RFFACT (NIL T) -7 NIL NIL) (-966 2359763 2360127 2360507 "RFDIST" 2361273 T RFDIST (NIL) -7 NIL NIL) (-965 2359221 2359313 2359473 "RETSOL" 2359665 NIL RETSOL (NIL T T) -7 NIL NIL) (-964 2358814 2358894 2358935 "RETRACT" 2359125 NIL RETRACT (NIL T) -9 NIL NIL) (-963 2358666 2358691 2358775 "RETRACT-" 2358780 NIL RETRACT- (NIL T T) -8 NIL NIL) (-962 2351524 2358323 2358448 "RESULT" 2358561 T RESULT (NIL) -8 NIL NIL) (-961 2350109 2350798 2350995 "RESRING" 2351427 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-960 2349749 2349798 2349894 "RESLATC" 2350046 NIL RESLATC (NIL T) -7 NIL NIL) (-959 2349458 2349492 2349597 "REPSQ" 2349708 NIL REPSQ (NIL T) -7 NIL NIL) (-958 2346889 2347469 2348069 "REP" 2348878 T REP (NIL) -7 NIL NIL) (-957 2346590 2346624 2346733 "REPDB" 2346848 NIL REPDB (NIL T) -7 NIL NIL) (-956 2340535 2341914 2343134 "REP2" 2345402 NIL REP2 (NIL T) -7 NIL NIL) (-955 2336941 2337622 2338427 "REP1" 2339762 NIL REP1 (NIL T) -7 NIL NIL) (-954 2329687 2335102 2335554 "REGSET" 2336572 NIL REGSET (NIL T T T T) -8 NIL NIL) (-953 2328508 2328843 2329091 "REF" 2329472 NIL REF (NIL T) -8 NIL NIL) (-952 2327889 2327992 2328157 "REDORDER" 2328392 NIL REDORDER (NIL T T) -7 NIL NIL) (-951 2323858 2327123 2327344 "RECLOS" 2327720 NIL RECLOS (NIL T) -8 NIL NIL) (-950 2322915 2323096 2323309 "REALSOLV" 2323665 T REALSOLV (NIL) -7 NIL NIL) (-949 2322763 2322804 2322832 "REAL" 2322837 T REAL (NIL) -9 NIL 2322872) (-948 2319254 2320056 2320938 "REAL0Q" 2321928 NIL REAL0Q (NIL T) -7 NIL NIL) (-947 2314865 2315853 2316912 "REAL0" 2318235 NIL REAL0 (NIL T) -7 NIL NIL) (-946 2314273 2314345 2314550 "RDIV" 2314787 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-945 2313346 2313520 2313731 "RDIST" 2314095 NIL RDIST (NIL T) -7 NIL NIL) (-944 2311950 2312237 2312606 "RDETRS" 2313054 NIL RDETRS (NIL T T) -7 NIL NIL) (-943 2309771 2310225 2310760 "RDETR" 2311492 NIL RDETR (NIL T T) -7 NIL NIL) (-942 2308387 2308665 2309066 "RDEEFS" 2309487 NIL RDEEFS (NIL T T) -7 NIL NIL) (-941 2306887 2307193 2307622 "RDEEF" 2308075 NIL RDEEF (NIL T T) -7 NIL NIL) (-940 2301172 2304104 2304132 "RCFIELD" 2305409 T RCFIELD (NIL) -9 NIL 2306139) (-939 2299241 2299745 2300438 "RCFIELD-" 2300511 NIL RCFIELD- (NIL T) -8 NIL NIL) (-938 2295573 2297358 2297399 "RCAGG" 2298470 NIL RCAGG (NIL T) -9 NIL 2298935) (-937 2295204 2295298 2295458 "RCAGG-" 2295463 NIL RCAGG- (NIL T T) -8 NIL NIL) (-936 2294548 2294660 2294822 "RATRET" 2295088 NIL RATRET (NIL T) -7 NIL NIL) (-935 2294105 2294172 2294291 "RATFACT" 2294476 NIL RATFACT (NIL T) -7 NIL NIL) (-934 2293420 2293540 2293690 "RANDSRC" 2293975 T RANDSRC (NIL) -7 NIL NIL) (-933 2293157 2293201 2293272 "RADUTIL" 2293369 T RADUTIL (NIL) -7 NIL NIL) (-932 2286164 2291900 2292217 "RADIX" 2292872 NIL RADIX (NIL NIL) -8 NIL NIL) (-931 2277734 2286008 2286136 "RADFF" 2286141 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-930 2277386 2277461 2277489 "RADCAT" 2277646 T RADCAT (NIL) -9 NIL NIL) (-929 2277171 2277219 2277316 "RADCAT-" 2277321 NIL RADCAT- (NIL T) -8 NIL NIL) (-928 2275322 2276946 2277035 "QUEUE" 2277115 NIL QUEUE (NIL T) -8 NIL NIL) (-927 2271819 2275259 2275304 "QUAT" 2275309 NIL QUAT (NIL T) -8 NIL NIL) (-926 2271457 2271500 2271627 "QUATCT2" 2271770 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-925 2265251 2268631 2268671 "QUATCAT" 2269450 NIL QUATCAT (NIL T) -9 NIL 2270215) (-924 2261395 2262432 2263819 "QUATCAT-" 2263913 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-923 2258916 2260480 2260521 "QUAGG" 2260896 NIL QUAGG (NIL T) -9 NIL 2261071) (-922 2257841 2258314 2258486 "QFORM" 2258788 NIL QFORM (NIL NIL T) -8 NIL NIL) (-921 2249138 2254396 2254436 "QFCAT" 2255094 NIL QFCAT (NIL T) -9 NIL 2256087) (-920 2244710 2245911 2247502 "QFCAT-" 2247596 NIL QFCAT- (NIL T T) -8 NIL NIL) (-919 2244348 2244391 2244518 "QFCAT2" 2244661 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-918 2243808 2243918 2244048 "QEQUAT" 2244238 T QEQUAT (NIL) -8 NIL NIL) (-917 2236994 2238065 2239247 "QCMPACK" 2242741 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-916 2234570 2234991 2235419 "QALGSET" 2236649 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-915 2233815 2233989 2234221 "QALGSET2" 2234390 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-914 2232506 2232729 2233046 "PWFFINTB" 2233588 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-913 2230694 2230862 2231215 "PUSHVAR" 2232320 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-912 2226612 2227666 2227707 "PTRANFN" 2229591 NIL PTRANFN (NIL T) -9 NIL NIL) (-911 2225024 2225315 2225636 "PTPACK" 2226323 NIL PTPACK (NIL T) -7 NIL NIL) (-910 2224660 2224717 2224824 "PTFUNC2" 2224961 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-909 2219137 2223478 2223518 "PTCAT" 2223886 NIL PTCAT (NIL T) -9 NIL 2224048) (-908 2218795 2218830 2218954 "PSQFR" 2219096 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-907 2217390 2217688 2218022 "PSEUDLIN" 2218493 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-906 2204198 2206562 2208885 "PSETPK" 2215150 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-905 2197285 2199999 2200093 "PSETCAT" 2203074 NIL PSETCAT (NIL T T T T) -9 NIL 2203888) (-904 2195123 2195757 2196576 "PSETCAT-" 2196581 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-903 2194472 2194637 2194665 "PSCURVE" 2194933 T PSCURVE (NIL) -9 NIL 2195100) (-902 2190924 2192450 2192514 "PSCAT" 2193350 NIL PSCAT (NIL T T T) -9 NIL 2193590) (-901 2189988 2190204 2190603 "PSCAT-" 2190608 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-900 2188640 2189273 2189487 "PRTITION" 2189794 T PRTITION (NIL) -8 NIL NIL) (-899 2177738 2179944 2182132 "PRS" 2186502 NIL PRS (NIL T T) -7 NIL NIL) (-898 2175597 2177089 2177129 "PRQAGG" 2177312 NIL PRQAGG (NIL T) -9 NIL 2177414) (-897 2175168 2175270 2175298 "PROPLOG" 2175483 T PROPLOG (NIL) -9 NIL NIL) (-896 2172291 2172856 2173383 "PROPFRML" 2174673 NIL PROPFRML (NIL T) -8 NIL NIL) (-895 2171751 2171861 2171991 "PROPERTY" 2172181 T PROPERTY (NIL) -8 NIL NIL) (-894 2165525 2169917 2170737 "PRODUCT" 2170977 NIL PRODUCT (NIL T T) -8 NIL NIL) (-893 2162801 2164985 2165218 "PR" 2165336 NIL PR (NIL T T) -8 NIL NIL) (-892 2162597 2162629 2162688 "PRINT" 2162762 T PRINT (NIL) -7 NIL NIL) (-891 2161937 2162054 2162206 "PRIMES" 2162477 NIL PRIMES (NIL T) -7 NIL NIL) (-890 2160002 2160403 2160869 "PRIMELT" 2161516 NIL PRIMELT (NIL T) -7 NIL NIL) (-889 2159731 2159780 2159808 "PRIMCAT" 2159932 T PRIMCAT (NIL) -9 NIL NIL) (-888 2155892 2159669 2159714 "PRIMARR" 2159719 NIL PRIMARR (NIL T) -8 NIL NIL) (-887 2154899 2155077 2155305 "PRIMARR2" 2155710 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-886 2154542 2154598 2154709 "PREASSOC" 2154837 NIL PREASSOC (NIL T T) -7 NIL NIL) (-885 2154017 2154150 2154178 "PPCURVE" 2154383 T PPCURVE (NIL) -9 NIL 2154519) (-884 2151376 2151775 2152367 "POLYROOT" 2153598 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-883 2145282 2150982 2151141 "POLY" 2151249 NIL POLY (NIL T) -8 NIL NIL) (-882 2144667 2144725 2144958 "POLYLIFT" 2145218 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-881 2140952 2141401 2142029 "POLYCATQ" 2144212 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-880 2127993 2133390 2133454 "POLYCAT" 2136939 NIL POLYCAT (NIL T T T) -9 NIL 2138866) (-879 2121444 2123305 2125688 "POLYCAT-" 2125693 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-878 2121033 2121101 2121220 "POLY2UP" 2121370 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-877 2120669 2120726 2120833 "POLY2" 2120970 NIL POLY2 (NIL T T) -7 NIL NIL) (-876 2119354 2119593 2119869 "POLUTIL" 2120443 NIL POLUTIL (NIL T T) -7 NIL NIL) (-875 2117716 2117993 2118323 "POLTOPOL" 2119076 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-874 2113239 2117653 2117698 "POINT" 2117703 NIL POINT (NIL T) -8 NIL NIL) (-873 2111426 2111783 2112158 "PNTHEORY" 2112884 T PNTHEORY (NIL) -7 NIL NIL) (-872 2109854 2110151 2110560 "PMTOOLS" 2111124 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-871 2109447 2109525 2109642 "PMSYM" 2109770 NIL PMSYM (NIL T) -7 NIL NIL) (-870 2108957 2109026 2109200 "PMQFCAT" 2109372 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-869 2108312 2108422 2108578 "PMPRED" 2108834 NIL PMPRED (NIL T) -7 NIL NIL) (-868 2107708 2107794 2107955 "PMPREDFS" 2108213 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-867 2106354 2106562 2106946 "PMPLCAT" 2107470 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-866 2105886 2105965 2106117 "PMLSAGG" 2106269 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-865 2105363 2105439 2105619 "PMKERNEL" 2105804 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-864 2104980 2105055 2105168 "PMINS" 2105282 NIL PMINS (NIL T) -7 NIL NIL) (-863 2104410 2104479 2104694 "PMFS" 2104905 NIL PMFS (NIL T T T) -7 NIL NIL) (-862 2103641 2103759 2103963 "PMDOWN" 2104287 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-861 2102804 2102963 2103145 "PMASS" 2103479 T PMASS (NIL) -7 NIL NIL) (-860 2102078 2102189 2102352 "PMASSFS" 2102690 NIL PMASSFS (NIL T T) -7 NIL NIL) (-859 2101733 2101801 2101895 "PLOTTOOL" 2102004 T PLOTTOOL (NIL) -7 NIL NIL) (-858 2096355 2097544 2098692 "PLOT" 2100605 T PLOT (NIL) -8 NIL NIL) (-857 2092169 2093203 2094124 "PLOT3D" 2095454 T PLOT3D (NIL) -8 NIL NIL) (-856 2091081 2091258 2091493 "PLOT1" 2091973 NIL PLOT1 (NIL T) -7 NIL NIL) (-855 2066475 2071147 2075998 "PLEQN" 2086347 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-854 2065793 2065915 2066095 "PINTERP" 2066340 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-853 2065486 2065533 2065636 "PINTERPA" 2065740 NIL PINTERPA (NIL T T) -7 NIL NIL) (-852 2064713 2065280 2065373 "PI" 2065413 T PI (NIL) -8 NIL NIL) (-851 2063105 2064090 2064118 "PID" 2064300 T PID (NIL) -9 NIL 2064434) (-850 2062830 2062867 2062955 "PICOERCE" 2063062 NIL PICOERCE (NIL T) -7 NIL NIL) (-849 2062150 2062289 2062465 "PGROEB" 2062686 NIL PGROEB (NIL T) -7 NIL NIL) (-848 2057737 2058551 2059456 "PGE" 2061265 T PGE (NIL) -7 NIL NIL) (-847 2055861 2056107 2056473 "PGCD" 2057454 NIL PGCD (NIL T T T T) -7 NIL NIL) (-846 2055199 2055302 2055463 "PFRPAC" 2055745 NIL PFRPAC (NIL T) -7 NIL NIL) (-845 2051814 2053747 2054100 "PFR" 2054878 NIL PFR (NIL T) -8 NIL NIL) (-844 2050203 2050447 2050772 "PFOTOOLS" 2051561 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-843 2048736 2048975 2049326 "PFOQ" 2049960 NIL PFOQ (NIL T T T) -7 NIL NIL) (-842 2047213 2047425 2047787 "PFO" 2048520 NIL PFO (NIL T T T T T) -7 NIL NIL) (-841 2043736 2047102 2047171 "PF" 2047176 NIL PF (NIL NIL) -8 NIL NIL) (-840 2041165 2042446 2042474 "PFECAT" 2043059 T PFECAT (NIL) -9 NIL 2043443) (-839 2040610 2040764 2040978 "PFECAT-" 2040983 NIL PFECAT- (NIL T) -8 NIL NIL) (-838 2039214 2039465 2039766 "PFBRU" 2040359 NIL PFBRU (NIL T T) -7 NIL NIL) (-837 2037081 2037432 2037864 "PFBR" 2038865 NIL PFBR (NIL T T T T) -7 NIL NIL) (-836 2032933 2034457 2035133 "PERM" 2036438 NIL PERM (NIL T) -8 NIL NIL) (-835 2028198 2029140 2030010 "PERMGRP" 2032096 NIL PERMGRP (NIL T) -8 NIL NIL) (-834 2026269 2027262 2027303 "PERMCAT" 2027749 NIL PERMCAT (NIL T) -9 NIL 2028054) (-833 2025924 2025965 2026088 "PERMAN" 2026222 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-832 2023364 2025493 2025624 "PENDTREE" 2025826 NIL PENDTREE (NIL T) -8 NIL NIL) (-831 2021437 2022215 2022256 "PDRING" 2022913 NIL PDRING (NIL T) -9 NIL 2023198) (-830 2020540 2020758 2021120 "PDRING-" 2021125 NIL PDRING- (NIL T T) -8 NIL NIL) (-829 2017681 2018432 2019123 "PDEPROB" 2019869 T PDEPROB (NIL) -8 NIL NIL) (-828 2015252 2015748 2016297 "PDEPACK" 2017152 T PDEPACK (NIL) -7 NIL NIL) (-827 2014164 2014354 2014605 "PDECOMP" 2015051 NIL PDECOMP (NIL T T) -7 NIL NIL) (-826 2011776 2012591 2012619 "PDECAT" 2013404 T PDECAT (NIL) -9 NIL 2014115) (-825 2011529 2011562 2011651 "PCOMP" 2011737 NIL PCOMP (NIL T T) -7 NIL NIL) (-824 2009736 2010332 2010628 "PBWLB" 2011259 NIL PBWLB (NIL T) -8 NIL NIL) (-823 2002244 2003813 2005149 "PATTERN" 2008421 NIL PATTERN (NIL T) -8 NIL NIL) (-822 2001876 2001933 2002042 "PATTERN2" 2002181 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-821 1999633 2000021 2000478 "PATTERN1" 2001465 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-820 1997028 1997582 1998063 "PATRES" 1999198 NIL PATRES (NIL T T) -8 NIL NIL) (-819 1996592 1996659 1996791 "PATRES2" 1996955 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-818 1994489 1994889 1995294 "PATMATCH" 1996261 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-817 1994026 1994209 1994250 "PATMAB" 1994357 NIL PATMAB (NIL T) -9 NIL 1994440) (-816 1992571 1992880 1993138 "PATLRES" 1993831 NIL PATLRES (NIL T T T) -8 NIL NIL) (-815 1992117 1992240 1992281 "PATAB" 1992286 NIL PATAB (NIL T) -9 NIL 1992458) (-814 1989598 1990130 1990703 "PARTPERM" 1991564 T PARTPERM (NIL) -7 NIL NIL) (-813 1989219 1989282 1989384 "PARSURF" 1989529 NIL PARSURF (NIL T) -8 NIL NIL) (-812 1988851 1988908 1989017 "PARSU2" 1989156 NIL PARSU2 (NIL T T) -7 NIL NIL) (-811 1988615 1988655 1988722 "PARSER" 1988804 T PARSER (NIL) -7 NIL NIL) (-810 1988236 1988299 1988401 "PARSCURV" 1988546 NIL PARSCURV (NIL T) -8 NIL NIL) (-809 1987868 1987925 1988034 "PARSC2" 1988173 NIL PARSC2 (NIL T T) -7 NIL NIL) (-808 1987507 1987565 1987662 "PARPCURV" 1987804 NIL PARPCURV (NIL T) -8 NIL NIL) (-807 1987139 1987196 1987305 "PARPC2" 1987444 NIL PARPC2 (NIL T T) -7 NIL NIL) (-806 1986659 1986745 1986864 "PAN2EXPR" 1987040 T PAN2EXPR (NIL) -7 NIL NIL) (-805 1985465 1985780 1986008 "PALETTE" 1986451 T PALETTE (NIL) -8 NIL NIL) (-804 1983933 1984470 1984830 "PAIR" 1985151 NIL PAIR (NIL T T) -8 NIL NIL) (-803 1977783 1983192 1983386 "PADICRC" 1983788 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-802 1970991 1977129 1977313 "PADICRAT" 1977631 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-801 1969295 1970928 1970973 "PADIC" 1970978 NIL PADIC (NIL NIL) -8 NIL NIL) (-800 1966500 1968074 1968114 "PADICCT" 1968695 NIL PADICCT (NIL NIL) -9 NIL 1968977) (-799 1965457 1965657 1965925 "PADEPAC" 1966287 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-798 1964669 1964802 1965008 "PADE" 1965319 NIL PADE (NIL T T T) -7 NIL NIL) (-797 1962680 1963512 1963827 "OWP" 1964437 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-796 1961789 1962285 1962457 "OVAR" 1962548 NIL OVAR (NIL NIL) -8 NIL NIL) (-795 1961053 1961174 1961335 "OUT" 1961648 T OUT (NIL) -7 NIL NIL) (-794 1950107 1952278 1954448 "OUTFORM" 1958903 T OUTFORM (NIL) -8 NIL NIL) (-793 1949515 1949836 1949925 "OSI" 1950038 T OSI (NIL) -8 NIL NIL) (-792 1948260 1948487 1948772 "ORTHPOL" 1949262 NIL ORTHPOL (NIL T) -7 NIL NIL) (-791 1945631 1947921 1948059 "OREUP" 1948203 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-790 1943027 1945324 1945450 "ORESUP" 1945573 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-789 1940562 1941062 1941622 "OREPCTO" 1942516 NIL OREPCTO (NIL T T) -7 NIL NIL) (-788 1934472 1936678 1936718 "OREPCAT" 1939039 NIL OREPCAT (NIL T) -9 NIL 1940142) (-787 1931620 1932402 1933459 "OREPCAT-" 1933464 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-786 1930798 1931070 1931098 "ORDSET" 1931407 T ORDSET (NIL) -9 NIL 1931571) (-785 1930317 1930439 1930632 "ORDSET-" 1930637 NIL ORDSET- (NIL T) -8 NIL NIL) (-784 1928931 1929732 1929760 "ORDRING" 1929962 T ORDRING (NIL) -9 NIL 1930086) (-783 1928576 1928670 1928814 "ORDRING-" 1928819 NIL ORDRING- (NIL T) -8 NIL NIL) (-782 1927952 1928433 1928461 "ORDMON" 1928466 T ORDMON (NIL) -9 NIL 1928487) (-781 1927114 1927261 1927456 "ORDFUNS" 1927801 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-780 1926626 1926985 1927013 "ORDFIN" 1927018 T ORDFIN (NIL) -9 NIL 1927039) (-779 1923138 1925212 1925621 "ORDCOMP" 1926250 NIL ORDCOMP (NIL T) -8 NIL NIL) (-778 1922404 1922531 1922717 "ORDCOMP2" 1922998 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-777 1918911 1919794 1920631 "OPTPROB" 1921587 T OPTPROB (NIL) -8 NIL NIL) (-776 1915753 1916382 1917076 "OPTPACK" 1918237 T OPTPACK (NIL) -7 NIL NIL) (-775 1913479 1914215 1914243 "OPTCAT" 1915058 T OPTCAT (NIL) -9 NIL 1915704) (-774 1913247 1913286 1913352 "OPQUERY" 1913433 T OPQUERY (NIL) -7 NIL NIL) (-773 1910383 1911574 1912074 "OP" 1912779 NIL OP (NIL T) -8 NIL NIL) (-772 1907148 1909180 1909549 "ONECOMP" 1910047 NIL ONECOMP (NIL T) -8 NIL NIL) (-771 1906453 1906568 1906742 "ONECOMP2" 1907020 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-770 1905872 1905978 1906108 "OMSERVER" 1906343 T OMSERVER (NIL) -7 NIL NIL) (-769 1902761 1905313 1905353 "OMSAGG" 1905414 NIL OMSAGG (NIL T) -9 NIL 1905478) (-768 1901384 1901647 1901929 "OMPKG" 1902499 T OMPKG (NIL) -7 NIL NIL) (-767 1900814 1900917 1900945 "OM" 1901244 T OM (NIL) -9 NIL NIL) (-766 1899353 1900366 1900534 "OMLO" 1900695 NIL OMLO (NIL T T) -8 NIL NIL) (-765 1898283 1898430 1898656 "OMEXPR" 1899179 NIL OMEXPR (NIL T) -7 NIL NIL) (-764 1897601 1897829 1897965 "OMERR" 1898167 T OMERR (NIL) -8 NIL NIL) (-763 1896779 1897022 1897182 "OMERRK" 1897461 T OMERRK (NIL) -8 NIL NIL) (-762 1896257 1896456 1896564 "OMENC" 1896691 T OMENC (NIL) -8 NIL NIL) (-761 1890152 1891337 1892508 "OMDEV" 1895106 T OMDEV (NIL) -8 NIL NIL) (-760 1889221 1889392 1889586 "OMCONN" 1889978 T OMCONN (NIL) -8 NIL NIL) (-759 1887837 1888823 1888851 "OINTDOM" 1888856 T OINTDOM (NIL) -9 NIL 1888877) (-758 1883599 1884829 1885544 "OFMONOID" 1887154 NIL OFMONOID (NIL T) -8 NIL NIL) (-757 1883037 1883536 1883581 "ODVAR" 1883586 NIL ODVAR (NIL T) -8 NIL NIL) (-756 1880162 1882534 1882719 "ODR" 1882912 NIL ODR (NIL T T NIL) -8 NIL NIL) (-755 1872468 1879941 1880065 "ODPOL" 1880070 NIL ODPOL (NIL T) -8 NIL NIL) (-754 1866291 1872340 1872445 "ODP" 1872450 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-753 1865057 1865272 1865547 "ODETOOLS" 1866065 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-752 1862026 1862682 1863398 "ODESYS" 1864390 NIL ODESYS (NIL T T) -7 NIL NIL) (-751 1856930 1857838 1858861 "ODERTRIC" 1861101 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-750 1856356 1856438 1856632 "ODERED" 1856842 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-749 1853258 1853806 1854481 "ODERAT" 1855779 NIL ODERAT (NIL T T) -7 NIL NIL) (-748 1850226 1850690 1851286 "ODEPRRIC" 1852787 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-747 1848095 1848664 1849173 "ODEPROB" 1849737 T ODEPROB (NIL) -8 NIL NIL) (-746 1844627 1845110 1845756 "ODEPRIM" 1847574 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-745 1843880 1843982 1844240 "ODEPAL" 1844519 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-744 1840082 1840863 1841717 "ODEPACK" 1843046 T ODEPACK (NIL) -7 NIL NIL) (-743 1839119 1839226 1839454 "ODEINT" 1839971 NIL ODEINT (NIL T T) -7 NIL NIL) (-742 1833220 1834645 1836092 "ODEIFTBL" 1837692 T ODEIFTBL (NIL) -8 NIL NIL) (-741 1828564 1829350 1830308 "ODEEF" 1832379 NIL ODEEF (NIL T T) -7 NIL NIL) (-740 1827901 1827990 1828219 "ODECONST" 1828469 NIL ODECONST (NIL T T T) -7 NIL NIL) (-739 1826059 1826692 1826720 "ODECAT" 1827323 T ODECAT (NIL) -9 NIL 1827852) (-738 1822931 1825771 1825890 "OCT" 1825972 NIL OCT (NIL T) -8 NIL NIL) (-737 1822569 1822612 1822739 "OCTCT2" 1822882 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-736 1817403 1819841 1819881 "OC" 1820977 NIL OC (NIL T) -9 NIL 1821834) (-735 1814630 1815378 1816368 "OC-" 1816462 NIL OC- (NIL T T) -8 NIL NIL) (-734 1814009 1814451 1814479 "OCAMON" 1814484 T OCAMON (NIL) -9 NIL 1814505) (-733 1813463 1813870 1813898 "OASGP" 1813903 T OASGP (NIL) -9 NIL 1813923) (-732 1812751 1813214 1813242 "OAMONS" 1813282 T OAMONS (NIL) -9 NIL 1813325) (-731 1812192 1812599 1812627 "OAMON" 1812632 T OAMON (NIL) -9 NIL 1812652) (-730 1811497 1811989 1812017 "OAGROUP" 1812022 T OAGROUP (NIL) -9 NIL 1812042) (-729 1811187 1811237 1811325 "NUMTUBE" 1811441 NIL NUMTUBE (NIL T) -7 NIL NIL) (-728 1804760 1806278 1807814 "NUMQUAD" 1809671 T NUMQUAD (NIL) -7 NIL NIL) (-727 1800516 1801504 1802529 "NUMODE" 1803755 T NUMODE (NIL) -7 NIL NIL) (-726 1797920 1798766 1798794 "NUMINT" 1799711 T NUMINT (NIL) -9 NIL 1800467) (-725 1796868 1797065 1797283 "NUMFMT" 1797722 T NUMFMT (NIL) -7 NIL NIL) (-724 1783250 1786184 1788714 "NUMERIC" 1794377 NIL NUMERIC (NIL T) -7 NIL NIL) (-723 1777651 1782703 1782797 "NTSCAT" 1782802 NIL NTSCAT (NIL T T T T) -9 NIL 1782840) (-722 1776845 1777010 1777203 "NTPOLFN" 1777490 NIL NTPOLFN (NIL T) -7 NIL NIL) (-721 1764661 1773687 1774497 "NSUP" 1776067 NIL NSUP (NIL T) -8 NIL NIL) (-720 1764297 1764354 1764461 "NSUP2" 1764598 NIL NSUP2 (NIL T T) -7 NIL NIL) (-719 1754259 1764076 1764206 "NSMP" 1764211 NIL NSMP (NIL T T) -8 NIL NIL) (-718 1752691 1752992 1753349 "NREP" 1753947 NIL NREP (NIL T) -7 NIL NIL) (-717 1751282 1751534 1751892 "NPCOEF" 1752434 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-716 1750348 1750463 1750679 "NORMRETR" 1751163 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-715 1748401 1748691 1749098 "NORMPK" 1750056 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-714 1748086 1748114 1748238 "NORMMA" 1748367 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-713 1747913 1748043 1748072 "NONE" 1748077 T NONE (NIL) -8 NIL NIL) (-712 1747702 1747731 1747800 "NONE1" 1747877 NIL NONE1 (NIL T) -7 NIL NIL) (-711 1747187 1747249 1747434 "NODE1" 1747634 NIL NODE1 (NIL T T) -7 NIL NIL) (-710 1745480 1746350 1746605 "NNI" 1746952 T NNI (NIL) -8 NIL NIL) (-709 1743900 1744213 1744577 "NLINSOL" 1745148 NIL NLINSOL (NIL T) -7 NIL NIL) (-708 1740067 1741035 1741957 "NIPROB" 1742998 T NIPROB (NIL) -8 NIL NIL) (-707 1738824 1739058 1739360 "NFINTBAS" 1739829 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-706 1737532 1737763 1738044 "NCODIV" 1738592 NIL NCODIV (NIL T T) -7 NIL NIL) (-705 1737294 1737331 1737406 "NCNTFRAC" 1737489 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-704 1735474 1735838 1736258 "NCEP" 1736919 NIL NCEP (NIL T) -7 NIL NIL) (-703 1734386 1735125 1735153 "NASRING" 1735263 T NASRING (NIL) -9 NIL 1735337) (-702 1734181 1734225 1734319 "NASRING-" 1734324 NIL NASRING- (NIL T) -8 NIL NIL) (-701 1733335 1733834 1733862 "NARNG" 1733979 T NARNG (NIL) -9 NIL 1734070) (-700 1733027 1733094 1733228 "NARNG-" 1733233 NIL NARNG- (NIL T) -8 NIL NIL) (-699 1731906 1732113 1732348 "NAGSP" 1732812 T NAGSP (NIL) -7 NIL NIL) (-698 1723330 1724976 1726611 "NAGS" 1730291 T NAGS (NIL) -7 NIL NIL) (-697 1721894 1722198 1722525 "NAGF07" 1723023 T NAGF07 (NIL) -7 NIL NIL) (-696 1716476 1717756 1719052 "NAGF04" 1720618 T NAGF04 (NIL) -7 NIL NIL) (-695 1709508 1711106 1712723 "NAGF02" 1714879 T NAGF02 (NIL) -7 NIL NIL) (-694 1704772 1705862 1706969 "NAGF01" 1708421 T NAGF01 (NIL) -7 NIL NIL) (-693 1698432 1699990 1701567 "NAGE04" 1703215 T NAGE04 (NIL) -7 NIL NIL) (-692 1689673 1691776 1693888 "NAGE02" 1696340 T NAGE02 (NIL) -7 NIL NIL) (-691 1685666 1686603 1687557 "NAGE01" 1688739 T NAGE01 (NIL) -7 NIL NIL) (-690 1683473 1684004 1684559 "NAGD03" 1685131 T NAGD03 (NIL) -7 NIL NIL) (-689 1675259 1677178 1679123 "NAGD02" 1681548 T NAGD02 (NIL) -7 NIL NIL) (-688 1669118 1670531 1671959 "NAGD01" 1673851 T NAGD01 (NIL) -7 NIL NIL) (-687 1665375 1666185 1667010 "NAGC06" 1668313 T NAGC06 (NIL) -7 NIL NIL) (-686 1663852 1664181 1664534 "NAGC05" 1665042 T NAGC05 (NIL) -7 NIL NIL) (-685 1663236 1663353 1663495 "NAGC02" 1663730 T NAGC02 (NIL) -7 NIL NIL) (-684 1662298 1662855 1662895 "NAALG" 1662974 NIL NAALG (NIL T) -9 NIL 1663035) (-683 1662133 1662162 1662252 "NAALG-" 1662257 NIL NAALG- (NIL T T) -8 NIL NIL) (-682 1656083 1657191 1658378 "MULTSQFR" 1661029 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-681 1655402 1655477 1655661 "MULTFACT" 1655995 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-680 1648596 1652507 1652559 "MTSCAT" 1653619 NIL MTSCAT (NIL T T) -9 NIL 1654133) (-679 1648308 1648362 1648454 "MTHING" 1648536 NIL MTHING (NIL T) -7 NIL NIL) (-678 1648100 1648133 1648193 "MSYSCMD" 1648268 T MSYSCMD (NIL) -7 NIL NIL) (-677 1644212 1646855 1647175 "MSET" 1647813 NIL MSET (NIL T) -8 NIL NIL) (-676 1641308 1643774 1643815 "MSETAGG" 1643820 NIL MSETAGG (NIL T) -9 NIL 1643854) (-675 1637164 1638706 1639447 "MRING" 1640611 NIL MRING (NIL T T) -8 NIL NIL) (-674 1636734 1636801 1636930 "MRF2" 1637091 NIL MRF2 (NIL T T T) -7 NIL NIL) (-673 1636352 1636387 1636531 "MRATFAC" 1636693 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-672 1633964 1634259 1634690 "MPRFF" 1636057 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-671 1627984 1633819 1633915 "MPOLY" 1633920 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-670 1627474 1627509 1627717 "MPCPF" 1627943 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-669 1626990 1627033 1627216 "MPC3" 1627425 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-668 1626191 1626272 1626491 "MPC2" 1626905 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-667 1624492 1624829 1625219 "MONOTOOL" 1625851 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-666 1623617 1623952 1623980 "MONOID" 1624257 T MONOID (NIL) -9 NIL 1624429) (-665 1622995 1623158 1623401 "MONOID-" 1623406 NIL MONOID- (NIL T) -8 NIL NIL) (-664 1613976 1619962 1620021 "MONOGEN" 1620695 NIL MONOGEN (NIL T T) -9 NIL 1621151) (-663 1611194 1611929 1612929 "MONOGEN-" 1613048 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-662 1610054 1610474 1610502 "MONADWU" 1610894 T MONADWU (NIL) -9 NIL 1611132) (-661 1609426 1609585 1609833 "MONADWU-" 1609838 NIL MONADWU- (NIL T) -8 NIL NIL) (-660 1608812 1609030 1609058 "MONAD" 1609265 T MONAD (NIL) -9 NIL 1609377) (-659 1608497 1608575 1608707 "MONAD-" 1608712 NIL MONAD- (NIL T) -8 NIL NIL) (-658 1606748 1607410 1607689 "MOEBIUS" 1608250 NIL MOEBIUS (NIL T) -8 NIL NIL) (-657 1606142 1606520 1606560 "MODULE" 1606565 NIL MODULE (NIL T) -9 NIL 1606591) (-656 1605710 1605806 1605996 "MODULE-" 1606001 NIL MODULE- (NIL T T) -8 NIL NIL) (-655 1603381 1604076 1604402 "MODRING" 1605535 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-654 1600337 1601502 1602019 "MODOP" 1602913 NIL MODOP (NIL T T) -8 NIL NIL) (-653 1598524 1598976 1599317 "MODMONOM" 1600136 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-652 1588203 1596728 1597150 "MODMON" 1598152 NIL MODMON (NIL T T) -8 NIL NIL) (-651 1585329 1587047 1587323 "MODFIELD" 1588078 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-650 1584333 1584610 1584800 "MMLFORM" 1585159 T MMLFORM (NIL) -8 NIL NIL) (-649 1583859 1583902 1584081 "MMAP" 1584284 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-648 1582096 1582873 1582913 "MLO" 1583330 NIL MLO (NIL T) -9 NIL 1583571) (-647 1579463 1579978 1580580 "MLIFT" 1581577 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-646 1578854 1578938 1579092 "MKUCFUNC" 1579374 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-645 1578453 1578523 1578646 "MKRECORD" 1578777 NIL MKRECORD (NIL T T) -7 NIL NIL) (-644 1577501 1577662 1577890 "MKFUNC" 1578264 NIL MKFUNC (NIL T) -7 NIL NIL) (-643 1576889 1576993 1577149 "MKFLCFN" 1577384 NIL MKFLCFN (NIL T) -7 NIL NIL) (-642 1576315 1576682 1576771 "MKCHSET" 1576833 NIL MKCHSET (NIL T) -8 NIL NIL) (-641 1575592 1575694 1575879 "MKBCFUNC" 1576208 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-640 1572276 1575146 1575282 "MINT" 1575476 T MINT (NIL) -8 NIL NIL) (-639 1571088 1571331 1571608 "MHROWRED" 1572031 NIL MHROWRED (NIL T) -7 NIL NIL) (-638 1566359 1569533 1569957 "MFLOAT" 1570684 T MFLOAT (NIL) -8 NIL NIL) (-637 1565716 1565792 1565963 "MFINFACT" 1566271 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-636 1562031 1562879 1563763 "MESH" 1564852 T MESH (NIL) -7 NIL NIL) (-635 1560421 1560733 1561086 "MDDFACT" 1561718 NIL MDDFACT (NIL T) -7 NIL NIL) (-634 1557264 1559581 1559622 "MDAGG" 1559877 NIL MDAGG (NIL T) -9 NIL 1560020) (-633 1546962 1556557 1556764 "MCMPLX" 1557077 T MCMPLX (NIL) -8 NIL NIL) (-632 1546103 1546249 1546449 "MCDEN" 1546811 NIL MCDEN (NIL T T) -7 NIL NIL) (-631 1543993 1544263 1544643 "MCALCFN" 1545833 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-630 1541615 1542138 1542699 "MATSTOR" 1543464 NIL MATSTOR (NIL T) -7 NIL NIL) (-629 1537624 1540990 1541237 "MATRIX" 1541400 NIL MATRIX (NIL T) -8 NIL NIL) (-628 1533393 1534097 1534833 "MATLIN" 1536981 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-627 1523591 1526729 1526805 "MATCAT" 1531643 NIL MATCAT (NIL T T T) -9 NIL 1533060) (-626 1519956 1520969 1522324 "MATCAT-" 1522329 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-625 1518558 1518711 1519042 "MATCAT2" 1519791 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-624 1516670 1516994 1517378 "MAPPKG3" 1518233 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-623 1515651 1515824 1516046 "MAPPKG2" 1516494 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-622 1514150 1514434 1514761 "MAPPKG1" 1515357 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-621 1513761 1513819 1513942 "MAPHACK3" 1514086 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-620 1513353 1513414 1513528 "MAPHACK2" 1513693 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-619 1512791 1512894 1513036 "MAPHACK1" 1513244 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-618 1510899 1511493 1511796 "MAGMA" 1512520 NIL MAGMA (NIL T) -8 NIL NIL) (-617 1507373 1509143 1509603 "M3D" 1510472 NIL M3D (NIL T) -8 NIL NIL) (-616 1501529 1505744 1505785 "LZSTAGG" 1506567 NIL LZSTAGG (NIL T) -9 NIL 1506862) (-615 1497502 1498660 1500117 "LZSTAGG-" 1500122 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-614 1494618 1495395 1495881 "LWORD" 1497048 NIL LWORD (NIL T) -8 NIL NIL) (-613 1487778 1494389 1494523 "LSQM" 1494528 NIL LSQM (NIL NIL T) -8 NIL NIL) (-612 1487002 1487141 1487369 "LSPP" 1487633 NIL LSPP (NIL T T T T) -7 NIL NIL) (-611 1484814 1485115 1485571 "LSMP" 1486691 NIL LSMP (NIL T T T T) -7 NIL NIL) (-610 1481593 1482267 1482997 "LSMP1" 1484116 NIL LSMP1 (NIL T) -7 NIL NIL) (-609 1475520 1480762 1480803 "LSAGG" 1480865 NIL LSAGG (NIL T) -9 NIL 1480943) (-608 1472215 1473139 1474352 "LSAGG-" 1474357 NIL LSAGG- (NIL T T) -8 NIL NIL) (-607 1469841 1471359 1471608 "LPOLY" 1472010 NIL LPOLY (NIL T T) -8 NIL NIL) (-606 1469423 1469508 1469631 "LPEFRAC" 1469750 NIL LPEFRAC (NIL T) -7 NIL NIL) (-605 1467770 1468517 1468770 "LO" 1469255 NIL LO (NIL T T T) -8 NIL NIL) (-604 1467424 1467536 1467564 "LOGIC" 1467675 T LOGIC (NIL) -9 NIL 1467755) (-603 1467286 1467309 1467380 "LOGIC-" 1467385 NIL LOGIC- (NIL T) -8 NIL NIL) (-602 1466479 1466619 1466812 "LODOOPS" 1467142 NIL LODOOPS (NIL T T) -7 NIL NIL) (-601 1463897 1466396 1466461 "LODO" 1466466 NIL LODO (NIL T NIL) -8 NIL NIL) (-600 1462443 1462678 1463029 "LODOF" 1463644 NIL LODOF (NIL T T) -7 NIL NIL) (-599 1458863 1461299 1461339 "LODOCAT" 1461771 NIL LODOCAT (NIL T) -9 NIL 1461982) (-598 1458597 1458655 1458781 "LODOCAT-" 1458786 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-597 1455911 1458438 1458556 "LODO2" 1458561 NIL LODO2 (NIL T T) -8 NIL NIL) (-596 1453340 1455848 1455893 "LODO1" 1455898 NIL LODO1 (NIL T) -8 NIL NIL) (-595 1452203 1452368 1452679 "LODEEF" 1453163 NIL LODEEF (NIL T T T) -7 NIL NIL) (-594 1447490 1450334 1450375 "LNAGG" 1451322 NIL LNAGG (NIL T) -9 NIL 1451766) (-593 1446637 1446851 1447193 "LNAGG-" 1447198 NIL LNAGG- (NIL T T) -8 NIL NIL) (-592 1442802 1443564 1444202 "LMOPS" 1446053 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-591 1442200 1442562 1442602 "LMODULE" 1442662 NIL LMODULE (NIL T) -9 NIL 1442704) (-590 1439446 1441845 1441968 "LMDICT" 1442110 NIL LMDICT (NIL T) -8 NIL NIL) (-589 1432673 1438392 1438690 "LIST" 1439181 NIL LIST (NIL T) -8 NIL NIL) (-588 1432198 1432272 1432411 "LIST3" 1432593 NIL LIST3 (NIL T T T) -7 NIL NIL) (-587 1431205 1431383 1431611 "LIST2" 1432016 NIL LIST2 (NIL T T) -7 NIL NIL) (-586 1429339 1429651 1430050 "LIST2MAP" 1430852 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-585 1428052 1428732 1428772 "LINEXP" 1429025 NIL LINEXP (NIL T) -9 NIL 1429173) (-584 1426699 1426959 1427256 "LINDEP" 1427804 NIL LINDEP (NIL T T) -7 NIL NIL) (-583 1423466 1424185 1424962 "LIMITRF" 1425954 NIL LIMITRF (NIL T) -7 NIL NIL) (-582 1421746 1422041 1422456 "LIMITPS" 1423161 NIL LIMITPS (NIL T T) -7 NIL NIL) (-581 1416201 1421257 1421485 "LIE" 1421567 NIL LIE (NIL T T) -8 NIL NIL) (-580 1415252 1415695 1415735 "LIECAT" 1415875 NIL LIECAT (NIL T) -9 NIL 1416026) (-579 1415093 1415120 1415208 "LIECAT-" 1415213 NIL LIECAT- (NIL T T) -8 NIL NIL) (-578 1407705 1414542 1414707 "LIB" 1414948 T LIB (NIL) -8 NIL NIL) (-577 1403342 1404223 1405158 "LGROBP" 1406822 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-576 1401208 1401482 1401844 "LF" 1403063 NIL LF (NIL T T) -7 NIL NIL) (-575 1400048 1400740 1400768 "LFCAT" 1400975 T LFCAT (NIL) -9 NIL 1401114) (-574 1396960 1397586 1398272 "LEXTRIPK" 1399414 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-573 1393666 1394530 1395033 "LEXP" 1396540 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-572 1392064 1392377 1392778 "LEADCDET" 1393348 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-571 1391260 1391334 1391561 "LAZM3PK" 1391985 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-570 1386177 1389339 1389876 "LAUPOL" 1390773 NIL LAUPOL (NIL T T) -8 NIL NIL) (-569 1385744 1385788 1385955 "LAPLACE" 1386127 NIL LAPLACE (NIL T T) -7 NIL NIL) (-568 1383672 1384845 1385096 "LA" 1385577 NIL LA (NIL T T T) -8 NIL NIL) (-567 1382735 1383329 1383369 "LALG" 1383430 NIL LALG (NIL T) -9 NIL 1383488) (-566 1382450 1382509 1382644 "LALG-" 1382649 NIL LALG- (NIL T T) -8 NIL NIL) (-565 1381360 1381547 1381844 "KOVACIC" 1382250 NIL KOVACIC (NIL T T) -7 NIL NIL) (-564 1381195 1381219 1381260 "KONVERT" 1381322 NIL KONVERT (NIL T) -9 NIL NIL) (-563 1381030 1381054 1381095 "KOERCE" 1381157 NIL KOERCE (NIL T) -9 NIL NIL) (-562 1378764 1379524 1379917 "KERNEL" 1380669 NIL KERNEL (NIL T) -8 NIL NIL) (-561 1378266 1378347 1378477 "KERNEL2" 1378678 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-560 1372118 1376806 1376860 "KDAGG" 1377237 NIL KDAGG (NIL T T) -9 NIL 1377443) (-559 1371647 1371771 1371976 "KDAGG-" 1371981 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-558 1364822 1371308 1371463 "KAFILE" 1371525 NIL KAFILE (NIL T) -8 NIL NIL) (-557 1359277 1364333 1364561 "JORDAN" 1364643 NIL JORDAN (NIL T T) -8 NIL NIL) (-556 1355577 1357483 1357537 "IXAGG" 1358466 NIL IXAGG (NIL T T) -9 NIL 1358925) (-555 1354496 1354802 1355221 "IXAGG-" 1355226 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-554 1350081 1354418 1354477 "IVECTOR" 1354482 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-553 1348847 1349084 1349350 "ITUPLE" 1349848 NIL ITUPLE (NIL T) -8 NIL NIL) (-552 1347283 1347460 1347766 "ITRIGMNP" 1348669 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-551 1346028 1346232 1346515 "ITFUN3" 1347059 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-550 1345660 1345717 1345826 "ITFUN2" 1345965 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-549 1343462 1344533 1344830 "ITAYLOR" 1345395 NIL ITAYLOR (NIL T) -8 NIL NIL) (-548 1332450 1337648 1338807 "ISUPS" 1342335 NIL ISUPS (NIL T) -8 NIL NIL) (-547 1331554 1331694 1331930 "ISUMP" 1332297 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-546 1326818 1331355 1331434 "ISTRING" 1331507 NIL ISTRING (NIL NIL) -8 NIL NIL) (-545 1326031 1326112 1326327 "IRURPK" 1326732 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-544 1324967 1325168 1325408 "IRSN" 1325811 T IRSN (NIL) -7 NIL NIL) (-543 1323002 1323357 1323792 "IRRF2F" 1324605 NIL IRRF2F (NIL T) -7 NIL NIL) (-542 1322749 1322787 1322863 "IRREDFFX" 1322958 NIL IRREDFFX (NIL T) -7 NIL NIL) (-541 1321364 1321623 1321922 "IROOT" 1322482 NIL IROOT (NIL T) -7 NIL NIL) (-540 1318002 1319053 1319743 "IR" 1320706 NIL IR (NIL T) -8 NIL NIL) (-539 1315615 1316110 1316676 "IR2" 1317480 NIL IR2 (NIL T T) -7 NIL NIL) (-538 1314691 1314804 1315024 "IR2F" 1315498 NIL IR2F (NIL T T) -7 NIL NIL) (-537 1314482 1314516 1314576 "IPRNTPK" 1314651 T IPRNTPK (NIL) -7 NIL NIL) (-536 1311036 1314371 1314440 "IPF" 1314445 NIL IPF (NIL NIL) -8 NIL NIL) (-535 1309353 1310961 1311018 "IPADIC" 1311023 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-534 1308852 1308910 1309099 "INVLAPLA" 1309289 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-533 1298501 1300854 1303240 "INTTR" 1306516 NIL INTTR (NIL T T) -7 NIL NIL) (-532 1294849 1295590 1296453 "INTTOOLS" 1297687 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-531 1294435 1294526 1294643 "INTSLPE" 1294752 T INTSLPE (NIL) -7 NIL NIL) (-530 1292385 1294358 1294417 "INTRVL" 1294422 NIL INTRVL (NIL T) -8 NIL NIL) (-529 1289992 1290504 1291078 "INTRF" 1291870 NIL INTRF (NIL T) -7 NIL NIL) (-528 1289407 1289504 1289645 "INTRET" 1289890 NIL INTRET (NIL T) -7 NIL NIL) (-527 1287409 1287798 1288267 "INTRAT" 1289015 NIL INTRAT (NIL T T) -7 NIL NIL) (-526 1284642 1285225 1285850 "INTPM" 1286894 NIL INTPM (NIL T T) -7 NIL NIL) (-525 1281351 1281950 1282694 "INTPAF" 1284028 NIL INTPAF (NIL T T T) -7 NIL NIL) (-524 1276594 1277540 1278575 "INTPACK" 1280336 T INTPACK (NIL) -7 NIL NIL) (-523 1273448 1276323 1276450 "INT" 1276487 T INT (NIL) -8 NIL NIL) (-522 1272700 1272852 1273060 "INTHERTR" 1273290 NIL INTHERTR (NIL T T) -7 NIL NIL) (-521 1272139 1272219 1272407 "INTHERAL" 1272614 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-520 1269985 1270428 1270885 "INTHEORY" 1271702 T INTHEORY (NIL) -7 NIL NIL) (-519 1261307 1262928 1264706 "INTG0" 1268337 NIL INTG0 (NIL T T T) -7 NIL NIL) (-518 1241880 1246670 1251480 "INTFTBL" 1256517 T INTFTBL (NIL) -8 NIL NIL) (-517 1241129 1241267 1241440 "INTFACT" 1241739 NIL INTFACT (NIL T) -7 NIL NIL) (-516 1238520 1238966 1239529 "INTEF" 1240683 NIL INTEF (NIL T T) -7 NIL NIL) (-515 1236982 1237731 1237759 "INTDOM" 1238060 T INTDOM (NIL) -9 NIL 1238267) (-514 1236351 1236525 1236767 "INTDOM-" 1236772 NIL INTDOM- (NIL T) -8 NIL NIL) (-513 1232844 1234776 1234830 "INTCAT" 1235629 NIL INTCAT (NIL T) -9 NIL 1235948) (-512 1232317 1232419 1232547 "INTBIT" 1232736 T INTBIT (NIL) -7 NIL NIL) (-511 1230992 1231146 1231459 "INTALG" 1232162 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-510 1230449 1230539 1230709 "INTAF" 1230896 NIL INTAF (NIL T T) -7 NIL NIL) (-509 1223903 1230259 1230399 "INTABL" 1230404 NIL INTABL (NIL T T T) -8 NIL NIL) (-508 1218854 1221583 1221611 "INS" 1222579 T INS (NIL) -9 NIL 1223260) (-507 1216094 1216865 1217839 "INS-" 1217912 NIL INS- (NIL T) -8 NIL NIL) (-506 1214873 1215100 1215397 "INPSIGN" 1215847 NIL INPSIGN (NIL T T) -7 NIL NIL) (-505 1213991 1214108 1214305 "INPRODPF" 1214753 NIL INPRODPF (NIL T T) -7 NIL NIL) (-504 1212885 1213002 1213239 "INPRODFF" 1213871 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-503 1211885 1212037 1212297 "INNMFACT" 1212721 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-502 1211082 1211179 1211367 "INMODGCD" 1211784 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-501 1209591 1209835 1210159 "INFSP" 1210827 NIL INFSP (NIL T T T) -7 NIL NIL) (-500 1208775 1208892 1209075 "INFPROD0" 1209471 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-499 1205785 1206944 1207435 "INFORM" 1208292 T INFORM (NIL) -8 NIL NIL) (-498 1205395 1205455 1205553 "INFORM1" 1205720 NIL INFORM1 (NIL T) -7 NIL NIL) (-497 1204918 1205007 1205121 "INFINITY" 1205301 T INFINITY (NIL) -7 NIL NIL) (-496 1203535 1203784 1204105 "INEP" 1204666 NIL INEP (NIL T T T) -7 NIL NIL) (-495 1202811 1203432 1203497 "INDE" 1203502 NIL INDE (NIL T) -8 NIL NIL) (-494 1202375 1202443 1202560 "INCRMAPS" 1202738 NIL INCRMAPS (NIL T) -7 NIL NIL) (-493 1197686 1198611 1199555 "INBFF" 1201463 NIL INBFF (NIL T) -7 NIL NIL) (-492 1194181 1197531 1197634 "IMATRIX" 1197639 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-491 1192893 1193016 1193331 "IMATQF" 1194037 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-490 1191113 1191340 1191677 "IMATLIN" 1192649 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-489 1185739 1191037 1191095 "ILIST" 1191100 NIL ILIST (NIL T NIL) -8 NIL NIL) (-488 1183692 1185599 1185712 "IIARRAY2" 1185717 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-487 1179060 1183603 1183667 "IFF" 1183672 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-486 1174103 1178352 1178540 "IFARRAY" 1178917 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-485 1173310 1174007 1174080 "IFAMON" 1174085 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-484 1172894 1172959 1173013 "IEVALAB" 1173220 NIL IEVALAB (NIL T T) -9 NIL NIL) (-483 1172569 1172637 1172797 "IEVALAB-" 1172802 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-482 1172227 1172483 1172546 "IDPO" 1172551 NIL IDPO (NIL T T) -8 NIL NIL) (-481 1171504 1172116 1172191 "IDPOAMS" 1172196 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-480 1170838 1171393 1171468 "IDPOAM" 1171473 NIL IDPOAM (NIL T T) -8 NIL NIL) (-479 1169924 1170174 1170227 "IDPC" 1170640 NIL IDPC (NIL T T) -9 NIL 1170789) (-478 1169420 1169816 1169889 "IDPAM" 1169894 NIL IDPAM (NIL T T) -8 NIL NIL) (-477 1168823 1169312 1169385 "IDPAG" 1169390 NIL IDPAG (NIL T T) -8 NIL NIL) (-476 1165078 1165926 1166821 "IDECOMP" 1167980 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-475 1157951 1159001 1160048 "IDEAL" 1164114 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-474 1157115 1157227 1157426 "ICDEN" 1157835 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-473 1156214 1156595 1156742 "ICARD" 1156988 T ICARD (NIL) -8 NIL NIL) (-472 1154286 1154599 1155002 "IBPTOOLS" 1155891 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-471 1149900 1153906 1154019 "IBITS" 1154205 NIL IBITS (NIL NIL) -8 NIL NIL) (-470 1146623 1147199 1147894 "IBATOOL" 1149317 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-469 1144403 1144864 1145397 "IBACHIN" 1146158 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-468 1142280 1144249 1144352 "IARRAY2" 1144357 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-467 1138433 1142206 1142263 "IARRAY1" 1142268 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-466 1132371 1136851 1137329 "IAN" 1137975 T IAN (NIL) -8 NIL NIL) (-465 1131882 1131939 1132112 "IALGFACT" 1132308 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-464 1131410 1131523 1131551 "HYPCAT" 1131758 T HYPCAT (NIL) -9 NIL NIL) (-463 1130948 1131065 1131251 "HYPCAT-" 1131256 NIL HYPCAT- (NIL T) -8 NIL NIL) (-462 1127628 1128959 1129000 "HOAGG" 1129981 NIL HOAGG (NIL T) -9 NIL 1130660) (-461 1126222 1126621 1127147 "HOAGG-" 1127152 NIL HOAGG- (NIL T T) -8 NIL NIL) (-460 1120052 1125663 1125829 "HEXADEC" 1126076 T HEXADEC (NIL) -8 NIL NIL) (-459 1118800 1119022 1119285 "HEUGCD" 1119829 NIL HEUGCD (NIL T) -7 NIL NIL) (-458 1117903 1118637 1118767 "HELLFDIV" 1118772 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-457 1116131 1117680 1117768 "HEAP" 1117847 NIL HEAP (NIL T) -8 NIL NIL) (-456 1109998 1116046 1116108 "HDP" 1116113 NIL HDP (NIL NIL T) -8 NIL NIL) (-455 1103710 1109635 1109786 "HDMP" 1109899 NIL HDMP (NIL NIL T) -8 NIL NIL) (-454 1103035 1103174 1103338 "HB" 1103566 T HB (NIL) -7 NIL NIL) (-453 1096532 1102881 1102985 "HASHTBL" 1102990 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-452 1094285 1096160 1096339 "HACKPI" 1096373 T HACKPI (NIL) -8 NIL NIL) (-451 1089981 1094139 1094251 "GTSET" 1094256 NIL GTSET (NIL T T T T) -8 NIL NIL) (-450 1083507 1089859 1089957 "GSTBL" 1089962 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-449 1075740 1082543 1082807 "GSERIES" 1083298 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-448 1074763 1075216 1075244 "GROUP" 1075505 T GROUP (NIL) -9 NIL 1075664) (-447 1073879 1074102 1074446 "GROUP-" 1074451 NIL GROUP- (NIL T) -8 NIL NIL) (-446 1072248 1072567 1072954 "GROEBSOL" 1073556 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-445 1071189 1071451 1071502 "GRMOD" 1072031 NIL GRMOD (NIL T T) -9 NIL 1072199) (-444 1070957 1070993 1071121 "GRMOD-" 1071126 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-443 1066283 1067311 1068311 "GRIMAGE" 1069977 T GRIMAGE (NIL) -8 NIL NIL) (-442 1064750 1065010 1065334 "GRDEF" 1065979 T GRDEF (NIL) -7 NIL NIL) (-441 1064194 1064310 1064451 "GRAY" 1064629 T GRAY (NIL) -7 NIL NIL) (-440 1063428 1063808 1063859 "GRALG" 1064012 NIL GRALG (NIL T T) -9 NIL 1064104) (-439 1063089 1063162 1063325 "GRALG-" 1063330 NIL GRALG- (NIL T T T) -8 NIL NIL) (-438 1059897 1062678 1062854 "GPOLSET" 1062996 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-437 1059253 1059310 1059567 "GOSPER" 1059834 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-436 1055012 1055691 1056217 "GMODPOL" 1058952 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-435 1054017 1054201 1054439 "GHENSEL" 1054824 NIL GHENSEL (NIL T T) -7 NIL NIL) (-434 1048083 1048926 1049952 "GENUPS" 1053101 NIL GENUPS (NIL T T) -7 NIL NIL) (-433 1047780 1047831 1047920 "GENUFACT" 1048026 NIL GENUFACT (NIL T) -7 NIL NIL) (-432 1047192 1047269 1047434 "GENPGCD" 1047698 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-431 1046666 1046701 1046914 "GENMFACT" 1047151 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-430 1045234 1045489 1045796 "GENEEZ" 1046409 NIL GENEEZ (NIL T T) -7 NIL NIL) (-429 1039108 1044847 1045008 "GDMP" 1045157 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-428 1028488 1032879 1033985 "GCNAALG" 1038091 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-427 1026910 1027782 1027810 "GCDDOM" 1028065 T GCDDOM (NIL) -9 NIL 1028222) (-426 1026380 1026507 1026722 "GCDDOM-" 1026727 NIL GCDDOM- (NIL T) -8 NIL NIL) (-425 1025052 1025237 1025541 "GB" 1026159 NIL GB (NIL T T T T) -7 NIL NIL) (-424 1013672 1015998 1018390 "GBINTERN" 1022743 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-423 1011509 1011801 1012222 "GBF" 1013347 NIL GBF (NIL T T T T) -7 NIL NIL) (-422 1010290 1010455 1010722 "GBEUCLID" 1011325 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-421 1009639 1009764 1009913 "GAUSSFAC" 1010161 T GAUSSFAC (NIL) -7 NIL NIL) (-420 1008016 1008318 1008631 "GALUTIL" 1009358 NIL GALUTIL (NIL T) -7 NIL NIL) (-419 1006333 1006607 1006930 "GALPOLYU" 1007743 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-418 1003722 1004012 1004417 "GALFACTU" 1006030 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-417 995528 997027 998635 "GALFACT" 1002154 NIL GALFACT (NIL T) -7 NIL NIL) (-416 992916 993574 993602 "FVFUN" 994758 T FVFUN (NIL) -9 NIL 995478) (-415 992182 992364 992392 "FVC" 992683 T FVC (NIL) -9 NIL 992866) (-414 991824 991979 992060 "FUNCTION" 992134 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-413 989494 990045 990534 "FT" 991355 T FT (NIL) -8 NIL NIL) (-412 988312 988795 988998 "FTEM" 989311 T FTEM (NIL) -8 NIL NIL) (-411 986577 986865 987267 "FSUPFACT" 988004 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-410 984974 985263 985595 "FST" 986265 T FST (NIL) -8 NIL NIL) (-409 984149 984255 984449 "FSRED" 984856 NIL FSRED (NIL T T) -7 NIL NIL) (-408 982828 983083 983437 "FSPRMELT" 983864 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-407 979913 980351 980850 "FSPECF" 982391 NIL FSPECF (NIL T T) -7 NIL NIL) (-406 962287 970844 970884 "FS" 974722 NIL FS (NIL T) -9 NIL 977004) (-405 950937 953927 957983 "FS-" 958280 NIL FS- (NIL T T) -8 NIL NIL) (-404 950453 950507 950683 "FSINT" 950878 NIL FSINT (NIL T T) -7 NIL NIL) (-403 948734 949446 949749 "FSERIES" 950232 NIL FSERIES (NIL T T) -8 NIL NIL) (-402 947752 947868 948098 "FSCINT" 948614 NIL FSCINT (NIL T T) -7 NIL NIL) (-401 943987 946697 946738 "FSAGG" 947108 NIL FSAGG (NIL T) -9 NIL 947367) (-400 941749 942350 943146 "FSAGG-" 943241 NIL FSAGG- (NIL T T) -8 NIL NIL) (-399 940791 940934 941161 "FSAGG2" 941602 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-398 938450 938729 939282 "FS2UPS" 940509 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-397 938036 938079 938232 "FS2" 938401 NIL FS2 (NIL T T T T) -7 NIL NIL) (-396 936896 937067 937375 "FS2EXPXP" 937861 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-395 936322 936437 936589 "FRUTIL" 936776 NIL FRUTIL (NIL T) -7 NIL NIL) (-394 927742 931821 933177 "FR" 934998 NIL FR (NIL T) -8 NIL NIL) (-393 922819 925462 925502 "FRNAALG" 926898 NIL FRNAALG (NIL T) -9 NIL 927505) (-392 918497 919568 920843 "FRNAALG-" 921593 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-391 918135 918178 918305 "FRNAAF2" 918448 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-390 916500 916992 917286 "FRMOD" 917948 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-389 914222 914891 915207 "FRIDEAL" 916291 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-388 913421 913508 913795 "FRIDEAL2" 914129 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-387 912679 913087 913128 "FRETRCT" 913133 NIL FRETRCT (NIL T) -9 NIL 913304) (-386 911791 912022 912373 "FRETRCT-" 912378 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-385 909001 910221 910280 "FRAMALG" 911162 NIL FRAMALG (NIL T T) -9 NIL 911454) (-384 907134 907590 908220 "FRAMALG-" 908443 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-383 901036 906609 906885 "FRAC" 906890 NIL FRAC (NIL T) -8 NIL NIL) (-382 900672 900729 900836 "FRAC2" 900973 NIL FRAC2 (NIL T T) -7 NIL NIL) (-381 900308 900365 900472 "FR2" 900609 NIL FR2 (NIL T T) -7 NIL NIL) (-380 894982 897895 897923 "FPS" 899042 T FPS (NIL) -9 NIL 899598) (-379 894431 894540 894704 "FPS-" 894850 NIL FPS- (NIL T) -8 NIL NIL) (-378 891880 893577 893605 "FPC" 893830 T FPC (NIL) -9 NIL 893972) (-377 891673 891713 891810 "FPC-" 891815 NIL FPC- (NIL T) -8 NIL NIL) (-376 890552 891162 891203 "FPATMAB" 891208 NIL FPATMAB (NIL T) -9 NIL 891360) (-375 888252 888728 889154 "FPARFRAC" 890189 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-374 883645 884144 884826 "FORTRAN" 887684 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-373 881361 881861 882400 "FORT" 883126 T FORT (NIL) -7 NIL NIL) (-372 879037 879599 879627 "FORTFN" 880687 T FORTFN (NIL) -9 NIL 881311) (-371 878801 878851 878879 "FORTCAT" 878938 T FORTCAT (NIL) -9 NIL 879000) (-370 876861 877344 877743 "FORMULA" 878422 T FORMULA (NIL) -8 NIL NIL) (-369 876649 876679 876748 "FORMULA1" 876825 NIL FORMULA1 (NIL T) -7 NIL NIL) (-368 876172 876224 876397 "FORDER" 876591 NIL FORDER (NIL T T T T) -7 NIL NIL) (-367 875268 875432 875625 "FOP" 875999 T FOP (NIL) -7 NIL NIL) (-366 873876 874548 874722 "FNLA" 875150 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-365 872545 872934 872962 "FNCAT" 873534 T FNCAT (NIL) -9 NIL 873827) (-364 872111 872504 872532 "FNAME" 872537 T FNAME (NIL) -8 NIL NIL) (-363 870771 871744 871772 "FMTC" 871777 T FMTC (NIL) -9 NIL 871812) (-362 867089 868296 868924 "FMONOID" 870176 NIL FMONOID (NIL T) -8 NIL NIL) (-361 866309 866832 866980 "FM" 866985 NIL FM (NIL T T) -8 NIL NIL) (-360 863733 864379 864407 "FMFUN" 865551 T FMFUN (NIL) -9 NIL 866259) (-359 863002 863183 863211 "FMC" 863501 T FMC (NIL) -9 NIL 863683) (-358 860232 861066 861119 "FMCAT" 862301 NIL FMCAT (NIL T T) -9 NIL 862795) (-357 859127 860000 860099 "FM1" 860177 NIL FM1 (NIL T T) -8 NIL NIL) (-356 856901 857317 857811 "FLOATRP" 858678 NIL FLOATRP (NIL T) -7 NIL NIL) (-355 850387 854557 855187 "FLOAT" 856291 T FLOAT (NIL) -8 NIL NIL) (-354 847825 848325 848903 "FLOATCP" 849854 NIL FLOATCP (NIL T) -7 NIL NIL) (-353 846614 847462 847502 "FLINEXP" 847507 NIL FLINEXP (NIL T) -9 NIL 847600) (-352 845769 846004 846331 "FLINEXP-" 846336 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-351 844845 844989 845213 "FLASORT" 845621 NIL FLASORT (NIL T T) -7 NIL NIL) (-350 842064 842906 842958 "FLALG" 844185 NIL FLALG (NIL T T) -9 NIL 844652) (-349 835849 839551 839592 "FLAGG" 840854 NIL FLAGG (NIL T) -9 NIL 841506) (-348 834575 834914 835404 "FLAGG-" 835409 NIL FLAGG- (NIL T T) -8 NIL NIL) (-347 833617 833760 833987 "FLAGG2" 834428 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-346 830590 831608 831667 "FINRALG" 832795 NIL FINRALG (NIL T T) -9 NIL 833303) (-345 829750 829979 830318 "FINRALG-" 830323 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-344 829157 829370 829398 "FINITE" 829594 T FINITE (NIL) -9 NIL 829701) (-343 821617 823778 823818 "FINAALG" 827485 NIL FINAALG (NIL T) -9 NIL 828938) (-342 816958 817999 819143 "FINAALG-" 820522 NIL FINAALG- (NIL T T) -8 NIL NIL) (-341 816353 816713 816816 "FILE" 816888 NIL FILE (NIL T) -8 NIL NIL) (-340 815038 815350 815404 "FILECAT" 816088 NIL FILECAT (NIL T T) -9 NIL 816304) (-339 812901 814457 814485 "FIELD" 814525 T FIELD (NIL) -9 NIL 814605) (-338 811521 811906 812417 "FIELD-" 812422 NIL FIELD- (NIL T) -8 NIL NIL) (-337 809336 810158 810504 "FGROUP" 811208 NIL FGROUP (NIL T) -8 NIL NIL) (-336 808426 808590 808810 "FGLMICPK" 809168 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-335 804228 808351 808408 "FFX" 808413 NIL FFX (NIL T NIL) -8 NIL NIL) (-334 803829 803890 804025 "FFSLPE" 804161 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-333 799822 800601 801397 "FFPOLY" 803065 NIL FFPOLY (NIL T) -7 NIL NIL) (-332 799326 799362 799571 "FFPOLY2" 799780 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-331 795147 799245 799308 "FFP" 799313 NIL FFP (NIL T NIL) -8 NIL NIL) (-330 790515 795058 795122 "FF" 795127 NIL FF (NIL NIL NIL) -8 NIL NIL) (-329 785611 789858 790048 "FFNBX" 790369 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-328 780520 784746 785004 "FFNBP" 785465 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-327 775123 779804 780015 "FFNB" 780353 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-326 773955 774153 774468 "FFINTBAS" 774920 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-325 770179 772419 772447 "FFIELDC" 773067 T FFIELDC (NIL) -9 NIL 773443) (-324 768842 769212 769709 "FFIELDC-" 769714 NIL FFIELDC- (NIL T) -8 NIL NIL) (-323 768412 768457 768581 "FFHOM" 768784 NIL FFHOM (NIL T T T) -7 NIL NIL) (-322 766110 766594 767111 "FFF" 767927 NIL FFF (NIL T) -7 NIL NIL) (-321 761698 765852 765953 "FFCGX" 766053 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-320 757300 761430 761537 "FFCGP" 761641 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-319 752453 757027 757135 "FFCG" 757236 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-318 734399 743522 743608 "FFCAT" 748773 NIL FFCAT (NIL T T T) -9 NIL 750260) (-317 729597 730644 731958 "FFCAT-" 733188 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-316 729008 729051 729286 "FFCAT2" 729548 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-315 718208 721998 723215 "FEXPR" 727863 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-314 717208 717643 717684 "FEVALAB" 717768 NIL FEVALAB (NIL T) -9 NIL 718029) (-313 716367 716577 716915 "FEVALAB-" 716920 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-312 714960 715750 715953 "FDIV" 716266 NIL FDIV (NIL T T T T) -8 NIL NIL) (-311 712027 712742 712857 "FDIVCAT" 714425 NIL FDIVCAT (NIL T T T T) -9 NIL 714862) (-310 711789 711816 711986 "FDIVCAT-" 711991 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-309 711009 711096 711373 "FDIV2" 711696 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-308 709695 709954 710243 "FCPAK1" 710740 T FCPAK1 (NIL) -7 NIL NIL) (-307 708823 709195 709336 "FCOMP" 709586 NIL FCOMP (NIL T) -8 NIL NIL) (-306 692458 695872 699433 "FC" 705282 T FC (NIL) -8 NIL NIL) (-305 685054 689100 689140 "FAXF" 690942 NIL FAXF (NIL T) -9 NIL 691633) (-304 682333 682988 683813 "FAXF-" 684278 NIL FAXF- (NIL T T) -8 NIL NIL) (-303 677433 681709 681885 "FARRAY" 682190 NIL FARRAY (NIL T) -8 NIL NIL) (-302 672824 674895 674947 "FAMR" 675959 NIL FAMR (NIL T T) -9 NIL 676419) (-301 671715 672017 672451 "FAMR-" 672456 NIL FAMR- (NIL T T T) -8 NIL NIL) (-300 670911 671637 671690 "FAMONOID" 671695 NIL FAMONOID (NIL T) -8 NIL NIL) (-299 668744 669428 669481 "FAMONC" 670422 NIL FAMONC (NIL T T) -9 NIL 670807) (-298 667436 668498 668635 "FAGROUP" 668640 NIL FAGROUP (NIL T) -8 NIL NIL) (-297 665239 665558 665960 "FACUTIL" 667117 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-296 664338 664523 664745 "FACTFUNC" 665049 NIL FACTFUNC (NIL T) -7 NIL NIL) (-295 656658 663589 663801 "EXPUPXS" 664194 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-294 654141 654681 655267 "EXPRTUBE" 656092 T EXPRTUBE (NIL) -7 NIL NIL) (-293 650335 650927 651664 "EXPRODE" 653480 NIL EXPRODE (NIL T T) -7 NIL NIL) (-292 635494 648994 649420 "EXPR" 649941 NIL EXPR (NIL T) -8 NIL NIL) (-291 629922 630509 631321 "EXPR2UPS" 634792 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-290 629558 629615 629722 "EXPR2" 629859 NIL EXPR2 (NIL T T) -7 NIL NIL) (-289 620912 628695 628990 "EXPEXPAN" 629396 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-288 620739 620869 620898 "EXIT" 620903 T EXIT (NIL) -8 NIL NIL) (-287 620366 620428 620541 "EVALCYC" 620671 NIL EVALCYC (NIL T) -7 NIL NIL) (-286 619907 620025 620066 "EVALAB" 620236 NIL EVALAB (NIL T) -9 NIL 620340) (-285 619388 619510 619731 "EVALAB-" 619736 NIL EVALAB- (NIL T T) -8 NIL NIL) (-284 616851 618163 618191 "EUCDOM" 618746 T EUCDOM (NIL) -9 NIL 619096) (-283 615256 615698 616288 "EUCDOM-" 616293 NIL EUCDOM- (NIL T) -8 NIL NIL) (-282 602834 605582 608322 "ESTOOLS" 612536 T ESTOOLS (NIL) -7 NIL NIL) (-281 602470 602527 602634 "ESTOOLS2" 602771 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-280 602221 602263 602343 "ESTOOLS1" 602422 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-279 596159 597883 597911 "ES" 600675 T ES (NIL) -9 NIL 602081) (-278 591106 592393 594210 "ES-" 594374 NIL ES- (NIL T) -8 NIL NIL) (-277 587481 588241 589021 "ESCONT" 590346 T ESCONT (NIL) -7 NIL NIL) (-276 587226 587258 587340 "ESCONT1" 587443 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-275 586901 586951 587051 "ES2" 587170 NIL ES2 (NIL T T) -7 NIL NIL) (-274 586531 586589 586698 "ES1" 586837 NIL ES1 (NIL T T) -7 NIL NIL) (-273 585747 585876 586052 "ERROR" 586375 T ERROR (NIL) -7 NIL NIL) (-272 579250 585606 585697 "EQTBL" 585702 NIL EQTBL (NIL T T) -8 NIL NIL) (-271 571687 574568 576015 "EQ" 577836 NIL -2533 (NIL T) -8 NIL NIL) (-270 571319 571376 571485 "EQ2" 571624 NIL EQ2 (NIL T T) -7 NIL NIL) (-269 566611 567657 568750 "EP" 570258 NIL EP (NIL T) -7 NIL NIL) (-268 565194 565494 565811 "ENV" 566314 T ENV (NIL) -8 NIL NIL) (-267 564354 564918 564946 "ENTIRER" 564951 T ENTIRER (NIL) -9 NIL 564996) (-266 560810 562309 562679 "EMR" 564153 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-265 559954 560139 560193 "ELTAGG" 560573 NIL ELTAGG (NIL T T) -9 NIL 560784) (-264 559673 559735 559876 "ELTAGG-" 559881 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-263 559462 559491 559545 "ELTAB" 559629 NIL ELTAB (NIL T T) -9 NIL NIL) (-262 558588 558734 558933 "ELFUTS" 559313 NIL ELFUTS (NIL T T) -7 NIL NIL) (-261 558330 558386 558414 "ELEMFUN" 558519 T ELEMFUN (NIL) -9 NIL NIL) (-260 558200 558221 558289 "ELEMFUN-" 558294 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-259 553092 556301 556342 "ELAGG" 557282 NIL ELAGG (NIL T) -9 NIL 557745) (-258 551377 551811 552474 "ELAGG-" 552479 NIL ELAGG- (NIL T T) -8 NIL NIL) (-257 550034 550314 550609 "ELABEXPR" 551102 T ELABEXPR (NIL) -8 NIL NIL) (-256 542902 544701 545528 "EFUPXS" 549310 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-255 536352 538153 538963 "EFULS" 542178 NIL EFULS (NIL T T T) -8 NIL NIL) (-254 533783 534141 534619 "EFSTRUC" 535984 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-253 522855 524420 525980 "EF" 532298 NIL EF (NIL T T) -7 NIL NIL) (-252 521956 522340 522489 "EAB" 522726 T EAB (NIL) -8 NIL NIL) (-251 521169 521915 521943 "E04UCFA" 521948 T E04UCFA (NIL) -8 NIL NIL) (-250 520382 521128 521156 "E04NAFA" 521161 T E04NAFA (NIL) -8 NIL NIL) (-249 519595 520341 520369 "E04MBFA" 520374 T E04MBFA (NIL) -8 NIL NIL) (-248 518808 519554 519582 "E04JAFA" 519587 T E04JAFA (NIL) -8 NIL NIL) (-247 518023 518767 518795 "E04GCFA" 518800 T E04GCFA (NIL) -8 NIL NIL) (-246 517238 517982 518010 "E04FDFA" 518015 T E04FDFA (NIL) -8 NIL NIL) (-245 516451 517197 517225 "E04DGFA" 517230 T E04DGFA (NIL) -8 NIL NIL) (-244 510636 511981 513343 "E04AGNT" 515109 T E04AGNT (NIL) -7 NIL NIL) (-243 509363 509843 509883 "DVARCAT" 510358 NIL DVARCAT (NIL T) -9 NIL 510556) (-242 508567 508779 509093 "DVARCAT-" 509098 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-241 501429 508369 508496 "DSMP" 508501 NIL DSMP (NIL T T T) -8 NIL NIL) (-240 496239 497374 498442 "DROPT" 500381 T DROPT (NIL) -8 NIL NIL) (-239 495904 495963 496061 "DROPT1" 496174 NIL DROPT1 (NIL T) -7 NIL NIL) (-238 491019 492145 493282 "DROPT0" 494787 T DROPT0 (NIL) -7 NIL NIL) (-237 489364 489689 490075 "DRAWPT" 490653 T DRAWPT (NIL) -7 NIL NIL) (-236 483951 484874 485953 "DRAW" 488338 NIL DRAW (NIL T) -7 NIL NIL) (-235 483584 483637 483755 "DRAWHACK" 483892 NIL DRAWHACK (NIL T) -7 NIL NIL) (-234 482315 482584 482875 "DRAWCX" 483313 T DRAWCX (NIL) -7 NIL NIL) (-233 481833 481901 482051 "DRAWCURV" 482241 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-232 472304 474263 476378 "DRAWCFUN" 479738 T DRAWCFUN (NIL) -7 NIL NIL) (-231 469118 471000 471041 "DQAGG" 471670 NIL DQAGG (NIL T) -9 NIL 471943) (-230 457625 464363 464445 "DPOLCAT" 466283 NIL DPOLCAT (NIL T T T T) -9 NIL 466827) (-229 452465 453811 455768 "DPOLCAT-" 455773 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-228 446549 452327 452424 "DPMO" 452429 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-227 440536 446330 446496 "DPMM" 446501 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-226 440049 440147 440267 "DOMAIN" 440436 T DOMAIN (NIL) -8 NIL NIL) (-225 433761 439686 439837 "DMP" 439950 NIL DMP (NIL NIL T) -8 NIL NIL) (-224 433361 433417 433561 "DLP" 433699 NIL DLP (NIL T) -7 NIL NIL) (-223 427005 432462 432689 "DLIST" 433166 NIL DLIST (NIL T) -8 NIL NIL) (-222 423852 425861 425902 "DLAGG" 426452 NIL DLAGG (NIL T) -9 NIL 426681) (-221 422562 423254 423282 "DIVRING" 423432 T DIVRING (NIL) -9 NIL 423540) (-220 421550 421803 422196 "DIVRING-" 422201 NIL DIVRING- (NIL T) -8 NIL NIL) (-219 419652 420009 420415 "DISPLAY" 421164 T DISPLAY (NIL) -7 NIL NIL) (-218 413541 419566 419629 "DIRPROD" 419634 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-217 412389 412592 412857 "DIRPROD2" 413334 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-216 402020 408025 408078 "DIRPCAT" 408486 NIL DIRPCAT (NIL NIL T) -9 NIL 409313) (-215 399346 399988 400869 "DIRPCAT-" 401206 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-214 398633 398793 398979 "DIOSP" 399180 T DIOSP (NIL) -7 NIL NIL) (-213 395336 397546 397587 "DIOPS" 398021 NIL DIOPS (NIL T) -9 NIL 398250) (-212 394885 394999 395190 "DIOPS-" 395195 NIL DIOPS- (NIL T T) -8 NIL NIL) (-211 393757 394395 394423 "DIFRING" 394610 T DIFRING (NIL) -9 NIL 394719) (-210 393403 393480 393632 "DIFRING-" 393637 NIL DIFRING- (NIL T) -8 NIL NIL) (-209 391193 392475 392515 "DIFEXT" 392874 NIL DIFEXT (NIL T) -9 NIL 393167) (-208 389479 389907 390572 "DIFEXT-" 390577 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-207 386802 389012 389053 "DIAGG" 389058 NIL DIAGG (NIL T) -9 NIL 389078) (-206 386186 386343 386595 "DIAGG-" 386600 NIL DIAGG- (NIL T T) -8 NIL NIL) (-205 381651 385145 385422 "DHMATRIX" 385955 NIL DHMATRIX (NIL T) -8 NIL NIL) (-204 377263 378172 379182 "DFSFUN" 380661 T DFSFUN (NIL) -7 NIL NIL) (-203 372049 375977 376342 "DFLOAT" 376918 T DFLOAT (NIL) -8 NIL NIL) (-202 370282 370563 370958 "DFINTTLS" 371757 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-201 367315 368317 368715 "DERHAM" 369949 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-200 365164 367090 367179 "DEQUEUE" 367259 NIL DEQUEUE (NIL T) -8 NIL NIL) (-199 364382 364515 364710 "DEGRED" 365026 NIL DEGRED (NIL T T) -7 NIL NIL) (-198 360782 361527 362379 "DEFINTRF" 363610 NIL DEFINTRF (NIL T) -7 NIL NIL) (-197 358313 358782 359380 "DEFINTEF" 360301 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-196 352143 357754 357920 "DECIMAL" 358167 T DECIMAL (NIL) -8 NIL NIL) (-195 349655 350113 350619 "DDFACT" 351687 NIL DDFACT (NIL T T) -7 NIL NIL) (-194 349251 349294 349445 "DBLRESP" 349606 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-193 346961 347295 347664 "DBASE" 349009 NIL DBASE (NIL T) -8 NIL NIL) (-192 346096 346920 346948 "D03FAFA" 346953 T D03FAFA (NIL) -8 NIL NIL) (-191 345232 346055 346083 "D03EEFA" 346088 T D03EEFA (NIL) -8 NIL NIL) (-190 343182 343648 344137 "D03AGNT" 344763 T D03AGNT (NIL) -7 NIL NIL) (-189 342500 343141 343169 "D02EJFA" 343174 T D02EJFA (NIL) -8 NIL NIL) (-188 341818 342459 342487 "D02CJFA" 342492 T D02CJFA (NIL) -8 NIL NIL) (-187 341136 341777 341805 "D02BHFA" 341810 T D02BHFA (NIL) -8 NIL NIL) (-186 340454 341095 341123 "D02BBFA" 341128 T D02BBFA (NIL) -8 NIL NIL) (-185 333652 335240 336846 "D02AGNT" 338868 T D02AGNT (NIL) -7 NIL NIL) (-184 331421 331943 332489 "D01WGTS" 333126 T D01WGTS (NIL) -7 NIL NIL) (-183 330524 331380 331408 "D01TRNS" 331413 T D01TRNS (NIL) -8 NIL NIL) (-182 329627 330483 330511 "D01GBFA" 330516 T D01GBFA (NIL) -8 NIL NIL) (-181 328730 329586 329614 "D01FCFA" 329619 T D01FCFA (NIL) -8 NIL NIL) (-180 327833 328689 328717 "D01ASFA" 328722 T D01ASFA (NIL) -8 NIL NIL) (-179 326936 327792 327820 "D01AQFA" 327825 T D01AQFA (NIL) -8 NIL NIL) (-178 326039 326895 326923 "D01APFA" 326928 T D01APFA (NIL) -8 NIL NIL) (-177 325142 325998 326026 "D01ANFA" 326031 T D01ANFA (NIL) -8 NIL NIL) (-176 324245 325101 325129 "D01AMFA" 325134 T D01AMFA (NIL) -8 NIL NIL) (-175 323348 324204 324232 "D01ALFA" 324237 T D01ALFA (NIL) -8 NIL NIL) (-174 322451 323307 323335 "D01AKFA" 323340 T D01AKFA (NIL) -8 NIL NIL) (-173 321554 322410 322438 "D01AJFA" 322443 T D01AJFA (NIL) -8 NIL NIL) (-172 314858 316407 317966 "D01AGNT" 320015 T D01AGNT (NIL) -7 NIL NIL) (-171 314195 314323 314475 "CYCLOTOM" 314726 T CYCLOTOM (NIL) -7 NIL NIL) (-170 310930 311643 312370 "CYCLES" 313488 T CYCLES (NIL) -7 NIL NIL) (-169 310242 310376 310547 "CVMP" 310791 NIL CVMP (NIL T) -7 NIL NIL) (-168 308023 308281 308656 "CTRIGMNP" 309970 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-167 307628 307711 307816 "CTORCALL" 307938 T CTORCALL (NIL) -8 NIL NIL) (-166 307002 307101 307254 "CSTTOOLS" 307525 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-165 302801 303458 304216 "CRFP" 306314 NIL CRFP (NIL T T) -7 NIL NIL) (-164 301848 302033 302261 "CRAPACK" 302605 NIL CRAPACK (NIL T) -7 NIL NIL) (-163 301232 301333 301537 "CPMATCH" 301724 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-162 300957 300985 301091 "CPIMA" 301198 NIL CPIMA (NIL T T T) -7 NIL NIL) (-161 297321 297993 298711 "COORDSYS" 300292 NIL COORDSYS (NIL T) -7 NIL NIL) (-160 296705 296834 296984 "CONTOUR" 297191 T CONTOUR (NIL) -8 NIL NIL) (-159 292566 294708 295200 "CONTFRAC" 296245 NIL CONTFRAC (NIL T) -8 NIL NIL) (-158 291720 292284 292312 "COMRING" 292317 T COMRING (NIL) -9 NIL 292368) (-157 290801 291078 291262 "COMPPROP" 291556 T COMPPROP (NIL) -8 NIL NIL) (-156 290462 290497 290625 "COMPLPAT" 290760 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-155 280443 290271 290380 "COMPLEX" 290385 NIL COMPLEX (NIL T) -8 NIL NIL) (-154 280079 280136 280243 "COMPLEX2" 280380 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-153 279797 279832 279930 "COMPFACT" 280038 NIL COMPFACT (NIL T T) -7 NIL NIL) (-152 264132 274426 274466 "COMPCAT" 275468 NIL COMPCAT (NIL T) -9 NIL 276861) (-151 253647 256571 260198 "COMPCAT-" 260554 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-150 253378 253406 253508 "COMMUPC" 253613 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-149 253173 253206 253265 "COMMONOP" 253339 T COMMONOP (NIL) -7 NIL NIL) (-148 252756 252924 253011 "COMM" 253106 T COMM (NIL) -8 NIL NIL) (-147 252005 252199 252227 "COMBOPC" 252565 T COMBOPC (NIL) -9 NIL 252740) (-146 250901 251111 251353 "COMBINAT" 251795 NIL COMBINAT (NIL T) -7 NIL NIL) (-145 247099 247672 248312 "COMBF" 250323 NIL COMBF (NIL T T) -7 NIL NIL) (-144 245885 246215 246450 "COLOR" 246884 T COLOR (NIL) -8 NIL NIL) (-143 245525 245572 245697 "CMPLXRT" 245832 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-142 241027 242055 243135 "CLIP" 244465 T CLIP (NIL) -7 NIL NIL) (-141 239365 240135 240373 "CLIF" 240855 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-140 235588 237512 237553 "CLAGG" 238482 NIL CLAGG (NIL T) -9 NIL 239018) (-139 234010 234467 235050 "CLAGG-" 235055 NIL CLAGG- (NIL T T) -8 NIL NIL) (-138 233554 233639 233779 "CINTSLPE" 233919 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-137 231055 231526 232074 "CHVAR" 233082 NIL CHVAR (NIL T T T) -7 NIL NIL) (-136 230278 230842 230870 "CHARZ" 230875 T CHARZ (NIL) -9 NIL 230889) (-135 230032 230072 230150 "CHARPOL" 230232 NIL CHARPOL (NIL T) -7 NIL NIL) (-134 229139 229736 229764 "CHARNZ" 229811 T CHARNZ (NIL) -9 NIL 229866) (-133 227164 227829 228164 "CHAR" 228824 T CHAR (NIL) -8 NIL NIL) (-132 226890 226951 226979 "CFCAT" 227090 T CFCAT (NIL) -9 NIL NIL) (-131 226135 226246 226428 "CDEN" 226774 NIL CDEN (NIL T T T) -7 NIL NIL) (-130 222127 225288 225568 "CCLASS" 225875 T CCLASS (NIL) -8 NIL NIL) (-129 222046 222072 222107 "CATEGORY" 222112 T -10 (NIL) -8 NIL NIL) (-128 217098 218075 218828 "CARTEN" 221349 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-127 216206 216354 216575 "CARTEN2" 216945 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-126 214504 215358 215614 "CARD" 215970 T CARD (NIL) -8 NIL NIL) (-125 213877 214205 214233 "CACHSET" 214365 T CACHSET (NIL) -9 NIL 214442) (-124 213374 213670 213698 "CABMON" 213748 T CABMON (NIL) -9 NIL 213804) (-123 210931 213066 213173 "BTREE" 213300 NIL BTREE (NIL T) -8 NIL NIL) (-122 208429 210579 210701 "BTOURN" 210841 NIL BTOURN (NIL T) -8 NIL NIL) (-121 205848 207901 207942 "BTCAT" 208010 NIL BTCAT (NIL T) -9 NIL 208087) (-120 205515 205595 205744 "BTCAT-" 205749 NIL BTCAT- (NIL T T) -8 NIL NIL) (-119 200736 204607 204635 "BTAGG" 204891 T BTAGG (NIL) -9 NIL 205070) (-118 200159 200303 200533 "BTAGG-" 200538 NIL BTAGG- (NIL T) -8 NIL NIL) (-117 197203 199437 199652 "BSTREE" 199976 NIL BSTREE (NIL T) -8 NIL NIL) (-116 196341 196467 196651 "BRILL" 197059 NIL BRILL (NIL T) -7 NIL NIL) (-115 193043 195070 195111 "BRAGG" 195760 NIL BRAGG (NIL T) -9 NIL 196017) (-114 191572 191978 192533 "BRAGG-" 192538 NIL BRAGG- (NIL T T) -8 NIL NIL) (-113 184780 190918 191102 "BPADICRT" 191420 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-112 183084 184717 184762 "BPADIC" 184767 NIL BPADIC (NIL NIL) -8 NIL NIL) (-111 182784 182814 182927 "BOUNDZRO" 183048 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-110 178299 179390 180257 "BOP" 181937 T BOP (NIL) -8 NIL NIL) (-109 175920 176364 176884 "BOP1" 177812 NIL BOP1 (NIL T) -7 NIL NIL) (-108 174539 175250 175473 "BOOLEAN" 175717 T BOOLEAN (NIL) -8 NIL NIL) (-107 173906 174284 174336 "BMODULE" 174341 NIL BMODULE (NIL T T) -9 NIL 174405) (-106 169716 173704 173777 "BITS" 173853 T BITS (NIL) -8 NIL NIL) (-105 168813 169248 169400 "BINFILE" 169584 T BINFILE (NIL) -8 NIL NIL) (-104 168225 168347 168489 "BINDING" 168691 T BINDING (NIL) -8 NIL NIL) (-103 162059 167669 167834 "BINARY" 168080 T BINARY (NIL) -8 NIL NIL) (-102 159887 161315 161356 "BGAGG" 161616 NIL BGAGG (NIL T) -9 NIL 161753) (-101 159718 159750 159841 "BGAGG-" 159846 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 158816 159102 159307 "BFUNCT" 159533 T BFUNCT (NIL) -8 NIL NIL) (-99 157517 157695 157980 "BEZOUT" 158640 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 154042 156377 156705 "BBTREE" 157220 NIL BBTREE (NIL T) -8 NIL NIL) (-97 153780 153833 153859 "BASTYPE" 153976 T BASTYPE (NIL) -9 NIL NIL) (-96 153635 153664 153734 "BASTYPE-" 153739 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 153073 153149 153299 "BALFACT" 153546 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 151895 152492 152677 "AUTOMOR" 152918 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151621 151626 151652 "ATTREG" 151657 T ATTREG (NIL) -9 NIL NIL) (-92 149900 150318 150670 "ATTRBUT" 151287 T ATTRBUT (NIL) -8 NIL NIL) (-91 149436 149549 149575 "ATRIG" 149776 T ATRIG (NIL) -9 NIL NIL) (-90 149245 149286 149373 "ATRIG-" 149378 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147442 149021 149109 "ASTACK" 149188 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145947 146244 146609 "ASSOCEQ" 147124 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144979 145606 145730 "ASP9" 145854 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144743 144927 144966 "ASP8" 144971 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143612 144348 144490 "ASP80" 144632 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142511 143247 143379 "ASP7" 143511 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141465 142188 142306 "ASP78" 142424 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140434 141145 141262 "ASP77" 141379 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139346 140072 140203 "ASP74" 140334 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 138246 138981 139113 "ASP73" 139245 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 137201 137923 138041 "ASP6" 138159 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136149 136878 136996 "ASP55" 137114 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135099 135823 135942 "ASP50" 136061 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134187 134800 134910 "ASP4" 135020 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 133275 133888 133998 "ASP49" 134108 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 132060 132814 132982 "ASP42" 133164 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130837 131593 131763 "ASP41" 131947 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129787 130514 130632 "ASP35" 130750 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129552 129735 129774 "ASP34" 129779 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 129289 129356 129432 "ASP33" 129507 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 128184 128924 129056 "ASP31" 129188 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127949 128132 128171 "ASP30" 128176 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127684 127753 127829 "ASP29" 127904 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127449 127632 127671 "ASP28" 127676 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 127214 127397 127436 "ASP27" 127441 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 126298 126912 127023 "ASP24" 127134 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 125214 125939 126069 "ASP20" 126199 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124302 124915 125025 "ASP1" 125135 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 123246 123976 124095 "ASP19" 124214 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122983 123050 123126 "ASP12" 123201 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121835 122582 122726 "ASP10" 122870 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119734 121679 121770 "ARRAY2" 121775 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115550 119382 119496 "ARRAY1" 119651 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114582 114755 114976 "ARRAY12" 115373 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108942 110813 110888 "ARR2CAT" 113518 NIL ARR2CAT (NIL T T T) -9 NIL 114276) (-54 106376 107120 108074 "ARR2CAT-" 108079 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 105136 105286 105589 "APPRULE" 106214 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 104789 104837 104955 "APPLYORE" 105082 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 103763 104054 104249 "ANY" 104612 T ANY (NIL) -8 NIL NIL) (-50 103041 103164 103321 "ANY1" 103637 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100573 101491 101816 "ANTISYM" 102766 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100088 100277 100374 "ANON" 100494 T ANON (NIL) -8 NIL NIL) (-47 94165 98633 99084 "AN" 99655 T AN (NIL) -8 NIL NIL) (-46 90519 91917 91967 "AMR" 92706 NIL AMR (NIL T T) -9 NIL 93305) (-45 89632 89853 90215 "AMR-" 90220 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74182 89549 89610 "ALIST" 89615 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71019 73776 73945 "ALGSC" 74100 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 67575 68129 68736 "ALGPKG" 70459 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 66852 66953 67137 "ALGMFACT" 67461 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 62602 63282 63936 "ALGMANIP" 66376 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 53921 62228 62378 "ALGFF" 62535 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53117 53248 53427 "ALGFACT" 53779 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52108 52718 52756 "ALGEBRA" 52816 NIL ALGEBRA (NIL T) -9 NIL 52874) (-36 51826 51885 52017 "ALGEBRA-" 52022 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34087 49830 49882 "ALAGG" 50018 NIL ALAGG (NIL T T) -9 NIL 50179) (-34 33623 33736 33762 "AHYP" 33963 T AHYP (NIL) -9 NIL NIL) (-33 32554 32802 32828 "AGG" 33327 T AGG (NIL) -9 NIL 33606) (-32 31988 32150 32364 "AGG-" 32369 NIL AGG- (NIL T) -8 NIL NIL) (-31 29675 30093 30510 "AF" 31631 NIL AF (NIL T T) -7 NIL NIL) (-30 28944 29202 29358 "ACPLOT" 29537 T ACPLOT (NIL) -8 NIL NIL) (-29 18411 26357 26408 "ACFS" 27119 NIL ACFS (NIL T) -9 NIL 27358) (-28 16425 16915 17690 "ACFS-" 17695 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12693 14649 14675 "ACF" 15554 T ACF (NIL) -9 NIL 15966) (-26 11397 11731 12224 "ACF-" 12229 NIL ACF- (NIL T) -8 NIL NIL) (-25 10996 11165 11191 "ABELSG" 11283 T ABELSG (NIL) -9 NIL 11348) (-24 10863 10888 10954 "ABELSG-" 10959 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10233 10494 10520 "ABELMON" 10690 T ABELMON (NIL) -9 NIL 10802) (-22 9897 9981 10119 "ABELMON-" 10124 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9232 9578 9604 "ABELGRP" 9729 T ABELGRP (NIL) -9 NIL 9811) (-20 8695 8824 9040 "ABELGRP-" 9045 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 8f45d042..ca080410 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,670 +1,526 @@ -(726160 . 3416412000) +(726160 . 3417125210) +(((*1 *2 *1) (-12 (-5 *2 (-710)) (-5 *1 (-836 *3)) (-4 *3 (-1016))))) (((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| -3844 (-383 (-523))) (|:| -3855 (-383 (-523))))) - (-5 *2 (-383 (-523))) (-5 *1 (-947 *4)) (-4 *4 (-1145 (-523)))))) -(((*1 *2 *3 *3 *4 *4 *4 *3) - (-12 (-5 *3 (-523)) (-5 *4 (-629 (-203))) (-5 *2 (-962)) - (-5 *1 (-691))))) -(((*1 *2 *3) (-12 (-5 *2 (-394 *3)) (-5 *1 (-517 *3)) (-4 *3 (-508)))) - ((*1 *2 *3) - (-12 (-4 *4 (-732)) (-4 *5 (-786)) (-4 *6 (-284)) (-5 *2 (-394 *3)) - (-5 *1 (-682 *4 *5 *6 *3)) (-4 *3 (-880 *6 *4 *5)))) - ((*1 *2 *3) - (-12 (-4 *4 (-732)) (-4 *5 (-786)) (-4 *6 (-284)) - (-4 *7 (-880 *6 *4 *5)) (-5 *2 (-394 (-1083 *7))) - (-5 *1 (-682 *4 *5 *6 *7)) (-5 *3 (-1083 *7)))) 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*1 (-6 -4248)) (-4 *1 (-140 *2)) (-4 *2 (-1123)) + (-4 *2 (-1016))))) +(((*1 *2 *2) (-12 (-5 *2 (-523)) (-5 *1 (-512))))) +(((*1 *2 *1) (-12 (-5 *2 (-1068 *3)) (-5 *1 (-159 *3)) (-4 *3 (-284))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-203)) (-5 *4 (-523)) (-5 *2 (-962)) (-5 *1 (-698))))) +(((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4249)) (-4 *1 (-115 *2)) (-4 *2 (-1123))))) +(((*1 *2) (-12 (-4 *1 (-380)) (-5 *2 (-852)))) ((*1 *1) (-4 *1 (-508))) + ((*1 *2 *2) (-12 (-5 *2 (-852)) (-5 *1 (-638)))) + ((*1 *2) (-12 (-5 *2 (-852)) (-5 *1 (-638)))) + ((*1 *2 *1) (-12 (-5 *2 (-589 *3)) (-5 *1 (-835 *3)) (-4 *3 (-1016))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-589 (-383 (-883 (-523))))) (-5 *2 (-589 (-589 (-271 (-883 *4))))) (-5 *1 (-356 *4)) @@ -5722,7 +2288,7 @@ (|partial| -12 (-5 *5 (-1087)) (-4 *6 (-13 (-786) (-284) (-964 (-523)) (-585 (-523)) (-136))) (-4 *4 (-13 (-29 *6) (-1109) (-889))) - (-5 *2 (-2 (|:| |particular| *4) (|:| -3760 (-589 *4)))) + (-5 *2 (-2 (|:| |particular| *4) (|:| -2922 (-589 *4)))) (-5 *1 (-595 *6 *4 *3)) (-4 *3 (-599 *4)))) ((*1 *2 *3 *2 *4 *2 *5) (|partial| -12 (-5 *4 (-1087)) (-5 *5 (-589 *2)) @@ -5733,40 +2299,40 @@ (-12 (-5 *3 (-629 *5)) (-4 *5 (-339)) (-5 *2 (-2 (|:| |particular| (-3 (-1169 *5) "failed")) - (|:| -3760 (-589 (-1169 *5))))) + (|:| -2922 (-589 (-1169 *5))))) (-5 *1 (-610 *5)) (-5 *4 (-1169 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-589 (-589 *5))) (-4 *5 (-339)) (-5 *2 (-2 (|:| |particular| (-3 (-1169 *5) "failed")) - (|:| -3760 (-589 (-1169 *5))))) + (|:| -2922 (-589 (-1169 *5))))) (-5 *1 (-610 *5)) (-5 *4 (-1169 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-629 *5)) (-4 *5 (-339)) (-5 *2 (-589 (-2 (|:| |particular| (-3 (-1169 *5) "failed")) - (|:| -3760 (-589 (-1169 *5)))))) + (|:| -2922 (-589 (-1169 *5)))))) (-5 *1 (-610 *5)) (-5 *4 (-589 (-1169 *5))))) ((*1 *2 *3 *4) (-12 (-5 *3 (-589 (-589 *5))) (-4 *5 (-339)) (-5 *2 (-589 (-2 (|:| |particular| (-3 (-1169 *5) "failed")) - (|:| -3760 (-589 (-1169 *5)))))) + (|:| -2922 (-589 (-1169 *5)))))) (-5 *1 (-610 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(-1169 *7)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-629 *6)) (-5 *4 (-1087)) @@ -5796,27 +2362,27 @@ (-5 *5 (-1087)) (-4 *7 (-13 (-29 *6) (-1109) (-889))) (-4 *6 (-13 (-786) (-284) (-964 (-523)) (-585 (-523)) (-136))) (-5 *2 - (-2 (|:| |particular| (-1169 *7)) (|:| -3760 (-589 (-1169 *7))))) + (-2 (|:| |particular| (-1169 *7)) (|:| -2922 (-589 (-1169 *7))))) (-5 *1 (-741 *6 *7)))) ((*1 *2 *3 *4 *5) (|partial| -12 (-5 *3 (-589 *7)) (-5 *4 (-589 (-110))) (-5 *5 (-1087)) (-4 *7 (-13 (-29 *6) (-1109) (-889))) (-4 *6 (-13 (-786) (-284) (-964 (-523)) (-585 (-523)) (-136))) (-5 *2 - (-2 (|:| |particular| (-1169 *7)) (|:| -3760 (-589 (-1169 *7))))) + (-2 (|:| |particular| (-1169 *7)) (|:| -2922 (-589 (-1169 *7))))) (-5 *1 (-741 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-271 *7)) (-5 *4 (-110)) (-5 *5 (-1087)) (-4 *7 (-13 (-29 *6) (-1109) (-889))) (-4 *6 (-13 (-786) (-284) (-964 (-523)) (-585 (-523)) (-136))) (-5 *2 - (-3 (-2 (|:| |particular| *7) (|:| -3760 (-589 *7))) *7 "failed")) + (-3 (-2 (|:| |particular| *7) (|:| -2922 (-589 *7))) *7 "failed")) (-5 *1 (-741 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *4 (-110)) (-5 *5 (-1087)) (-4 *6 (-13 (-786) (-284) (-964 (-523)) (-585 (-523)) (-136))) (-5 *2 - (-3 (-2 (|:| |particular| *3) (|:| -3760 (-589 *3))) *3 "failed")) + (-3 (-2 (|:| |particular| *3) (|:| -2922 (-589 *3))) *3 "failed")) (-5 *1 (-741 *6 *3)) (-4 *3 (-13 (-29 *6) (-1109) (-889))))) ((*1 *2 *3 *4 *3 *5) (|partial| -12 (-5 *3 (-271 *2)) (-5 *4 (-110)) (-5 *5 (-589 *2)) @@ -5852,10 +2418,10 @@ (|partial| -12 (-5 *5 (-1 - (-3 (-2 (|:| |particular| *6) (|:| -3760 (-589 *6))) "failed") + (-3 (-2 (|:| |particular| *6) (|:| -2922 (-589 *6))) "failed") *7 *6)) (-4 *6 (-339)) (-4 *7 (-599 *6)) - (-5 *2 (-2 (|:| |particular| (-1169 *6)) (|:| -3760 (-629 *6)))) + (-5 *2 (-2 (|:| |particular| (-1169 *6)) (|:| -2922 (-629 *6)))) (-5 *1 (-752 *6 *7)) (-5 *3 (-629 *6)) (-5 *4 (-1169 *6)))) ((*1 *2 *3) (-12 (-5 *3 (-829)) (-5 *2 (-962)) (-5 *1 (-828)))) ((*1 *2 *3 *4) @@ -5928,13 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(-732)) - (-4 *2 (-786)))) - ((*1 *1 *1 *1) +(((*1 *1) (-12 (-5 *1 (-205 *2)) (-4 *2 (-13 (-339) (-1109)))))) +(((*1 *2 *3) + (-12 (-4 *4 (-515)) (-5 *2 (-589 *3)) (-5 *1 (-42 *4 *3)) + (-4 *3 (-393 *4))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1169 (-1169 *4))) (-4 *4 (-973)) (-5 *2 (-629 *4)) + (-5 *1 (-956 *4))))) +(((*1 *2 *3 *3 *2) + (-12 (-5 *2 (-1068 *4)) (-5 *3 (-523)) (-4 *4 (-973)) + (-5 *1 (-1072 *4)))) + ((*1 *1 *2 *2 *1) + (-12 (-5 *2 (-523)) (-5 *1 (-1161 *3 *4 *5)) (-4 *3 (-973)) + (-14 *4 (-1087)) (-14 *5 *3)))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-3 + (|:| |noa| + (-2 (|:| |fn| (-292 (-203))) (|:| -4105 (-589 (-203))) + (|:| |lb| (-589 (-779 (-203)))) + (|:| |cf| (-589 (-292 (-203)))) + (|:| |ub| (-589 (-779 (-203)))))) + (|:| |lsa| + (-2 (|:| |lfn| (-589 (-292 (-203)))) + (|:| -4105 (-589 (-203))))))) + (-5 *2 (-589 (-1070))) (-5 *1 (-244))))) +(((*1 *2 *2) (-12 (-5 *2 (-108)) (-5 *1 (-126))))) +(((*1 *2) + (-12 (-4 *3 (-515)) (-5 *2 (-589 *4)) (-5 *1 (-42 *3 *4)) + (-4 *4 (-393 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(-1011 (-383 (-523))))) (-5 *1 (-240)))) - ((*1 *1 *2) (-12 (-5 *2 (-589 (-1011 (-355)))) (-5 *1 (-240))))) -(((*1 *2 *2) (-12 (-5 *2 (-710)) (-5 *1 (-420 *3)) (-4 *3 (-973)))) - ((*1 *2) (-12 (-5 *2 (-710)) (-5 *1 (-420 *3)) (-4 *3 (-973))))) -(((*1 *1 *1) - (-12 (|has| *1 (-6 -4248)) (-4 *1 (-140 *2)) (-4 *2 (-1123)) - (-4 *2 (-1016))))) -(((*1 *2 *3 *1) - (-12 (-5 *2 (-589 (-1087))) (-5 *1 (-1090)) (-5 *3 (-1087))))) -(((*1 *2 *3 *4 *4 *5 *3 *3 *4 *3 *3 *3) - (-12 (-5 *3 (-523)) (-5 *5 (-629 (-203))) (-5 *4 (-203)) - (-5 *2 (-962)) (-5 *1 (-692))))) +(((*1 *1 *2 *2 *2 *2) (-12 (-5 *1 (-658 *2)) (-4 *2 (-339))))) (((*1 *2 *1) (-12 (-4 *1 (-152 *2)) (-4 *2 (-158)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-515) (-786) (-964 (-523)))) (-5 *2 (-292 *4)) @@ -9415,47 +4249,44 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-427) (-786) (-964 (-523)) (-585 (-523)))) (-5 *1 (-1113 *3 *2)) (-4 *2 (-13 (-27) (-1109) (-406 *3)))))) -(((*1 *1 *1) (-4 *1 (-1056)))) -(((*1 *2) - (-12 (-4 *1 (-325)) - (-5 *2 (-589 (-2 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(-12 (-5 *2 (-710)) (-5 *1 (-486 *3 *4)) (-4 *3 (-1123)) + (-14 *4 (-523))))) +(((*1 *2 *1) (-12 (-5 *2 (-589 (-1070))) (-5 *1 (-370))))) +(((*1 *2 *3 *2) (-12 (-5 *3 (-710)) (-5 *1 (-792 *2)) (-4 *2 (-158)))) ((*1 *2 *3) - (-12 (-4 *4 (-515)) (-4 *4 (-158)) (-4 *5 (-349 *4)) - (-4 *6 (-349 *4)) (-5 *2 (-589 *6)) (-5 *1 (-628 *4 *5 *6 *3)) - (-4 *3 (-627 *4 *5 *6)))) - ((*1 *2 *1) - (-12 (-4 *1 (-976 *3 *4 *5 *6 *7)) (-4 *5 (-973)) - (-4 *6 (-216 *4 *5)) (-4 *7 (-216 *3 *5)) (-4 *5 (-515)) - (-5 *2 (-589 *7))))) -(((*1 *1) - (-12 (-4 *3 (-1016)) (-5 *1 (-816 *2 *3 *4)) (-4 *2 (-1016)) - (-4 *4 (-609 *3)))) - ((*1 *1) (-12 (-5 *1 (-820 *2 *3)) (-4 *2 (-1016)) (-4 *3 (-1016))))) -(((*1 *1 *2 *2 *1) (-12 (-5 *1 (-590 *2)) (-4 *2 (-1016))))) -(((*1 *2 *3) - (-12 (-5 *3 (-292 (-355))) (-5 *2 (-292 (-203))) (-5 *1 (-282))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-912 *2)) (-4 *2 (-1109))))) -(((*1 *2 *1) - (-12 (-5 *2 (-108)) (-5 *1 (-292 *3)) (-4 *3 (-515)) (-4 *3 (-786))))) + (-12 (-5 *2 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*3) (-12 (-5 *3 (-1070)) (-5 *2 (-1174)) (-5 *1 (-219)))) + ((*1 *2 *3) + (-12 (-5 *3 (-589 (-1070))) (-5 *2 (-1174)) (-5 *1 (-219))))) +(((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-126))))) +(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-1087)) (-5 *3 (-355)) (-5 *1 (-985))))) +(((*1 *1) (-5 *1 (-144)))) (((*1 *2 *1) (-12 (-4 *1 (-152 *2)) (-4 *2 (-158)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-515) (-786) (-964 (-523)))) (-5 *2 (-292 *4)) @@ -9465,53 +4296,42 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-427) (-786) (-964 (-523)) (-585 (-523)))) (-5 *1 (-1113 *3 *2)) (-4 *2 (-13 (-27) (-1109) (-406 *3)))))) -(((*1 *1 *1 *1 *1) (-4 *1 (-508)))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-1 (-589 *5) *6)) - (-4 *5 (-13 (-339) (-136) (-964 (-383 (-523))))) (-4 *6 (-1145 *5)) - (-5 *2 (-589 (-2 (|:| |poly| *6) (|:| -2849 *3)))) - (-5 *1 (-748 *5 *6 *3 *7)) (-4 *3 (-599 *6)) - (-4 *7 (-599 (-383 *6))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-1 (-589 *5) *6)) - (-4 *5 (-13 (-339) (-136) (-964 (-523)) (-964 (-383 (-523))))) - (-4 *6 (-1145 *5)) 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*1 (-1092))))) +(((*1 *2 *1) + (-12 (-5 *2 (-589 (-523))) (-5 *1 (-932 *3)) (-14 *3 (-523))))) +(((*1 *1 *1) + (-12 (-5 *1 (-548 *2)) (-4 *2 (-37 (-383 (-523)))) (-4 *2 (-973))))) +(((*1 *1 *1) (-5 *1 (-499)))) +(((*1 *2 *3) + (-12 (-5 *2 (-589 (-1083 (-523)))) (-5 *1 (-171)) (-5 *3 (-523))))) +(((*1 *1 *1 *2 *1) (-12 (-4 *1 (-121 *2)) (-4 *2 (-1016))))) +(((*1 *2 *1) (-12 (-4 *1 (-1048 *3)) (-4 *3 (-973)) (-5 *2 (-108))))) +(((*1 *2 *2) (-12 (-5 *2 (-523)) (-5 *1 (-858))))) +(((*1 *2 *1 *1) + (-12 (-4 *3 (-515)) (-4 *3 (-973)) + (-5 *2 (-2 (|:| -3429 *1) (|:| -3143 *1))) (-4 *1 (-788 *3)))) ((*1 *2 *3 *3 *4) - (-12 (-5 *3 (-589 (-629 *5))) (-5 *4 (-523)) (-5 *2 (-629 *5)) - (-5 *1 (-956 *5)) (-4 *5 (-339)) (-4 *5 (-973))))) -(((*1 *2 *3) (-12 (-5 *3 (-852)) (-5 *2 (-835 (-523))) (-5 *1 (-848)))) - ((*1 *2 *3) - (-12 (-5 *3 (-589 (-523))) (-5 *2 (-835 (-523))) (-5 *1 (-848))))) + (-12 (-5 *4 (-94 *5)) (-4 *5 (-515)) (-4 *5 (-973)) + (-5 *2 (-2 (|:| -3429 *3) (|:| -3143 *3))) (-5 *1 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*2 *2) - (-12 (-5 *2 (-1068 *3)) (-4 *3 (-37 (-383 (-523)))) - (-5 *1 (-1073 *3)))) - ((*1 *2 *2) - (-12 (-5 *2 (-1068 *3)) (-4 *3 (-37 (-383 (-523)))) - (-5 *1 (-1074 *3))))) + (-12 (-4 *3 (-13 (-339) (-136))) + (-5 *2 (-589 (-2 (|:| -3262 (-710)) (|:| -3882 *4) (|:| |num| *4)))) + (-5 *1 (-375 *3 *4)) (-4 *4 (-1145 *3))))) +(((*1 *2 *3 *2 *4) + (-12 (-5 *3 (-110)) (-5 *4 (-710)) (-4 *5 (-427)) (-4 *5 (-786)) + (-4 *5 (-964 (-523))) (-4 *5 (-515)) (-5 *1 (-40 *5 *2)) + (-4 *2 (-406 *5)) + (-4 *2 + (-13 (-339) (-279) + (-10 -8 (-15 -2164 ((-1039 *5 (-562 $)) $)) + (-15 -2171 ((-1039 *5 (-562 $)) $)) + (-15 -3976 ($ (-1039 *5 (-562 $)))))))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-786) (-427))) (-5 *1 (-1115 *3 *2)) + (-4 *2 (-13 (-406 *3) (-1109)))))) +(((*1 *2 *2) + (-12 (-4 *3 (-1145 (-383 (-523)))) (-5 *1 (-844 *3 *2)) + (-4 *2 (-1145 (-383 *3)))))) +(((*1 *1 *2) + (-12 (-5 *2 (-589 (-589 *3))) (-4 *3 (-973)) (-4 *1 (-627 *3 *4 *5)) + (-4 *4 (-349 *3)) (-4 *5 (-349 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-589 (-589 (-794)))) (-5 *1 (-794)))) + ((*1 *2 *1) + (-12 (-5 *2 (-1054 *3 *4)) (-5 *1 (-922 *3 *4)) (-14 *3 (-852)) + (-4 *4 (-339)))) + ((*1 *1 *2) + (-12 (-5 *2 (-589 (-589 *5))) (-4 *5 (-973)) + (-4 *1 (-976 *3 *4 *5 *6 *7)) (-4 *6 (-216 *4 *5)) + (-4 *7 (-216 *3 *5))))) (((*1 *2 *3) (-12 (-4 *5 (-13 (-564 *2) (-158))) (-5 *2 (-823 *4)) (-5 *1 (-156 *4 *5 *3)) (-4 *4 (-1016)) (-4 *3 (-152 *5)))) @@ -15752,9 +7112,9 @@ (-12 (-5 *2 (-883 *3)) (-4 *3 (-973)) (-4 *1 (-987 *3 *4 *5)) (-4 *5 (-564 (-1087))) (-4 *4 (-732)) (-4 *5 (-786)))) ((*1 *1 *2) - (-3172 + (-3255 (-12 (-5 *2 (-883 (-523))) (-4 *1 (-987 *3 *4 *5)) - (-12 (-4179 (-4 *3 (-37 (-383 (-523))))) (-4 *3 (-37 (-523))) + (-12 (-2575 (-4 *3 (-37 (-383 (-523))))) (-4 *3 (-37 (-523))) (-4 *5 (-564 (-1087)))) (-4 *3 (-973)) (-4 *4 (-732)) (-4 *5 (-786))) (-12 (-5 *2 (-883 (-523))) (-4 *1 (-987 *3 *4 *5)) @@ -15765,7 +7125,7 @@ (-4 *3 (-37 (-383 (-523)))) (-4 *5 (-564 (-1087))) (-4 *3 (-973)) (-4 *4 (-732)) (-4 *5 (-786)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-589 *7)) (|:| -3643 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-589 *7)) (|:| -2394 *8))) (-4 *7 (-987 *4 *5 *6)) (-4 *8 (-992 *4 *5 *6 *7)) (-4 *4 (-427)) (-4 *5 (-732)) (-4 *6 (-786)) (-5 *2 (-1070)) (-5 *1 (-990 *4 *5 *6 *7 *8)))) @@ -15790,7 +7150,7 @@ (-12 (-5 *2 (-589 *1)) (-4 *1 (-1019 *3 *4 *5 *6 *7)) (-4 *3 (-1016)) (-4 *4 (-1016)) (-4 *5 (-1016)) (-4 *6 (-1016)) (-4 *7 (-1016)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-589 *7)) (|:| -3643 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-589 *7)) (|:| -2394 *8))) (-4 *7 (-987 *4 *5 *6)) (-4 *8 (-1025 *4 *5 *6 *7)) (-4 *4 (-427)) (-4 *5 (-732)) (-4 *6 (-786)) (-5 *2 (-1070)) (-5 *1 (-1057 *4 *5 *6 *7 *8)))) @@ -15823,18 +7183,38 @@ (-5 *2 (-589 (-719 *4 (-796 *6)))) (-5 *1 (-1193 *4 *5 *6)) (-14 *5 (-589 (-1087)))))) (((*1 *2 *3) - (|partial| -12 - (-5 *3 - (-2 (|:| |var| (-1087)) (|:| |fn| (-292 (-203))) - (|:| -2464 (-1011 (-779 (-203)))) (|:| |abserr| (-203)) - (|:| |relerr| (-203)))) - 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(-4 *1 (-265 *3 *2)) (-4 *3 (-1016)) + (-4 *2 (-1123))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-515) (-786) (-964 (-523)))) (-5 *1 (-168 *3 *2)) + (-4 *2 (-13 (-27) (-1109) (-406 (-155 *3)))))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1087)) (-4 *4 (-13 (-515) (-786) (-964 (-523)))) + (-5 *1 (-168 *4 *2)) (-4 *2 (-13 (-27) (-1109) (-406 (-155 *4)))))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-427) (-786) (-964 (-523)) (-585 (-523)))) + (-5 *1 (-1113 *3 *2)) (-4 *2 (-13 (-27) (-1109) (-406 *3))))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1087)) + (-4 *4 (-13 (-427) (-786) (-964 (-523)) (-585 (-523)))) + (-5 *1 (-1113 *4 *2)) (-4 *2 (-13 (-27) (-1109) (-406 *4)))))) (((*1 *1 *1) (-4 *1 (-221))) ((*1 *1 *1) (-12 (-4 *2 (-158)) (-5 *1 (-266 *2 *3 *4 *5 *6 *7)) @@ -15842,7 +7222,7 @@ (-14 *6 (-1 (-3 *4 "failed") *4 *4)) (-14 *7 (-1 (-3 *3 "failed") *3 *3 *4)))) ((*1 *1 *1) - (-3172 (-12 (-5 *1 (-271 *2)) (-4 *2 (-339)) (-4 *2 (-1123))) + (-3255 (-12 (-5 *1 (-271 *2)) (-4 *2 (-339)) (-4 *2 (-1123))) (-12 (-5 *1 (-271 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(-3992 . 53808) (-3993 . 53755) (-3994 . 53504) (-3995 . 53392) + (-3996 . 53262) (-3997 . 53206) (-3998 . 53154) (-3999 . 53027) + (-4000 . 52975) (-4001 . 52817) (-4002 . 52764) (-4003 . 52687) + (-4004 . 52592) (-4005 . 52482) (-4006 . 52399) (-4007 . 52220) + (-4008 . 52054) (-4009 . 52002) (-4010 . 51804) (-4011 . 51675) + (-4012 . 50941) (-4013 . 50822) (-4014 . 50745) (-4015 . 50689) + (-4016 . 50445) (-4017 . 50359) (-4018 . 50213) (-4019 . 50096) + (-4020 . 49842) (-4021 . 49682) (-4022 . 49459) (-4023 . 49265) + (-4024 . 47113) (-4025 . 47042) (-4026 . 46989) (-4027 . 46541) + (-4028 . 46272) (-4029 . 46086) (-4030 . 45839) (-4031 . 45024) + (-4032 . 44969) (-4033 . 44840) (-4034 . 44623) (-4035 . 44453) + (-4036 . 44241) (-4037 . 43973) (-4038 . 43694) (-4039 . 43486) + (-4040 . 42190) (-4041 . 42050) (-4042 . 41789) (-4043 . 41669) + (-4044 . 41582) (-4045 . 41504) (-4046 . 41355) (-4047 . 41048) + (-4048 . 40954) (-4049 . 40876) (-4050 . 40629) (-4051 . 40472) + (-4052 . 40166) (-4053 . 39465) (-4054 . 39271) (-4055 . 38895) + (-4056 . 38821) (-4057 . 38241) (-4058 . 38168) (-4059 . 38085) + (-4060 . 37555) (-4061 . 37468) (-4062 . 37373) (-4063 . 37250) + (-4064 . 36990) (-4065 . 36883) (-4066 . 36787) (-4067 . 36528) + (-4068 . 36426) (-4069 . 36312) (-4070 . 36153) (-4071 . 35821) + (-4072 . 35738) (-4073 . 35533) (-4074 . 35370) (-4075 . 35234) + (-4076 . 35090) (-4077 . 34819) (-4078 . 34732) (-4079 . 34521) + (-4080 . 34336) (-4081 . 34206) (-4082 . 33982) (-4083 . 33706) + (-4084 . 33656) (-4085 . 33453) (-4086 . 33352) (-4087 . 33218) + (-4088 . 33106) (-4089 . 32765) (-4090 . 32191) (-4091 . 31966) + (-4092 . 31857) (-4093 . 31675) (-4094 . 31385) (-4095 . 31112) + (-4096 . 31033) (-4097 . 30960) (-4098 . 30622) (-4099 . 30518) + (-4100 . 30377) (-4101 . 29076) (-4102 . 28467) (-4103 . 27283) + (-4104 . 26835) (-4105 . 26712) (-4106 . 26597) (-4107 . 26370) + (-4108 . 26215) (-4109 . 26122) (-4110 . 26025) (-4111 . 25617) + (-4112 . 25504) (-4113 . 25438) (-4114 . 25326) (-4115 . 24148) + (-4116 . 24120) (-4117 . 24020) (-4118 . 23992) (-4119 . 23622) + (-4120 . 23481) (-4121 . 23447) (-4122 . 23322) (-4123 . 23269) + (-4124 . 22943) (-4125 . 20745) (-4126 . 20647) (-4127 . 20548) + (-4128 . 20364) (-4129 . 20146) (-4130 . 20080) (-4131 . 19655) + (-4132 . 19503) (-4133 . 19323) (-4134 . 19252) (-4135 . 19126) + (-4136 . 19052) (-4137 . 18841) (-4138 . 18545) (-4139 . 18253) + (-4140 . 17776) (-4141 . 17617) (-4142 . 17485) (-4143 . 17277) + (-4144 . 17175) (-4145 . 17098) (-4146 . 17002) (-4147 . 16917) + (-4148 . 16690) (-4149 . 16505) (-4150 . 16295) (-4151 . 16081) + (-4152 . 15808) (-4153 . 15737) (-4154 . 15578) (-4155 . 15504) + (-4156 . 15324) (-4157 . 15062) (-4158 . 14979) (-4159 . 14788) + (-4160 . 14636) (-4161 . 14436) (-4162 . 14383) (-4163 . 14306) + (-4164 . 14111) (-4165 . 13984) (-4166 . 13839) (-4167 . 13749) + (-4168 . 13678) (-4169 . 13583) (-4170 . 13476) (-4171 . 13335) + (-4172 . 13171) (-4173 . 13114) (-4174 . 12891) (-4175 . 12794) + (-4176 . 12693) (-4177 . 12227) (-4178 . 10931) (-4179 . 10816) + (-4180 . 10618) (-4181 . 9508) (-4182 . 9391) (-4183 . 9319) + (-4184 . 9246) (-4185 . 9063) (-4186 . 8950) (-4187 . 8897) + (-4188 . 8622) (-4189 . 8555) (-4190 . 8502) (-4191 . 8056) + (-4192 . 7961) (-4193 . 7904) (-4194 . 7662) (-4195 . 7517) + (-4196 . 6998) (-4197 . 6969) (-4198 . 6888) (-4199 . 6860) + (-4200 . 6780) (-4201 . 6479) (-4202 . 6377) (-4203 . 6306) + (-4204 . 6228) (-4205 . 6176) (-4206 . 5633) (-4207 . 5383) + (-4208 . 5237) (-4209 . 5144) (-4210 . 4852) (-4211 . 3640) + (-4212 . 3591) (-4213 . 3521) (-4214 . 3162) (-4215 . 3080) + (-4216 . 2876) (-4217 . 2781) (-4218 . 2674) (-4219 . 2622) + (-4220 . 2445) (-4221 . 2392) (-4222 . 1476) (-4223 . 1375) + (-4224 . 1312) (-4225 . 674) (-4226 . 349) (-4227 . 101) (-4228 . 30))
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